Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.4% → 98.3%

Time: 13.2s

Alternatives: 27

Speedup: 0.8×

• 36.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;\left(t\_2 + t\_1\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq \infty:\\ \;\;\;\;\left(t\_2 + b \cdot \left(\left(y + t\right) + -2\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (+ x (* z (- 1.0 y)))))
   (if (<= (+ (+ t_2 t_1) (* (- (+ y t) 2.0) b)) INFINITY)
     (+ (+ t_2 (* b (+ (+ y t) -2.0))) t_1)
     (+ a (* y (- b z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (z * (1.0 - y));
	double tmp;
	if (((t_2 + t_1) + (((y + t) - 2.0) * b)) <= ((double) INFINITY)) {
		tmp = (t_2 + (b * ((y + t) + -2.0))) + t_1;
	} else {
		tmp = a + (y * (b - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (z * (1.0 - y));
	double tmp;
	if (((t_2 + t_1) + (((y + t) - 2.0) * b)) <= Double.POSITIVE_INFINITY) {
		tmp = (t_2 + (b * ((y + t) + -2.0))) + t_1;
	} else {
		tmp = a + (y * (b - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (z * (1.0 - y))
	tmp = 0
	if ((t_2 + t_1) + (((y + t) - 2.0) * b)) <= math.inf:
		tmp = (t_2 + (b * ((y + t) + -2.0))) + t_1
	else:
		tmp = a + (y * (b - z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (Float64(Float64(t_2 + t_1) + Float64(Float64(Float64(y + t) - 2.0) * b)) <= Inf)
		tmp = Float64(Float64(t_2 + Float64(b * Float64(Float64(y + t) + -2.0))) + t_1);
	else
		tmp = Float64(a + Float64(y * Float64(b - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (((t_2 + t_1) + (((y + t) - 2.0) * b)) <= Inf)
		tmp = (t_2 + (b * ((y + t) + -2.0))) + t_1;
	else
		tmp = a + (y * (b - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$2 + t$95$1), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(t$95$2 + N[(b * N[(N[(y + t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(a + N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b + \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right), \color{blue}{\left(\left(t - 1\right) \cdot a\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) - 2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(\color{blue}{t} - 1\right) \cdot a\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) + \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y + t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \left(\left(y - 1\right) \cdot z\right)\right)\right), \left(\left(t - \color{blue}{1}\right) \cdot a\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - 1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t - 1\right), \color{blue}{a}\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t + \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      18. metadata-eval 100.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) + -2\right) \cdot b + \left(x - \left(y + -1\right) \cdot z\right)\right) - \left(t + -1\right) \cdot a} \]

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b + \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right), \color{blue}{\left(\left(t - 1\right) \cdot a\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) - 2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(\color{blue}{t} - 1\right) \cdot a\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) + \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y + t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \left(\left(y - 1\right) \cdot z\right)\right)\right), \left(\left(t - \color{blue}{1}\right) \cdot a\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - 1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t - 1\right), \color{blue}{a}\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t + \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      18. metadata-eval 0.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   4. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) + -2\right) \cdot b + \left(x - \left(y + -1\right) \cdot z\right)\right) - \left(t + -1\right) \cdot a} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(b - z\right)\right)}, \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(b - z\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(t, -1\right)}, a\right)\right) \]

      2. --lowering--.f64 66.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \color{blue}{-1}\right), a\right)\right) \]

   7. Simplified 66.7%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} - \left(t + -1\right) \cdot a \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{y \cdot \left(b - z\right) - -1 \cdot a} \]
   9. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto y \cdot \left(b - z\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot a} \]

      2. metadata-eval N/A

         \[\leadsto y \cdot \left(b - z\right) + 1 \cdot a \]

      3. *-lft-identity N/A

         \[\leadsto y \cdot \left(b - z\right) + a \]

      4. +-commutative N/A

         \[\leadsto a + \color{blue}{y \cdot \left(b - z\right)} \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(y \cdot \left(b - z\right)\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right)\right) \]

      7. --lowering--.f64 68.6%

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 68.6%

       \[\leadsto \color{blue}{a + y \cdot \left(b - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq \infty:\\ \;\;\;\;\left(\left(x + z \cdot \left(1 - y\right)\right) + b \cdot \left(\left(y + t\right) + -2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) (* (- (+ y t) 2.0) b))))
   (if (<= t_1 INFINITY) t_1 (+ a (* y (- b z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a + (y * (b - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a + (y * (b - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a + (y * (b - z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(a * Float64(1.0 - t))) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(y * Float64(b - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a + (y * (b - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a + N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b + \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right), \color{blue}{\left(\left(t - 1\right) \cdot a\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) - 2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(\color{blue}{t} - 1\right) \cdot a\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) + \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y + t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \left(\left(y - 1\right) \cdot z\right)\right)\right), \left(\left(t - \color{blue}{1}\right) \cdot a\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - 1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t - 1\right), \color{blue}{a}\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t + \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      18. metadata-eval 0.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   4. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) + -2\right) \cdot b + \left(x - \left(y + -1\right) \cdot z\right)\right) - \left(t + -1\right) \cdot a} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(b - z\right)\right)}, \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(b - z\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(t, -1\right)}, a\right)\right) \]

      2. --lowering--.f64 66.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \color{blue}{-1}\right), a\right)\right) \]

   7. Simplified 66.7%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} - \left(t + -1\right) \cdot a \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{y \cdot \left(b - z\right) - -1 \cdot a} \]
   9. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto y \cdot \left(b - z\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot a} \]

      2. metadata-eval N/A

         \[\leadsto y \cdot \left(b - z\right) + 1 \cdot a \]

      3. *-lft-identity N/A

         \[\leadsto y \cdot \left(b - z\right) + a \]

      4. +-commutative N/A

         \[\leadsto a + \color{blue}{y \cdot \left(b - z\right)} \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(y \cdot \left(b - z\right)\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right)\right) \]

      7. --lowering--.f64 68.6%

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 68.6%

       \[\leadsto \color{blue}{a + y \cdot \left(b - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq \infty:\\ \;\;\;\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := \left(b \cdot \left(y + \left(t + -2\right)\right) + t\_1\right) - t \cdot a\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+113}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-19}:\\ \;\;\;\;x + \left(t\_1 + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (- (+ (* b (+ y (+ t -2.0))) t_1) (* t a))))
   (if (<= b -3.3e+113)
     (+ x (* (- (+ y t) 2.0) b))
     (if (<= b -1.5e-59)
       t_2
       (if (<= b 2.15e-19) (+ x (+ t_1 (* a (- 1.0 t)))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = ((b * (y + (t + -2.0))) + t_1) - (t * a);
	double tmp;
	if (b <= -3.3e+113) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (b <= -1.5e-59) {
		tmp = t_2;
	} else if (b <= 2.15e-19) {
		tmp = x + (t_1 + (a * (1.0 - t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = ((b * (y + (t + (-2.0d0)))) + t_1) - (t * a)
    if (b <= (-3.3d+113)) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else if (b <= (-1.5d-59)) then
        tmp = t_2
    else if (b <= 2.15d-19) then
        tmp = x + (t_1 + (a * (1.0d0 - t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = ((b * (y + (t + -2.0))) + t_1) - (t * a);
	double tmp;
	if (b <= -3.3e+113) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (b <= -1.5e-59) {
		tmp = t_2;
	} else if (b <= 2.15e-19) {
		tmp = x + (t_1 + (a * (1.0 - t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = ((b * (y + (t + -2.0))) + t_1) - (t * a)
	tmp = 0
	if b <= -3.3e+113:
		tmp = x + (((y + t) - 2.0) * b)
	elif b <= -1.5e-59:
		tmp = t_2
	elif b <= 2.15e-19:
		tmp = x + (t_1 + (a * (1.0 - t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(Float64(Float64(b * Float64(y + Float64(t + -2.0))) + t_1) - Float64(t * a))
	tmp = 0.0
	if (b <= -3.3e+113)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (b <= -1.5e-59)
		tmp = t_2;
	elseif (b <= 2.15e-19)
		tmp = Float64(x + Float64(t_1 + Float64(a * Float64(1.0 - t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = ((b * (y + (t + -2.0))) + t_1) - (t * a);
	tmp = 0.0;
	if (b <= -3.3e+113)
		tmp = x + (((y + t) - 2.0) * b);
	elseif (b <= -1.5e-59)
		tmp = t_2;
	elseif (b <= 2.15e-19)
		tmp = x + (t_1 + (a * (1.0 - t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.3e+113], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.5e-59], t$95$2, If[LessEqual[b, 2.15e-19], N[(x + N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.3000000000000003e113

   1. Initial program 88.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 88.2%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -3.3000000000000003e113 < b < -1.5e-59 or 2.15e-19 < b

   1. Initial program 95.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b + \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right), \color{blue}{\left(\left(t - 1\right) \cdot a\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) - 2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(\color{blue}{t} - 1\right) \cdot a\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) + \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y + t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \left(\left(y - 1\right) \cdot z\right)\right)\right), \left(\left(t - \color{blue}{1}\right) \cdot a\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - 1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t - 1\right), \color{blue}{a}\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t + \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      18. metadata-eval 95.9%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   4. Applied egg-rr 95.9%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) + -2\right) \cdot b + \left(x - \left(y + -1\right) \cdot z\right)\right) - \left(t + -1\right) \cdot a} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot \left(\left(t + y\right) - 2\right) - z \cdot \left(y - 1\right)\right)}, \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]
   6. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot \left(\left(t + y\right) - 2\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(t, -1\right)}, a\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(t + y\right) - 2\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{t}, -1\right), a\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(y + t\right) - 2\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      4. associate-+r- N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(t - 2\right)\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(t - 2\right) + y\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(t - 2\right), y\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(t + \left(\mathsf{neg}\left(2\right)\right)\right), y\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(t + -2\right), y\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \mathsf{*.f64}\left(z, \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \color{blue}{-1}\right), a\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \mathsf{*.f64}\left(z, \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \mathsf{*.f64}\left(z, \left(y + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \mathsf{*.f64}\left(z, \left(-1 + y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      14. +-lowering-+.f64 93.9%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   7. Simplified 93.9%

      \[\leadsto \color{blue}{\left(b \cdot \left(\left(t + -2\right) + y\right) - z \cdot \left(-1 + y\right)\right)} - \left(t + -1\right) \cdot a \]

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, y\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{t}, a\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 89.7%

       \[\leadsto \left(b \cdot \left(\left(t + -2\right) + y\right) - z \cdot \left(-1 + y\right)\right) - \color{blue}{t} \cdot a \]

   if -1.5e-59 < b < 2.15e-19

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\left(z \cdot \left(y - 1\right) + a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right)\right) \]

      22. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right)\right)\right) \]

      24. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

   5. Simplified 96.4%

      \[\leadsto \color{blue}{x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+113}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;\left(b \cdot \left(y + \left(t + -2\right)\right) + z \cdot \left(1 - y\right)\right) - t \cdot a\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-19}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot \left(y + \left(t + -2\right)\right) + z \cdot \left(1 - y\right)\right) - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 45.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.38 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.0275:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+51}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+173}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= z -1.38e+107)
     t_1
     (if (<= z -0.0275)
       (+ x (* t b))
       (if (<= z 1.25e-48)
         (* b (+ t (+ y -2.0)))
         (if (<= z 9.5e+51)
           (+ x z)
           (if (<= z 4.8e+173) (* a (- 1.0 t)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -1.38e+107) {
		tmp = t_1;
	} else if (z <= -0.0275) {
		tmp = x + (t * b);
	} else if (z <= 1.25e-48) {
		tmp = b * (t + (y + -2.0));
	} else if (z <= 9.5e+51) {
		tmp = x + z;
	} else if (z <= 4.8e+173) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if (z <= (-1.38d+107)) then
        tmp = t_1
    else if (z <= (-0.0275d0)) then
        tmp = x + (t * b)
    else if (z <= 1.25d-48) then
        tmp = b * (t + (y + (-2.0d0)))
    else if (z <= 9.5d+51) then
        tmp = x + z
    else if (z <= 4.8d+173) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -1.38e+107) {
		tmp = t_1;
	} else if (z <= -0.0275) {
		tmp = x + (t * b);
	} else if (z <= 1.25e-48) {
		tmp = b * (t + (y + -2.0));
	} else if (z <= 9.5e+51) {
		tmp = x + z;
	} else if (z <= 4.8e+173) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if z <= -1.38e+107:
		tmp = t_1
	elif z <= -0.0275:
		tmp = x + (t * b)
	elif z <= 1.25e-48:
		tmp = b * (t + (y + -2.0))
	elif z <= 9.5e+51:
		tmp = x + z
	elif z <= 4.8e+173:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -1.38e+107)
		tmp = t_1;
	elseif (z <= -0.0275)
		tmp = Float64(x + Float64(t * b));
	elseif (z <= 1.25e-48)
		tmp = Float64(b * Float64(t + Float64(y + -2.0)));
	elseif (z <= 9.5e+51)
		tmp = Float64(x + z);
	elseif (z <= 4.8e+173)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (z <= -1.38e+107)
		tmp = t_1;
	elseif (z <= -0.0275)
		tmp = x + (t * b);
	elseif (z <= 1.25e-48)
		tmp = b * (t + (y + -2.0));
	elseif (z <= 9.5e+51)
		tmp = x + z;
	elseif (z <= 4.8e+173)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.38e+107], t$95$1, If[LessEqual[z, -0.0275], N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-48], N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+51], N[(x + z), $MachinePrecision], If[LessEqual[z, 4.8e+173], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.38e107 or 4.7999999999999998e173 < z

   1. Initial program 89.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto z \cdot \left(1 + -1 \cdot \color{blue}{y}\right) \]

      3. +-commutative N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) \]

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right) \]

      18. --lowering--.f64 72.7%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 72.7%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   if -1.38e107 < z < -0.0275000000000000001

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 54.5%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(b \cdot t\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{b}\right)\right) \]

      2. *-lowering-*.f64 47.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{b}\right)\right) \]

   8. Simplified 47.8%

      \[\leadsto x + \color{blue}{t \cdot b} \]

   if -0.0275000000000000001 < z < 1.25e-48

   1. Initial program 99.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 55.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 55.7%

      \[\leadsto \color{blue}{b \cdot \left(t + \left(y + -2\right)\right)} \]

   if 1.25e-48 < z < 9.4999999999999999e51

   1. Initial program 94.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + \left(x + \left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)} \]

      2. associate-+r+ N/A

         \[\leadsto \left(\left(a + x\right) + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{z \cdot \left(1 - y\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(x + a\right) + -1 \cdot \left(a \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(x + \left(a + -1 \cdot \left(a \cdot t\right)\right)\right) + \color{blue}{z} \cdot \left(1 - y\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \left(x + \left(a \cdot 1 + -1 \cdot \left(a \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + \left(\mathsf{neg}\left(a \cdot t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(\mathsf{neg}\left(t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(-1 \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \left(x + a \cdot \left(1 + -1 \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + a \cdot \left(1 + -1 \cdot t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(1 + -1 \cdot t\right)\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      17. --lowering--.f64 88.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 88.6%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
   10. Step-by-step derivation

       1. sub-neg N/A

          \[\leadsto x + z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{1}\right) \]

       3. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

       4. distribute-neg-in N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

       6. sub-neg N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) \]

       8. distribute-lft-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(y - 1\right)} \]

       9. cancel-sign-sub-inv N/A

          \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]

       10. --lowering--.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(z \cdot \left(y - 1\right)\right)}\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(y - 1\right)}\right)\right) \]

       12. sub-neg N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

       13. metadata-eval N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + -1\right)\right)\right) \]

       14. +-commutative N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{y}\right)\right)\right) \]

       15. +-lowering-+.f64 69.5%

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 69.5%

       \[\leadsto \color{blue}{x - z \cdot \left(-1 + y\right)} \]

   12. Taylor expanded in y around 0

       \[\leadsto \color{blue}{x - -1 \cdot z} \]
   13. Step-by-step derivation

       1. cancel-sign-sub-inv N/A

          \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot z} \]

       2. metadata-eval N/A

          \[\leadsto x + 1 \cdot z \]

       3. *-lft-identity N/A

          \[\leadsto x + z \]

       4. +-commutative N/A

          \[\leadsto z + \color{blue}{x} \]

       5. +-lowering-+.f64 63.5%

          \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   14. Simplified 63.5%

       \[\leadsto \color{blue}{z + x} \]

   if 9.4999999999999999e51 < z < 4.7999999999999998e173

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto a \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot -1 + \left(\mathsf{neg}\left(\color{blue}{t}\right)\right)\right) \]

      3. neg-mul-1 N/A

         \[\leadsto a \cdot \left(-1 \cdot -1 + -1 \cdot \color{blue}{t}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(-1 + t\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \color{blue}{-1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t - \color{blue}{1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

      16. --lowering--.f64 55.1%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

   5. Simplified 55.1%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -0.0275:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+51}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+173}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+212}:\\ \;\;\;\;a + \left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right)\\ \mathbf{elif}\;a \leq 10^{-16}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x + t\_1\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot \left(y + \left(t + -2\right)\right) + t\_1\right) + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= a -3.8e+212)
     (+ a (+ (* b (+ y -2.0)) (* t (- b a))))
     (if (<= a 1e-16)
       (+ (* (- (+ y t) 2.0) b) (- (+ x t_1) (* t a)))
       (+ (+ (* b (+ y (+ t -2.0))) t_1) (* a (- 1.0 t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (a <= -3.8e+212) {
		tmp = a + ((b * (y + -2.0)) + (t * (b - a)));
	} else if (a <= 1e-16) {
		tmp = (((y + t) - 2.0) * b) + ((x + t_1) - (t * a));
	} else {
		tmp = ((b * (y + (t + -2.0))) + t_1) + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if (a <= (-3.8d+212)) then
        tmp = a + ((b * (y + (-2.0d0))) + (t * (b - a)))
    else if (a <= 1d-16) then
        tmp = (((y + t) - 2.0d0) * b) + ((x + t_1) - (t * a))
    else
        tmp = ((b * (y + (t + (-2.0d0)))) + t_1) + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (a <= -3.8e+212) {
		tmp = a + ((b * (y + -2.0)) + (t * (b - a)));
	} else if (a <= 1e-16) {
		tmp = (((y + t) - 2.0) * b) + ((x + t_1) - (t * a));
	} else {
		tmp = ((b * (y + (t + -2.0))) + t_1) + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if a <= -3.8e+212:
		tmp = a + ((b * (y + -2.0)) + (t * (b - a)))
	elif a <= 1e-16:
		tmp = (((y + t) - 2.0) * b) + ((x + t_1) - (t * a))
	else:
		tmp = ((b * (y + (t + -2.0))) + t_1) + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (a <= -3.8e+212)
		tmp = Float64(a + Float64(Float64(b * Float64(y + -2.0)) + Float64(t * Float64(b - a))));
	elseif (a <= 1e-16)
		tmp = Float64(Float64(Float64(Float64(y + t) - 2.0) * b) + Float64(Float64(x + t_1) - Float64(t * a)));
	else
		tmp = Float64(Float64(Float64(b * Float64(y + Float64(t + -2.0))) + t_1) + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (a <= -3.8e+212)
		tmp = a + ((b * (y + -2.0)) + (t * (b - a)));
	elseif (a <= 1e-16)
		tmp = (((y + t) - 2.0) * b) + ((x + t_1) - (t * a));
	else
		tmp = ((b * (y + (t + -2.0))) + t_1) + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+212], N[(a + N[(N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-16], N[(N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x + t$95$1), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.79999999999999988e212

   1. Initial program 90.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 95.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \color{blue}{a}\right) \]
   7. Step-by-step derivation

   8. Simplified 95.3%

      \[\leadsto \left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{a} \]

   if -3.79999999999999988e212 < a < 9.9999999999999998e-17

   1. Initial program 97.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, 1\right), z\right)\right), \color{blue}{\left(a \cdot t\right)}\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, 1\right), z\right)\right), \left(t \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. *-lowering-*.f64 93.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, 1\right), z\right)\right), \mathsf{*.f64}\left(t, a\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 93.8%

      \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{t \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   if 9.9999999999999998e-17 < a

   1. Initial program 97.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b + \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right), \color{blue}{\left(\left(t - 1\right) \cdot a\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) - 2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(\color{blue}{t} - 1\right) \cdot a\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) + \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y + t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \left(\left(y - 1\right) \cdot z\right)\right)\right), \left(\left(t - \color{blue}{1}\right) \cdot a\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - 1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t - 1\right), \color{blue}{a}\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t + \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      18. metadata-eval 97.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   4. Applied egg-rr 97.0%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) + -2\right) \cdot b + \left(x - \left(y + -1\right) \cdot z\right)\right) - \left(t + -1\right) \cdot a} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot \left(\left(t + y\right) - 2\right) - z \cdot \left(y - 1\right)\right)}, \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]
   6. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot \left(\left(t + y\right) - 2\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(t, -1\right)}, a\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(t + y\right) - 2\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{t}, -1\right), a\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(y + t\right) - 2\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      4. associate-+r- N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(t - 2\right)\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(t - 2\right) + y\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(t - 2\right), y\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(t + \left(\mathsf{neg}\left(2\right)\right)\right), y\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(t + -2\right), y\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \left(z \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \mathsf{*.f64}\left(z, \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \color{blue}{-1}\right), a\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \mathsf{*.f64}\left(z, \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \mathsf{*.f64}\left(z, \left(y + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \mathsf{*.f64}\left(z, \left(-1 + y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

      14. +-lowering-+.f64 91.7%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(t, -2\right), y\right)\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   7. Simplified 91.7%

      \[\leadsto \color{blue}{\left(b \cdot \left(\left(t + -2\right) + y\right) - z \cdot \left(-1 + y\right)\right)} - \left(t + -1\right) \cdot a \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+212}:\\ \;\;\;\;a + \left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right)\\ \mathbf{elif}\;a \leq 10^{-16}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x + z \cdot \left(1 - y\right)\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot \left(y + \left(t + -2\right)\right) + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{+210}:\\ \;\;\;\;a + \left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+69}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x + t\_1\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= a -2.25e+210)
     (+ a (+ (* b (+ y -2.0)) (* t (- b a))))
     (if (<= a 1.7e+69)
       (+ (* (- (+ y t) 2.0) b) (- (+ x t_1) (* t a)))
       (+ x (+ t_1 (* a (- 1.0 t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (a <= -2.25e+210) {
		tmp = a + ((b * (y + -2.0)) + (t * (b - a)));
	} else if (a <= 1.7e+69) {
		tmp = (((y + t) - 2.0) * b) + ((x + t_1) - (t * a));
	} else {
		tmp = x + (t_1 + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if (a <= (-2.25d+210)) then
        tmp = a + ((b * (y + (-2.0d0))) + (t * (b - a)))
    else if (a <= 1.7d+69) then
        tmp = (((y + t) - 2.0d0) * b) + ((x + t_1) - (t * a))
    else
        tmp = x + (t_1 + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (a <= -2.25e+210) {
		tmp = a + ((b * (y + -2.0)) + (t * (b - a)));
	} else if (a <= 1.7e+69) {
		tmp = (((y + t) - 2.0) * b) + ((x + t_1) - (t * a));
	} else {
		tmp = x + (t_1 + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if a <= -2.25e+210:
		tmp = a + ((b * (y + -2.0)) + (t * (b - a)))
	elif a <= 1.7e+69:
		tmp = (((y + t) - 2.0) * b) + ((x + t_1) - (t * a))
	else:
		tmp = x + (t_1 + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (a <= -2.25e+210)
		tmp = Float64(a + Float64(Float64(b * Float64(y + -2.0)) + Float64(t * Float64(b - a))));
	elseif (a <= 1.7e+69)
		tmp = Float64(Float64(Float64(Float64(y + t) - 2.0) * b) + Float64(Float64(x + t_1) - Float64(t * a)));
	else
		tmp = Float64(x + Float64(t_1 + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (a <= -2.25e+210)
		tmp = a + ((b * (y + -2.0)) + (t * (b - a)));
	elseif (a <= 1.7e+69)
		tmp = (((y + t) - 2.0) * b) + ((x + t_1) - (t * a));
	else
		tmp = x + (t_1 + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.25e+210], N[(a + N[(N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+69], N[(N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x + t$95$1), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.25000000000000002e210

   1. Initial program 90.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 95.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \color{blue}{a}\right) \]
   7. Step-by-step derivation

   8. Simplified 95.3%

      \[\leadsto \left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{a} \]

   if -2.25000000000000002e210 < a < 1.69999999999999993e69

   1. Initial program 97.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, 1\right), z\right)\right), \color{blue}{\left(a \cdot t\right)}\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, 1\right), z\right)\right), \left(t \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. *-lowering-*.f64 93.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, 1\right), z\right)\right), \mathsf{*.f64}\left(t, a\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 93.9%

      \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{t \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   if 1.69999999999999993e69 < a

   1. Initial program 96.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\left(z \cdot \left(y - 1\right) + a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right)\right) \]

      22. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right)\right)\right) \]

      24. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

   5. Simplified 88.7%

      \[\leadsto \color{blue}{x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{+210}:\\ \;\;\;\;a + \left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+69}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x + z \cdot \left(1 - y\right)\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+114}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+71}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.1e+114)
   (+ x (* (- (+ y t) 2.0) b))
   (if (<= b -1.5e-59)
     (+ z (+ (* y (- b z)) (* b (+ t -2.0))))
     (if (<= b 6e+71)
       (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t))))
       (+ a (+ (* b (+ y -2.0)) (* t (- b a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.1e+114) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (b <= -1.5e-59) {
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)));
	} else if (b <= 6e+71) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = a + ((b * (y + -2.0)) + (t * (b - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.1d+114)) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else if (b <= (-1.5d-59)) then
        tmp = z + ((y * (b - z)) + (b * (t + (-2.0d0))))
    else if (b <= 6d+71) then
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    else
        tmp = a + ((b * (y + (-2.0d0))) + (t * (b - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.1e+114) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (b <= -1.5e-59) {
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)));
	} else if (b <= 6e+71) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = a + ((b * (y + -2.0)) + (t * (b - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.1e+114:
		tmp = x + (((y + t) - 2.0) * b)
	elif b <= -1.5e-59:
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)))
	elif b <= 6e+71:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	else:
		tmp = a + ((b * (y + -2.0)) + (t * (b - a)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.1e+114)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (b <= -1.5e-59)
		tmp = Float64(z + Float64(Float64(y * Float64(b - z)) + Float64(b * Float64(t + -2.0))));
	elseif (b <= 6e+71)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	else
		tmp = Float64(a + Float64(Float64(b * Float64(y + -2.0)) + Float64(t * Float64(b - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.1e+114)
		tmp = x + (((y + t) - 2.0) * b);
	elseif (b <= -1.5e-59)
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)));
	elseif (b <= 6e+71)
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	else
		tmp = a + ((b * (y + -2.0)) + (t * (b - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.1e+114], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.5e-59], N[(z + N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e+71], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.1e114

   1. Initial program 90.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 90.4%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -3.1e114 < b < -1.5e-59

   1. Initial program 97.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(1 - y\right)\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot y + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      4. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right)}, b\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      18. --lowering--.f64 86.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 86.2%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z + \left(b \cdot \left(t - 2\right) + y \cdot \left(b + -1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(b \cdot \left(t - 2\right) + y \cdot \left(b + -1 \cdot z\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(y \cdot \left(b + -1 \cdot z\right) + \color{blue}{b \cdot \left(t - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot \left(b + -1 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(t - 2\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(b + -1 \cdot z\right)\right), \left(\color{blue}{b} \cdot \left(t - 2\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(\mathsf{neg}\left(z\right)\right)\right)\right), \left(b \cdot \left(t - 2\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(b - z\right)\right), \left(b \cdot \left(t - 2\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \left(b \cdot \left(t - 2\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(b, \color{blue}{\left(t - 2\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(b, \left(t + -2\right)\right)\right)\right) \]

      11. +-lowering-+.f64 89.1%

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{-2}\right)\right)\right)\right) \]

   8. Simplified 89.1%

      \[\leadsto \color{blue}{z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)} \]

   if -1.5e-59 < b < 6.00000000000000025e71

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\left(z \cdot \left(y - 1\right) + a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right)\right) \]

      22. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right)\right)\right) \]

      24. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

   5. Simplified 93.8%

      \[\leadsto \color{blue}{x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)} \]

   if 6.00000000000000025e71 < b

   1. Initial program 91.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 93.7%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \color{blue}{a}\right) \]
   7. Step-by-step derivation

   8. Simplified 85.4%

      \[\leadsto \left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+114}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+71}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+114}:\\ \;\;\;\;x + t\_2\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+71}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -2.4e+114)
     (+ x t_2)
     (if (<= b -1.5e-59)
       (+ z (+ (* y (- b z)) (* b (+ t -2.0))))
       (if (<= b 4.5e+71) (+ x (+ (* z (- 1.0 y)) t_1)) (+ t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.4e+114) {
		tmp = x + t_2;
	} else if (b <= -1.5e-59) {
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)));
	} else if (b <= 4.5e+71) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-2.4d+114)) then
        tmp = x + t_2
    else if (b <= (-1.5d-59)) then
        tmp = z + ((y * (b - z)) + (b * (t + (-2.0d0))))
    else if (b <= 4.5d+71) then
        tmp = x + ((z * (1.0d0 - y)) + t_1)
    else
        tmp = t_2 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.4e+114) {
		tmp = x + t_2;
	} else if (b <= -1.5e-59) {
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)));
	} else if (b <= 4.5e+71) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -2.4e+114:
		tmp = x + t_2
	elif b <= -1.5e-59:
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)))
	elif b <= 4.5e+71:
		tmp = x + ((z * (1.0 - y)) + t_1)
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.4e+114)
		tmp = Float64(x + t_2);
	elseif (b <= -1.5e-59)
		tmp = Float64(z + Float64(Float64(y * Float64(b - z)) + Float64(b * Float64(t + -2.0))));
	elseif (b <= 4.5e+71)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + t_1));
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -2.4e+114)
		tmp = x + t_2;
	elseif (b <= -1.5e-59)
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)));
	elseif (b <= 4.5e+71)
		tmp = x + ((z * (1.0 - y)) + t_1);
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.4e+114], N[(x + t$95$2), $MachinePrecision], If[LessEqual[b, -1.5e-59], N[(z + N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+71], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.4e114

   1. Initial program 90.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 90.4%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -2.4e114 < b < -1.5e-59

   1. Initial program 97.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(1 - y\right)\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot y + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      4. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right)}, b\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      18. --lowering--.f64 86.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 86.2%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z + \left(b \cdot \left(t - 2\right) + y \cdot \left(b + -1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(b \cdot \left(t - 2\right) + y \cdot \left(b + -1 \cdot z\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(y \cdot \left(b + -1 \cdot z\right) + \color{blue}{b \cdot \left(t - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot \left(b + -1 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(t - 2\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(b + -1 \cdot z\right)\right), \left(\color{blue}{b} \cdot \left(t - 2\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(\mathsf{neg}\left(z\right)\right)\right)\right), \left(b \cdot \left(t - 2\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(b - z\right)\right), \left(b \cdot \left(t - 2\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \left(b \cdot \left(t - 2\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(b, \color{blue}{\left(t - 2\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(b, \left(t + -2\right)\right)\right)\right) \]

      11. +-lowering-+.f64 89.1%

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{-2}\right)\right)\right)\right) \]

   8. Simplified 89.1%

      \[\leadsto \color{blue}{z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)} \]

   if -1.5e-59 < b < 4.50000000000000043e71

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\left(z \cdot \left(y - 1\right) + a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right)\right) \]

      22. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right)\right)\right) \]

      24. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

   5. Simplified 93.8%

      \[\leadsto \color{blue}{x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)} \]

   if 4.50000000000000043e71 < b

   1. Initial program 91.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot \left(1 - t\right)\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot -1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      3. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot -1 + -1 \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot \left(-1 + t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot \left(t + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(-1 \cdot \left(t - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot \left(t - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right)}, b\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot t + -1 \cdot -1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(1 - t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      16. --lowering--.f64 85.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 85.4%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+114}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+71}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+194}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -3.1e+114)
     t_1
     (if (<= b -1.5e-59)
       (+ z (+ (* y (- b z)) (* b (+ t -2.0))))
       (if (<= b 1.3e+194) (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.1e+114) {
		tmp = t_1;
	} else if (b <= -1.5e-59) {
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)));
	} else if (b <= 1.3e+194) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-3.1d+114)) then
        tmp = t_1
    else if (b <= (-1.5d-59)) then
        tmp = z + ((y * (b - z)) + (b * (t + (-2.0d0))))
    else if (b <= 1.3d+194) then
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.1e+114) {
		tmp = t_1;
	} else if (b <= -1.5e-59) {
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)));
	} else if (b <= 1.3e+194) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -3.1e+114:
		tmp = t_1
	elif b <= -1.5e-59:
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)))
	elif b <= 1.3e+194:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -3.1e+114)
		tmp = t_1;
	elseif (b <= -1.5e-59)
		tmp = Float64(z + Float64(Float64(y * Float64(b - z)) + Float64(b * Float64(t + -2.0))));
	elseif (b <= 1.3e+194)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -3.1e+114)
		tmp = t_1;
	elseif (b <= -1.5e-59)
		tmp = z + ((y * (b - z)) + (b * (t + -2.0)));
	elseif (b <= 1.3e+194)
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+114], t$95$1, If[LessEqual[b, -1.5e-59], N[(z + N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.3e+194], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.1e114 or 1.2999999999999999e194 < b

   1. Initial program 91.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 87.5%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -3.1e114 < b < -1.5e-59

   1. Initial program 97.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(1 - y\right)\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot y + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      4. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right)}, b\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      18. --lowering--.f64 86.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 86.2%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z + \left(b \cdot \left(t - 2\right) + y \cdot \left(b + -1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(b \cdot \left(t - 2\right) + y \cdot \left(b + -1 \cdot z\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(y \cdot \left(b + -1 \cdot z\right) + \color{blue}{b \cdot \left(t - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot \left(b + -1 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(t - 2\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(b + -1 \cdot z\right)\right), \left(\color{blue}{b} \cdot \left(t - 2\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(\mathsf{neg}\left(z\right)\right)\right)\right), \left(b \cdot \left(t - 2\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(b - z\right)\right), \left(b \cdot \left(t - 2\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \left(b \cdot \left(t - 2\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(b, \color{blue}{\left(t - 2\right)}\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(b, \left(t + -2\right)\right)\right)\right) \]

      11. +-lowering-+.f64 89.1%

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{-2}\right)\right)\right)\right) \]

   8. Simplified 89.1%

      \[\leadsto \color{blue}{z + \left(y \cdot \left(b - z\right) + b \cdot \left(t + -2\right)\right)} \]

   if -1.5e-59 < b < 1.2999999999999999e194

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\left(z \cdot \left(y - 1\right) + a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right)\right) \]

      22. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right)\right)\right) \]

      24. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

   5. Simplified 89.1%

      \[\leadsto \color{blue}{x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 58.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-254}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+17}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -1.5e-59)
     t_1
     (if (<= b -1.35e-254)
       (+ x (* a (- 1.0 t)))
       (if (<= b 6.4e+17)
         (+ x (* z (- 1.0 y)))
         (if (<= b 1.15e+135) (* t (- b a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -1.5e-59) {
		tmp = t_1;
	} else if (b <= -1.35e-254) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 6.4e+17) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 1.15e+135) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t + (y + (-2.0d0)))
    if (b <= (-1.5d-59)) then
        tmp = t_1
    else if (b <= (-1.35d-254)) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 6.4d+17) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 1.15d+135) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -1.5e-59) {
		tmp = t_1;
	} else if (b <= -1.35e-254) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 6.4e+17) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 1.15e+135) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + (y + -2.0))
	tmp = 0
	if b <= -1.5e-59:
		tmp = t_1
	elif b <= -1.35e-254:
		tmp = x + (a * (1.0 - t))
	elif b <= 6.4e+17:
		tmp = x + (z * (1.0 - y))
	elif b <= 1.15e+135:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -1.5e-59)
		tmp = t_1;
	elseif (b <= -1.35e-254)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 6.4e+17)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 1.15e+135)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + (y + -2.0));
	tmp = 0.0;
	if (b <= -1.5e-59)
		tmp = t_1;
	elseif (b <= -1.35e-254)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 6.4e+17)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 1.15e+135)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.5e-59], t$95$1, If[LessEqual[b, -1.35e-254], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.4e+17], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+135], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.5e-59 or 1.1500000000000001e135 < b

   1. Initial program 92.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 68.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 68.9%

      \[\leadsto \color{blue}{b \cdot \left(t + \left(y + -2\right)\right)} \]

   if -1.5e-59 < b < -1.35000000000000003e-254

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b + \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right), \color{blue}{\left(\left(t - 1\right) \cdot a\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) - 2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(\color{blue}{t} - 1\right) \cdot a\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) + \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y + t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \left(\left(y - 1\right) \cdot z\right)\right)\right), \left(\left(t - \color{blue}{1}\right) \cdot a\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - 1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t - 1\right), \color{blue}{a}\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t + \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      18. metadata-eval 100.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) + -2\right) \cdot b + \left(x - \left(y + -1\right) \cdot z\right)\right) - \left(t + -1\right) \cdot a} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 67.5%

      \[\leadsto \color{blue}{x} - \left(t + -1\right) \cdot a \]

   if -1.35000000000000003e-254 < b < 6.4e17

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + \left(x + \left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)} \]

      2. associate-+r+ N/A

         \[\leadsto \left(\left(a + x\right) + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{z \cdot \left(1 - y\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(x + a\right) + -1 \cdot \left(a \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(x + \left(a + -1 \cdot \left(a \cdot t\right)\right)\right) + \color{blue}{z} \cdot \left(1 - y\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \left(x + \left(a \cdot 1 + -1 \cdot \left(a \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + \left(\mathsf{neg}\left(a \cdot t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(\mathsf{neg}\left(t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(-1 \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \left(x + a \cdot \left(1 + -1 \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + a \cdot \left(1 + -1 \cdot t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(1 + -1 \cdot t\right)\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      17. --lowering--.f64 95.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 95.1%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
   10. Step-by-step derivation

       1. sub-neg N/A

          \[\leadsto x + z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{1}\right) \]

       3. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

       4. distribute-neg-in N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

       6. sub-neg N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) \]

       8. distribute-lft-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(y - 1\right)} \]

       9. cancel-sign-sub-inv N/A

          \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]

       10. --lowering--.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(z \cdot \left(y - 1\right)\right)}\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(y - 1\right)}\right)\right) \]

       12. sub-neg N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

       13. metadata-eval N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + -1\right)\right)\right) \]

       14. +-commutative N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{y}\right)\right)\right) \]

       15. +-lowering-+.f64 64.6%

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 64.6%

       \[\leadsto \color{blue}{x - z \cdot \left(-1 + y\right)} \]

   if 6.4e17 < b < 1.1500000000000001e135

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 66.7%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-254}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+17}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t + \left(y + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-48}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+196}:\\ \;\;\;\;y \cdot \left(b - z\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -3.2e-35)
     t_1
     (if (<= b 3.8e-48)
       (- (+ x a) (* z (+ y -1.0)))
       (if (<= b 3.5e+196) (+ (* y (- b z)) (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.2e-35) {
		tmp = t_1;
	} else if (b <= 3.8e-48) {
		tmp = (x + a) - (z * (y + -1.0));
	} else if (b <= 3.5e+196) {
		tmp = (y * (b - z)) + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-3.2d-35)) then
        tmp = t_1
    else if (b <= 3.8d-48) then
        tmp = (x + a) - (z * (y + (-1.0d0)))
    else if (b <= 3.5d+196) then
        tmp = (y * (b - z)) + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.2e-35) {
		tmp = t_1;
	} else if (b <= 3.8e-48) {
		tmp = (x + a) - (z * (y + -1.0));
	} else if (b <= 3.5e+196) {
		tmp = (y * (b - z)) + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -3.2e-35:
		tmp = t_1
	elif b <= 3.8e-48:
		tmp = (x + a) - (z * (y + -1.0))
	elif b <= 3.5e+196:
		tmp = (y * (b - z)) + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -3.2e-35)
		tmp = t_1;
	elseif (b <= 3.8e-48)
		tmp = Float64(Float64(x + a) - Float64(z * Float64(y + -1.0)));
	elseif (b <= 3.5e+196)
		tmp = Float64(Float64(y * Float64(b - z)) + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -3.2e-35)
		tmp = t_1;
	elseif (b <= 3.8e-48)
		tmp = (x + a) - (z * (y + -1.0));
	elseif (b <= 3.5e+196)
		tmp = (y * (b - z)) + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e-35], t$95$1, If[LessEqual[b, 3.8e-48], N[(N[(x + a), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+196], N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.1999999999999998e-35 or 3.4999999999999998e196 < b

   1. Initial program 92.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 78.8%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -3.1999999999999998e-35 < b < 3.80000000000000002e-48

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + \left(x + \left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)} \]

      2. associate-+r+ N/A

         \[\leadsto \left(\left(a + x\right) + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{z \cdot \left(1 - y\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(x + a\right) + -1 \cdot \left(a \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(x + \left(a + -1 \cdot \left(a \cdot t\right)\right)\right) + \color{blue}{z} \cdot \left(1 - y\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \left(x + \left(a \cdot 1 + -1 \cdot \left(a \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + \left(\mathsf{neg}\left(a \cdot t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(\mathsf{neg}\left(t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(-1 \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \left(x + a \cdot \left(1 + -1 \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + a \cdot \left(1 + -1 \cdot t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(1 + -1 \cdot t\right)\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      17. --lowering--.f64 95.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 95.6%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a + x\right)}, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right)\right) \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + a\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{\_.f64}\left(1, y\right)\right)\right) \]

       2. +-lowering-+.f64 77.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{\_.f64}\left(1, y\right)\right)\right) \]

   11. Simplified 77.3%

       \[\leadsto \color{blue}{\left(x + a\right)} + z \cdot \left(1 - y\right) \]

   if 3.80000000000000002e-48 < b < 3.4999999999999998e196

   1. Initial program 95.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b + \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right), \color{blue}{\left(\left(t - 1\right) \cdot a\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) - 2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(\color{blue}{t} - 1\right) \cdot a\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) + \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y + t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \left(\left(y - 1\right) \cdot z\right)\right)\right), \left(\left(t - \color{blue}{1}\right) \cdot a\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - 1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t - 1\right), \color{blue}{a}\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t + \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      18. metadata-eval 95.2%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   4. Applied egg-rr 95.2%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) + -2\right) \cdot b + \left(x - \left(y + -1\right) \cdot z\right)\right) - \left(t + -1\right) \cdot a} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(b - z\right)\right)}, \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(b - z\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(t, -1\right)}, a\right)\right) \]

      2. --lowering--.f64 64.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \color{blue}{-1}\right), a\right)\right) \]

   7. Simplified 64.7%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} - \left(t + -1\right) \cdot a \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{-35}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-48}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+196}:\\ \;\;\;\;y \cdot \left(b - z\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 95.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \left(b - z\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.5e+134)
   (+ (* y (- b z)) (* a (- 1.0 t)))
   (+ (+ (* b (+ y -2.0)) (* t (- b a))) (- (+ x a) (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.5e+134) {
		tmp = (y * (b - z)) + (a * (1.0 - t));
	} else {
		tmp = ((b * (y + -2.0)) + (t * (b - a))) + ((x + a) - (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.5d+134)) then
        tmp = (y * (b - z)) + (a * (1.0d0 - t))
    else
        tmp = ((b * (y + (-2.0d0))) + (t * (b - a))) + ((x + a) - (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.5e+134) {
		tmp = (y * (b - z)) + (a * (1.0 - t));
	} else {
		tmp = ((b * (y + -2.0)) + (t * (b - a))) + ((x + a) - (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.5e+134:
		tmp = (y * (b - z)) + (a * (1.0 - t))
	else:
		tmp = ((b * (y + -2.0)) + (t * (b - a))) + ((x + a) - (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.5e+134)
		tmp = Float64(Float64(y * Float64(b - z)) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(Float64(Float64(b * Float64(y + -2.0)) + Float64(t * Float64(b - a))) + Float64(Float64(x + a) - Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.5e+134)
		tmp = (y * (b - z)) + (a * (1.0 - t));
	else
		tmp = ((b * (y + -2.0)) + (t * (b - a))) + ((x + a) - (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.5e+134], N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x + a), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e134

   1. Initial program 83.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b + \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right), \color{blue}{\left(\left(t - 1\right) \cdot a\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) - 2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(\color{blue}{t} - 1\right) \cdot a\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) + \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y + t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \left(\left(y - 1\right) \cdot z\right)\right)\right), \left(\left(t - \color{blue}{1}\right) \cdot a\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - 1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t - 1\right), \color{blue}{a}\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t + \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      18. metadata-eval 83.3%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   4. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) + -2\right) \cdot b + \left(x - \left(y + -1\right) \cdot z\right)\right) - \left(t + -1\right) \cdot a} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(b - z\right)\right)}, \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(b - z\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(t, -1\right)}, a\right)\right) \]

      2. --lowering--.f64 94.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \color{blue}{-1}\right), a\right)\right) \]

   7. Simplified 94.4%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} - \left(t + -1\right) \cdot a \]

   if -6.5e134 < y

   1. Initial program 98.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 99.5%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \left(b - z\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 96.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{+263}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(t + -2\right)\right) + \left(y \cdot \left(b - z\right) + \left(z + a \cdot \left(1 - t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.95e+263)
   (+ x (* (- (+ y t) 2.0) b))
   (+ (+ x (* b (+ t -2.0))) (+ (* y (- b z)) (+ z (* a (- 1.0 t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.95e+263) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = (x + (b * (t + -2.0))) + ((y * (b - z)) + (z + (a * (1.0 - t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.95d+263)) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = (x + (b * (t + (-2.0d0)))) + ((y * (b - z)) + (z + (a * (1.0d0 - t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.95e+263) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = (x + (b * (t + -2.0))) + ((y * (b - z)) + (z + (a * (1.0 - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.95e+263:
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = (x + (b * (t + -2.0))) + ((y * (b - z)) + (z + (a * (1.0 - t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.95e+263)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(t + -2.0))) + Float64(Float64(y * Float64(b - z)) + Float64(z + Float64(a * Float64(1.0 - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.95e+263)
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = (x + (b * (t + -2.0))) + ((y * (b - z)) + (z + (a * (1.0 - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.95e+263], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.95000000000000014e263

   1. Initial program 76.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 100.0%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -1.95000000000000014e263 < b

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(\left(x + b \cdot \left(t - 2\right)\right) + y \cdot \left(b - z\right)\right) - \left(\color{blue}{-1 \cdot z} + a \cdot \left(t - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(x + b \cdot \left(t - 2\right)\right) + \color{blue}{\left(y \cdot \left(b - z\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + b \cdot \left(t - 2\right)\right), \color{blue}{\left(y \cdot \left(b - z\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(t - 2\right)\right)\right), \left(\color{blue}{y \cdot \left(b - z\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(t - 2\right)\right)\right), \left(y \cdot \color{blue}{\left(b - z\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(t + \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \left(y \cdot \left(b - \color{blue}{z}\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(2\right)\right)\right)\right)\right), \left(y \cdot \left(b - \color{blue}{z}\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \left(y \cdot \left(b - z\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \left(y \cdot \left(b - z\right) + \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \mathsf{+.f64}\left(\left(y \cdot \left(b - z\right)\right), \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(b - z\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)}\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \left(\mathsf{neg}\left(\left(-1 \cdot z + \color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right)\right) \]

      13. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \left(\left(\mathsf{neg}\left(-1 \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \left(\mathsf{neg}\left(\color{blue}{a} \cdot \left(t - 1\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \left(z + \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right)\right) \]

      16. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{+.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{+.f64}\left(z, \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{+.f64}\left(z, \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, -2\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right)\right) \]

   5. Simplified 98.3%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t + -2\right)\right) + \left(y \cdot \left(b - z\right) + \left(z + a \cdot \left(1 - t\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 68.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+18}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -3.3e-35)
     t_1
     (if (<= b 1.85e+18)
       (- (+ x a) (* z (+ y -1.0)))
       (if (<= b 1.15e+135) (* t (- b a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.3e-35) {
		tmp = t_1;
	} else if (b <= 1.85e+18) {
		tmp = (x + a) - (z * (y + -1.0));
	} else if (b <= 1.15e+135) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-3.3d-35)) then
        tmp = t_1
    else if (b <= 1.85d+18) then
        tmp = (x + a) - (z * (y + (-1.0d0)))
    else if (b <= 1.15d+135) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.3e-35) {
		tmp = t_1;
	} else if (b <= 1.85e+18) {
		tmp = (x + a) - (z * (y + -1.0));
	} else if (b <= 1.15e+135) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -3.3e-35:
		tmp = t_1
	elif b <= 1.85e+18:
		tmp = (x + a) - (z * (y + -1.0))
	elif b <= 1.15e+135:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -3.3e-35)
		tmp = t_1;
	elseif (b <= 1.85e+18)
		tmp = Float64(Float64(x + a) - Float64(z * Float64(y + -1.0)));
	elseif (b <= 1.15e+135)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -3.3e-35)
		tmp = t_1;
	elseif (b <= 1.85e+18)
		tmp = (x + a) - (z * (y + -1.0));
	elseif (b <= 1.15e+135)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.3e-35], t$95$1, If[LessEqual[b, 1.85e+18], N[(N[(x + a), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+135], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.3e-35 or 1.1500000000000001e135 < b

   1. Initial program 91.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 76.2%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -3.3e-35 < b < 1.85e18

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + \left(x + \left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)} \]

      2. associate-+r+ N/A

         \[\leadsto \left(\left(a + x\right) + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{z \cdot \left(1 - y\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(x + a\right) + -1 \cdot \left(a \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(x + \left(a + -1 \cdot \left(a \cdot t\right)\right)\right) + \color{blue}{z} \cdot \left(1 - y\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \left(x + \left(a \cdot 1 + -1 \cdot \left(a \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + \left(\mathsf{neg}\left(a \cdot t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(\mathsf{neg}\left(t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(-1 \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \left(x + a \cdot \left(1 + -1 \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + a \cdot \left(1 + -1 \cdot t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(1 + -1 \cdot t\right)\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      17. --lowering--.f64 93.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 93.8%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a + x\right)}, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right)\right) \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + a\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{\_.f64}\left(1, y\right)\right)\right) \]

       2. +-lowering-+.f64 76.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{\_.f64}\left(1, y\right)\right)\right) \]

   11. Simplified 76.4%

       \[\leadsto \color{blue}{\left(x + a\right)} + z \cdot \left(1 - y\right) \]

   if 1.85e18 < b < 1.1500000000000001e135

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 66.7%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{-35}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+18}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 79.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+194}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -3.4e-35)
     t_1
     (if (<= b 1.3e+194) (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.4e-35) {
		tmp = t_1;
	} else if (b <= 1.3e+194) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-3.4d-35)) then
        tmp = t_1
    else if (b <= 1.3d+194) then
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.4e-35) {
		tmp = t_1;
	} else if (b <= 1.3e+194) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -3.4e-35:
		tmp = t_1
	elif b <= 1.3e+194:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -3.4e-35)
		tmp = t_1;
	elseif (b <= 1.3e+194)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -3.4e-35)
		tmp = t_1;
	elseif (b <= 1.3e+194)
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e-35], t$95$1, If[LessEqual[b, 1.3e+194], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.4000000000000003e-35 or 1.2999999999999999e194 < b

   1. Initial program 92.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 78.8%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -3.4000000000000003e-35 < b < 1.2999999999999999e194

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\left(z \cdot \left(y - 1\right) + a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{a \cdot \left(t - 1\right)}\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \left(\mathsf{neg}\left(a \cdot \left(\color{blue}{t} - 1\right)\right)\right)\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(\mathsf{neg}\left(a \cdot \left(t - \color{blue}{1}\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(\mathsf{neg}\left(a \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)}\right)\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \left(a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right)\right)\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right)\right)\right) \]

      22. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right)\right)\right) \]

      24. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right)\right)\right) \]

      25. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right) \]

   5. Simplified 88.3%

      \[\leadsto \color{blue}{x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 60.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.38 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-55}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+173}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))))
   (if (<= z -1.38e+107)
     t_1
     (if (<= z 4.4e-55)
       (+ x (* (- (+ y t) 2.0) b))
       (if (<= z 4.8e+173) (+ x (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double tmp;
	if (z <= -1.38e+107) {
		tmp = t_1;
	} else if (z <= 4.4e-55) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (z <= 4.8e+173) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    if (z <= (-1.38d+107)) then
        tmp = t_1
    else if (z <= 4.4d-55) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else if (z <= 4.8d+173) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double tmp;
	if (z <= -1.38e+107) {
		tmp = t_1;
	} else if (z <= 4.4e-55) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (z <= 4.8e+173) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	tmp = 0
	if z <= -1.38e+107:
		tmp = t_1
	elif z <= 4.4e-55:
		tmp = x + (((y + t) - 2.0) * b)
	elif z <= 4.8e+173:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (z <= -1.38e+107)
		tmp = t_1;
	elseif (z <= 4.4e-55)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (z <= 4.8e+173)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (z <= -1.38e+107)
		tmp = t_1;
	elseif (z <= 4.4e-55)
		tmp = x + (((y + t) - 2.0) * b);
	elseif (z <= 4.8e+173)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.38e+107], t$95$1, If[LessEqual[z, 4.4e-55], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+173], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.38e107 or 4.7999999999999998e173 < z

   1. Initial program 89.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 91.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + \left(x + \left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)} \]

      2. associate-+r+ N/A

         \[\leadsto \left(\left(a + x\right) + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{z \cdot \left(1 - y\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(x + a\right) + -1 \cdot \left(a \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(x + \left(a + -1 \cdot \left(a \cdot t\right)\right)\right) + \color{blue}{z} \cdot \left(1 - y\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \left(x + \left(a \cdot 1 + -1 \cdot \left(a \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + \left(\mathsf{neg}\left(a \cdot t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(\mathsf{neg}\left(t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(-1 \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \left(x + a \cdot \left(1 + -1 \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + a \cdot \left(1 + -1 \cdot t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(1 + -1 \cdot t\right)\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      17. --lowering--.f64 85.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 85.3%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
   10. Step-by-step derivation

       1. sub-neg N/A

          \[\leadsto x + z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{1}\right) \]

       3. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

       4. distribute-neg-in N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

       6. sub-neg N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) \]

       8. distribute-lft-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(y - 1\right)} \]

       9. cancel-sign-sub-inv N/A

          \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]

       10. --lowering--.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(z \cdot \left(y - 1\right)\right)}\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(y - 1\right)}\right)\right) \]

       12. sub-neg N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

       13. metadata-eval N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + -1\right)\right)\right) \]

       14. +-commutative N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{y}\right)\right)\right) \]

       15. +-lowering-+.f64 76.1%

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 76.1%

       \[\leadsto \color{blue}{x - z \cdot \left(-1 + y\right)} \]

   if -1.38e107 < z < 4.3999999999999999e-55

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 67.2%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if 4.3999999999999999e-55 < z < 4.7999999999999998e173

   1. Initial program 97.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b + \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right), \color{blue}{\left(\left(t - 1\right) \cdot a\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) - 2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(\color{blue}{t} - 1\right) \cdot a\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) + \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y + t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \left(\left(y - 1\right) \cdot z\right)\right)\right), \left(\left(t - \color{blue}{1}\right) \cdot a\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - 1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t - 1\right), \color{blue}{a}\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t + \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      18. metadata-eval 97.7%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   4. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) + -2\right) \cdot b + \left(x - \left(y + -1\right) \cdot z\right)\right) - \left(t + -1\right) \cdot a} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 61.7%

      \[\leadsto \color{blue}{x} - \left(t + -1\right) \cdot a \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{+107}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-55}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+173}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -1.65e-37)
     t_1
     (if (<= b 1.32e+14)
       (+ x (* z (- 1.0 y)))
       (if (<= b 1.15e+135) (* t (- b a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -1.65e-37) {
		tmp = t_1;
	} else if (b <= 1.32e+14) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 1.15e+135) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t + (y + (-2.0d0)))
    if (b <= (-1.65d-37)) then
        tmp = t_1
    else if (b <= 1.32d+14) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 1.15d+135) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -1.65e-37) {
		tmp = t_1;
	} else if (b <= 1.32e+14) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 1.15e+135) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + (y + -2.0))
	tmp = 0
	if b <= -1.65e-37:
		tmp = t_1
	elif b <= 1.32e+14:
		tmp = x + (z * (1.0 - y))
	elif b <= 1.15e+135:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -1.65e-37)
		tmp = t_1;
	elseif (b <= 1.32e+14)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 1.15e+135)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + (y + -2.0));
	tmp = 0.0;
	if (b <= -1.65e-37)
		tmp = t_1;
	elseif (b <= 1.32e+14)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 1.15e+135)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.65e-37], t$95$1, If[LessEqual[b, 1.32e+14], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+135], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.64999999999999991e-37 or 1.1500000000000001e135 < b

   1. Initial program 91.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(t + y\right) - 2\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(y - 2\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{\left(y - 2\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \left(y + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      6. metadata-eval 69.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \mathsf{+.f64}\left(y, -2\right)\right)\right) \]

   5. Simplified 69.7%

      \[\leadsto \color{blue}{b \cdot \left(t + \left(y + -2\right)\right)} \]

   if -1.64999999999999991e-37 < b < 1.32e14

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + \left(x + \left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)} \]

      2. associate-+r+ N/A

         \[\leadsto \left(\left(a + x\right) + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{z \cdot \left(1 - y\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(x + a\right) + -1 \cdot \left(a \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(x + \left(a + -1 \cdot \left(a \cdot t\right)\right)\right) + \color{blue}{z} \cdot \left(1 - y\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \left(x + \left(a \cdot 1 + -1 \cdot \left(a \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + \left(\mathsf{neg}\left(a \cdot t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(\mathsf{neg}\left(t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(-1 \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \left(x + a \cdot \left(1 + -1 \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + a \cdot \left(1 + -1 \cdot t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(1 + -1 \cdot t\right)\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      17. --lowering--.f64 94.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 94.4%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
   10. Step-by-step derivation

       1. sub-neg N/A

          \[\leadsto x + z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{1}\right) \]

       3. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

       4. distribute-neg-in N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

       6. sub-neg N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) \]

       8. distribute-lft-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(y - 1\right)} \]

       9. cancel-sign-sub-inv N/A

          \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]

       10. --lowering--.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(z \cdot \left(y - 1\right)\right)}\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(y - 1\right)}\right)\right) \]

       12. sub-neg N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

       13. metadata-eval N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + -1\right)\right)\right) \]

       14. +-commutative N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{y}\right)\right)\right) \]

       15. +-lowering-+.f64 61.0%

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 61.0%

       \[\leadsto \color{blue}{x - z \cdot \left(-1 + y\right)} \]

   if 1.32e14 < b < 1.1500000000000001e135

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 66.7%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{-37}:\\ \;\;\;\;b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t + \left(y + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -33:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 245000000000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -33.0)
     t_1
     (if (<= y 2.9e-174)
       (+ x z)
       (if (<= y 245000000000.0) (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -33.0) {
		tmp = t_1;
	} else if (y <= 2.9e-174) {
		tmp = x + z;
	} else if (y <= 245000000000.0) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-33.0d0)) then
        tmp = t_1
    else if (y <= 2.9d-174) then
        tmp = x + z
    else if (y <= 245000000000.0d0) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -33.0) {
		tmp = t_1;
	} else if (y <= 2.9e-174) {
		tmp = x + z;
	} else if (y <= 245000000000.0) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -33.0:
		tmp = t_1
	elif y <= 2.9e-174:
		tmp = x + z
	elif y <= 245000000000.0:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -33.0)
		tmp = t_1;
	elseif (y <= 2.9e-174)
		tmp = Float64(x + z);
	elseif (y <= 245000000000.0)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -33.0)
		tmp = t_1;
	elseif (y <= 2.9e-174)
		tmp = x + z;
	elseif (y <= 245000000000.0)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -33.0], t$95$1, If[LessEqual[y, 2.9e-174], N[(x + z), $MachinePrecision], If[LessEqual[y, 245000000000.0], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -33 or 2.45e11 < y

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right) \]

      2. --lowering--.f64 67.5%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 67.5%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   if -33 < y < 2.9000000000000001e-174

   1. Initial program 96.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + \left(x + \left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)} \]

      2. associate-+r+ N/A

         \[\leadsto \left(\left(a + x\right) + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{z \cdot \left(1 - y\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(x + a\right) + -1 \cdot \left(a \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(x + \left(a + -1 \cdot \left(a \cdot t\right)\right)\right) + \color{blue}{z} \cdot \left(1 - y\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \left(x + \left(a \cdot 1 + -1 \cdot \left(a \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + \left(\mathsf{neg}\left(a \cdot t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(\mathsf{neg}\left(t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(-1 \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \left(x + a \cdot \left(1 + -1 \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + a \cdot \left(1 + -1 \cdot t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(1 + -1 \cdot t\right)\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      17. --lowering--.f64 67.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 67.8%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
   10. Step-by-step derivation

       1. sub-neg N/A

          \[\leadsto x + z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{1}\right) \]

       3. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

       4. distribute-neg-in N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

       6. sub-neg N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) \]

       8. distribute-lft-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(y - 1\right)} \]

       9. cancel-sign-sub-inv N/A

          \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]

       10. --lowering--.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(z \cdot \left(y - 1\right)\right)}\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(y - 1\right)}\right)\right) \]

       12. sub-neg N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

       13. metadata-eval N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + -1\right)\right)\right) \]

       14. +-commutative N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{y}\right)\right)\right) \]

       15. +-lowering-+.f64 44.8%

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 44.8%

       \[\leadsto \color{blue}{x - z \cdot \left(-1 + y\right)} \]

   12. Taylor expanded in y around 0

       \[\leadsto \color{blue}{x - -1 \cdot z} \]
   13. Step-by-step derivation

       1. cancel-sign-sub-inv N/A

          \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot z} \]

       2. metadata-eval N/A

          \[\leadsto x + 1 \cdot z \]

       3. *-lft-identity N/A

          \[\leadsto x + z \]

       4. +-commutative N/A

          \[\leadsto z + \color{blue}{x} \]

       5. +-lowering-+.f64 43.5%

          \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   14. Simplified 43.5%

       \[\leadsto \color{blue}{z + x} \]

   if 2.9000000000000001e-174 < y < 2.45e11

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto a \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot -1 + \left(\mathsf{neg}\left(\color{blue}{t}\right)\right)\right) \]

      3. neg-mul-1 N/A

         \[\leadsto a \cdot \left(-1 \cdot -1 + -1 \cdot \color{blue}{t}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(-1 + t\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \color{blue}{-1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t - \color{blue}{1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

      16. --lowering--.f64 43.2%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

   5. Simplified 43.2%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -33:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 245000000000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-60}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+17}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+246}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.75e-60)
   (* y b)
   (if (<= b 3.6e+17) (+ x z) (if (<= b 1.6e+246) (* t b) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e-60) {
		tmp = y * b;
	} else if (b <= 3.6e+17) {
		tmp = x + z;
	} else if (b <= 1.6e+246) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.75d-60)) then
        tmp = y * b
    else if (b <= 3.6d+17) then
        tmp = x + z
    else if (b <= 1.6d+246) then
        tmp = t * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e-60) {
		tmp = y * b;
	} else if (b <= 3.6e+17) {
		tmp = x + z;
	} else if (b <= 1.6e+246) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.75e-60:
		tmp = y * b
	elif b <= 3.6e+17:
		tmp = x + z
	elif b <= 1.6e+246:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.75e-60)
		tmp = Float64(y * b);
	elseif (b <= 3.6e+17)
		tmp = Float64(x + z);
	elseif (b <= 1.6e+246)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.75e-60)
		tmp = y * b;
	elseif (b <= 3.6e+17)
		tmp = x + z;
	elseif (b <= 1.6e+246)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.75e-60], N[(y * b), $MachinePrecision], If[LessEqual[b, 3.6e+17], N[(x + z), $MachinePrecision], If[LessEqual[b, 1.6e+246], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.74999999999999988e-60 or 1.60000000000000007e246 < b

   1. Initial program 92.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right) \]

      2. --lowering--.f64 49.7%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 49.7%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{b} \]

      2. *-lowering-*.f64 38.1%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{b}\right) \]

   8. Simplified 38.1%

      \[\leadsto \color{blue}{y \cdot b} \]

   if -1.74999999999999988e-60 < b < 3.6e17

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + \left(x + \left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)} \]

      2. associate-+r+ N/A

         \[\leadsto \left(\left(a + x\right) + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{z \cdot \left(1 - y\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(x + a\right) + -1 \cdot \left(a \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(x + \left(a + -1 \cdot \left(a \cdot t\right)\right)\right) + \color{blue}{z} \cdot \left(1 - y\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \left(x + \left(a \cdot 1 + -1 \cdot \left(a \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + \left(\mathsf{neg}\left(a \cdot t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(\mathsf{neg}\left(t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(-1 \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \left(x + a \cdot \left(1 + -1 \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + a \cdot \left(1 + -1 \cdot t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(1 + -1 \cdot t\right)\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      17. --lowering--.f64 95.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 95.1%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
   10. Step-by-step derivation

       1. sub-neg N/A

          \[\leadsto x + z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{1}\right) \]

       3. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

       4. distribute-neg-in N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

       6. sub-neg N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) \]

       8. distribute-lft-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(y - 1\right)} \]

       9. cancel-sign-sub-inv N/A

          \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]

       10. --lowering--.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(z \cdot \left(y - 1\right)\right)}\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(y - 1\right)}\right)\right) \]

       12. sub-neg N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

       13. metadata-eval N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + -1\right)\right)\right) \]

       14. +-commutative N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{y}\right)\right)\right) \]

       15. +-lowering-+.f64 60.8%

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 60.8%

       \[\leadsto \color{blue}{x - z \cdot \left(-1 + y\right)} \]

   12. Taylor expanded in y around 0

       \[\leadsto \color{blue}{x - -1 \cdot z} \]
   13. Step-by-step derivation

       1. cancel-sign-sub-inv N/A

          \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot z} \]

       2. metadata-eval N/A

          \[\leadsto x + 1 \cdot z \]

       3. *-lft-identity N/A

          \[\leadsto x + z \]

       4. +-commutative N/A

          \[\leadsto z + \color{blue}{x} \]

       5. +-lowering-+.f64 40.7%

          \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   14. Simplified 40.7%

       \[\leadsto \color{blue}{z + x} \]

   if 3.6e17 < b < 1.60000000000000007e246

   1. Initial program 95.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 52.2%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto t \cdot \color{blue}{b} \]

      2. *-lowering-*.f64 33.3%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{b}\right) \]

   8. Simplified 33.3%

      \[\leadsto \color{blue}{t \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-60}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+17}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+246}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{-41}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-143}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 2.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.2e-41)
   (* t b)
   (if (<= b -2.3e-143) z (if (<= b 2.5) x (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.2e-41) {
		tmp = t * b;
	} else if (b <= -2.3e-143) {
		tmp = z;
	} else if (b <= 2.5) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.2d-41)) then
        tmp = t * b
    else if (b <= (-2.3d-143)) then
        tmp = z
    else if (b <= 2.5d0) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.2e-41) {
		tmp = t * b;
	} else if (b <= -2.3e-143) {
		tmp = z;
	} else if (b <= 2.5) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.2e-41:
		tmp = t * b
	elif b <= -2.3e-143:
		tmp = z
	elif b <= 2.5:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.2e-41)
		tmp = Float64(t * b);
	elseif (b <= -2.3e-143)
		tmp = z;
	elseif (b <= 2.5)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.2e-41)
		tmp = t * b;
	elseif (b <= -2.3e-143)
		tmp = z;
	elseif (b <= 2.5)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.2e-41], N[(t * b), $MachinePrecision], If[LessEqual[b, -2.3e-143], z, If[LessEqual[b, 2.5], x, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.20000000000000041e-41 or 2.5 < b

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 67.7%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto t \cdot \color{blue}{b} \]

      2. *-lowering-*.f64 29.7%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{b}\right) \]

   8. Simplified 29.7%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -9.20000000000000041e-41 < b < -2.30000000000000011e-143

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto z \cdot \left(1 + -1 \cdot \color{blue}{y}\right) \]

      3. +-commutative N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) \]

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right) \]

      18. --lowering--.f64 47.2%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 47.2%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 30.9%

      \[\leadsto \color{blue}{z} \]

   if -2.30000000000000011e-143 < b < 2.5

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 27.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 60.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8500:\\ \;\;\;\;z + b \cdot \left(t + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (* y (- b z)))))
   (if (<= y -3.2e+14) t_1 (if (<= y 8500.0) (+ z (* b (+ t -2.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (y * (b - z));
	double tmp;
	if (y <= -3.2e+14) {
		tmp = t_1;
	} else if (y <= 8500.0) {
		tmp = z + (b * (t + -2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (y * (b - z))
    if (y <= (-3.2d+14)) then
        tmp = t_1
    else if (y <= 8500.0d0) then
        tmp = z + (b * (t + (-2.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (y * (b - z));
	double tmp;
	if (y <= -3.2e+14) {
		tmp = t_1;
	} else if (y <= 8500.0) {
		tmp = z + (b * (t + -2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (y * (b - z))
	tmp = 0
	if y <= -3.2e+14:
		tmp = t_1
	elif y <= 8500.0:
		tmp = z + (b * (t + -2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(y * Float64(b - z)))
	tmp = 0.0
	if (y <= -3.2e+14)
		tmp = t_1;
	elseif (y <= 8500.0)
		tmp = Float64(z + Float64(b * Float64(t + -2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (y * (b - z));
	tmp = 0.0;
	if (y <= -3.2e+14)
		tmp = t_1;
	elseif (y <= 8500.0)
		tmp = z + (b * (t + -2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+14], t$95$1, If[LessEqual[y, 8500.0], N[(z + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e14 or 8500 < y

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b + \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right), \color{blue}{\left(\left(t - 1\right) \cdot a\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) - 2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(\color{blue}{t} - 1\right) \cdot a\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) + \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y + t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \left(\left(y - 1\right) \cdot z\right)\right)\right), \left(\left(t - \color{blue}{1}\right) \cdot a\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - 1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t - 1\right), \color{blue}{a}\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t + \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      18. metadata-eval 94.9%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   4. Applied egg-rr 94.9%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) + -2\right) \cdot b + \left(x - \left(y + -1\right) \cdot z\right)\right) - \left(t + -1\right) \cdot a} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(b - z\right)\right)}, \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(b - z\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(t, -1\right)}, a\right)\right) \]

      2. --lowering--.f64 86.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \color{blue}{-1}\right), a\right)\right) \]

   7. Simplified 86.1%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} - \left(t + -1\right) \cdot a \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{y \cdot \left(b - z\right) - -1 \cdot a} \]
   9. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto y \cdot \left(b - z\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot a} \]

      2. metadata-eval N/A

         \[\leadsto y \cdot \left(b - z\right) + 1 \cdot a \]

      3. *-lft-identity N/A

         \[\leadsto y \cdot \left(b - z\right) + a \]

      4. +-commutative N/A

         \[\leadsto a + \color{blue}{y \cdot \left(b - z\right)} \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(y \cdot \left(b - z\right)\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right)\right) \]

      7. --lowering--.f64 73.8%

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 73.8%

       \[\leadsto \color{blue}{a + y \cdot \left(b - z\right)} \]

   if -3.2e14 < y < 8500

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(1 - y\right)\right)}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot y + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      4. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y - 1\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right)}, b\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot -1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + -1 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(1 - y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

      18. --lowering--.f64 54.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, y\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), \color{blue}{2}\right), b\right)\right) \]

   5. Simplified 54.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z + b \cdot \left(t - 2\right)} \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(b \cdot \left(t - 2\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(b, \color{blue}{\left(t - 2\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(b, \left(t + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(b, \left(t + -2\right)\right)\right) \]

      5. +-lowering-+.f64 52.4%

         \[\leadsto \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(t, \color{blue}{-2}\right)\right)\right) \]

   8. Simplified 52.4%

      \[\leadsto \color{blue}{z + b \cdot \left(t + -2\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 60.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 72000000:\\ \;\;\;\;a + y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -7e+27) t_1 (if (<= t 72000000.0) (+ a (* y (- b z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -7e+27) {
		tmp = t_1;
	} else if (t <= 72000000.0) {
		tmp = a + (y * (b - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-7d+27)) then
        tmp = t_1
    else if (t <= 72000000.0d0) then
        tmp = a + (y * (b - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -7e+27) {
		tmp = t_1;
	} else if (t <= 72000000.0) {
		tmp = a + (y * (b - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -7e+27:
		tmp = t_1
	elif t <= 72000000.0:
		tmp = a + (y * (b - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7e+27)
		tmp = t_1;
	elseif (t <= 72000000.0)
		tmp = Float64(a + Float64(y * Float64(b - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -7e+27)
		tmp = t_1;
	elseif (t <= 72000000.0)
		tmp = a + (y * (b - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+27], t$95$1, If[LessEqual[t, 72000000.0], N[(a + N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.0000000000000004e27 or 7.2e7 < t

   1. Initial program 92.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 66.8%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 66.8%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -7.0000000000000004e27 < t < 7.2e7

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b + \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      2. associate-+r- N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right), \color{blue}{\left(\left(t - 1\right) \cdot a\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\left(\left(y + t\right) - 2\right) \cdot b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) - 2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(\color{blue}{t} - 1\right) \cdot a\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(y + t\right) + \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y + t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), \left(\mathsf{neg}\left(2\right)\right)\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \left(x - \left(y - 1\right) \cdot z\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \left(\left(y - 1\right) \cdot z\right)\right)\right), \left(\left(t - \color{blue}{1}\right) \cdot a\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - 1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(1\right)\right)\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \left(\left(t - 1\right) \cdot a\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t - 1\right), \color{blue}{a}\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\left(t + \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \left(\mathsf{neg}\left(1\right)\right)\right), a\right)\right) \]

      18. metadata-eval 99.3%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(y, t\right), -2\right), b\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(y, -1\right), z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]

   4. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) + -2\right) \cdot b + \left(x - \left(y + -1\right) \cdot z\right)\right) - \left(t + -1\right) \cdot a} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(b - z\right)\right)}, \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, -1\right), a\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(b - z\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(t, -1\right)}, a\right)\right) \]

      2. --lowering--.f64 58.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, \color{blue}{-1}\right), a\right)\right) \]

   7. Simplified 58.3%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} - \left(t + -1\right) \cdot a \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{y \cdot \left(b - z\right) - -1 \cdot a} \]
   9. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto y \cdot \left(b - z\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot a} \]

      2. metadata-eval N/A

         \[\leadsto y \cdot \left(b - z\right) + 1 \cdot a \]

      3. *-lft-identity N/A

         \[\leadsto y \cdot \left(b - z\right) + a \]

      4. +-commutative N/A

         \[\leadsto a + \color{blue}{y \cdot \left(b - z\right)} \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(y \cdot \left(b - z\right)\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right)\right) \]

      7. --lowering--.f64 57.9%

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 57.9%

       \[\leadsto \color{blue}{a + y \cdot \left(b - z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 47.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 45000000:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -6.2e-6) t_1 (if (<= t 45000000.0) (+ x z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -6.2e-6) {
		tmp = t_1;
	} else if (t <= 45000000.0) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-6.2d-6)) then
        tmp = t_1
    else if (t <= 45000000.0d0) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -6.2e-6) {
		tmp = t_1;
	} else if (t <= 45000000.0) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -6.2e-6:
		tmp = t_1
	elif t <= 45000000.0:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6.2e-6)
		tmp = t_1;
	elseif (t <= 45000000.0)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -6.2e-6)
		tmp = t_1;
	elseif (t <= 45000000.0)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e-6], t$95$1, If[LessEqual[t, 45000000.0], N[(x + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.1999999999999999e-6 or 4.5e7 < t

   1. Initial program 93.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(b - a\right)}\right) \]

      2. --lowering--.f64 64.7%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, \color{blue}{a}\right)\right) \]

   5. Simplified 64.7%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -6.1999999999999999e-6 < t < 4.5e7

   1. Initial program 99.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 99.2%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + \left(x + \left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)} \]

      2. associate-+r+ N/A

         \[\leadsto \left(\left(a + x\right) + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{z \cdot \left(1 - y\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(x + a\right) + -1 \cdot \left(a \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(x + \left(a + -1 \cdot \left(a \cdot t\right)\right)\right) + \color{blue}{z} \cdot \left(1 - y\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \left(x + \left(a \cdot 1 + -1 \cdot \left(a \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + \left(\mathsf{neg}\left(a \cdot t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(\mathsf{neg}\left(t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(-1 \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \left(x + a \cdot \left(1 + -1 \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + a \cdot \left(1 + -1 \cdot t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(1 + -1 \cdot t\right)\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      17. --lowering--.f64 70.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 70.7%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
   10. Step-by-step derivation

       1. sub-neg N/A

          \[\leadsto x + z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{1}\right) \]

       3. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

       4. distribute-neg-in N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

       6. sub-neg N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) \]

       8. distribute-lft-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(y - 1\right)} \]

       9. cancel-sign-sub-inv N/A

          \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]

       10. --lowering--.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(z \cdot \left(y - 1\right)\right)}\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(y - 1\right)}\right)\right) \]

       12. sub-neg N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

       13. metadata-eval N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + -1\right)\right)\right) \]

       14. +-commutative N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{y}\right)\right)\right) \]

       15. +-lowering-+.f64 52.9%

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 52.9%

       \[\leadsto \color{blue}{x - z \cdot \left(-1 + y\right)} \]

   12. Taylor expanded in y around 0

       \[\leadsto \color{blue}{x - -1 \cdot z} \]
   13. Step-by-step derivation

       1. cancel-sign-sub-inv N/A

          \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot z} \]

       2. metadata-eval N/A

          \[\leadsto x + 1 \cdot z \]

       3. *-lft-identity N/A

          \[\leadsto x + z \]

       4. +-commutative N/A

          \[\leadsto z + \color{blue}{x} \]

       5. +-lowering-+.f64 31.5%

          \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   14. Simplified 31.5%

       \[\leadsto \color{blue}{z + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 45000000:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 41.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-15}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.4e+132) t_1 (if (<= a 1.75e-15) (+ x z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.4e+132) {
		tmp = t_1;
	} else if (a <= 1.75e-15) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-1.4d+132)) then
        tmp = t_1
    else if (a <= 1.75d-15) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.4e+132) {
		tmp = t_1;
	} else if (a <= 1.75e-15) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -1.4e+132:
		tmp = t_1
	elif a <= 1.75e-15:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.4e+132)
		tmp = t_1;
	elseif (a <= 1.75e-15)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.4e+132)
		tmp = t_1;
	elseif (a <= 1.75e-15)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+132], t$95$1, If[LessEqual[a, 1.75e-15], N[(x + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4e132 or 1.75e-15 < a

   1. Initial program 95.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto a \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot -1 + \left(\mathsf{neg}\left(\color{blue}{t}\right)\right)\right) \]

      3. neg-mul-1 N/A

         \[\leadsto a \cdot \left(-1 \cdot -1 + -1 \cdot \color{blue}{t}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(-1 + t\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \color{blue}{-1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t - \color{blue}{1}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot \left(t + -1\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(-1 \cdot t + 1\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \color{blue}{-1 \cdot t}\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(1 - \color{blue}{t}\right)\right) \]

      16. --lowering--.f64 52.1%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{t}\right)\right) \]

   5. Simplified 52.1%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -1.4e132 < a < 1.75e-15

   1. Initial program 97.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right), \color{blue}{\left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(\color{blue}{x} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y - 2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(y + \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, \left(\mathsf{neg}\left(2\right)\right)\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \left(t \cdot \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \left(b - a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      11. associate--r+ N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) - \color{blue}{z \cdot \left(y - 1\right)}\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \left(\left(x - -1 \cdot a\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x - -1 \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(z \cdot \left(\color{blue}{y} - 1\right)\right)\right)\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\left(x + a\right), \left(\mathsf{neg}\left(z \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(y - 1\right)}\right)\right)\right)\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)}\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right)\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(y, -2\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(b, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, a\right), \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 96.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y + -2\right) + t \cdot \left(b - a\right)\right) + \left(\left(x + a\right) + z \cdot \left(1 - y\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + \left(x + \left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(a + x\right) + \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)} \]

      2. associate-+r+ N/A

         \[\leadsto \left(\left(a + x\right) + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{z \cdot \left(1 - y\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(x + a\right) + -1 \cdot \left(a \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      4. associate-+r+ N/A

         \[\leadsto \left(x + \left(a + -1 \cdot \left(a \cdot t\right)\right)\right) + \color{blue}{z} \cdot \left(1 - y\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \left(x + \left(a \cdot 1 + -1 \cdot \left(a \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + \left(\mathsf{neg}\left(a \cdot t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(\mathsf{neg}\left(t\right)\right)\right)\right) + z \cdot \left(1 - y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(x + \left(a \cdot 1 + a \cdot \left(-1 \cdot t\right)\right)\right) + z \cdot \left(1 - y\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \left(x + a \cdot \left(1 + -1 \cdot t\right)\right) + z \cdot \left(1 - y\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x + a \cdot \left(1 + -1 \cdot t\right)\right), \color{blue}{\left(z \cdot \left(1 - y\right)\right)}\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(a \cdot \left(1 + -1 \cdot t\right)\right)\right), \left(\color{blue}{z} \cdot \left(1 - y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + -1 \cdot t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \left(1 - t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \left(z \cdot \left(1 - y\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 - y\right)}\right)\right) \]

      17. --lowering--.f64 57.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(1, t\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 57.4%

      \[\leadsto \color{blue}{\left(x + a \cdot \left(1 - t\right)\right) + z \cdot \left(1 - y\right)} \]

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + z \cdot \left(1 - y\right)} \]
   10. Step-by-step derivation

       1. sub-neg N/A

          \[\leadsto x + z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{1}\right) \]

       3. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

       4. distribute-neg-in N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

       6. sub-neg N/A

          \[\leadsto x + z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) \]

       8. distribute-lft-neg-in N/A

          \[\leadsto x + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(y - 1\right)} \]

       9. cancel-sign-sub-inv N/A

          \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]

       10. --lowering--.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(z \cdot \left(y - 1\right)\right)}\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(y - 1\right)}\right)\right) \]

       12. sub-neg N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

       13. metadata-eval N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(y + -1\right)\right)\right) \]

       14. +-commutative N/A

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{y}\right)\right)\right) \]

       15. +-lowering-+.f64 49.3%

           \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 49.3%

       \[\leadsto \color{blue}{x - z \cdot \left(-1 + y\right)} \]

   12. Taylor expanded in y around 0

       \[\leadsto \color{blue}{x - -1 \cdot z} \]
   13. Step-by-step derivation

       1. cancel-sign-sub-inv N/A

          \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot z} \]

       2. metadata-eval N/A

          \[\leadsto x + 1 \cdot z \]

       3. *-lft-identity N/A

          \[\leadsto x + z \]

       4. +-commutative N/A

          \[\leadsto z + \color{blue}{x} \]

       5. +-lowering-+.f64 33.0%

          \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

   14. Simplified 33.0%

       \[\leadsto \color{blue}{z + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+132}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-15}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 27.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+40}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+96}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.5e+40) (* y b) (if (<= y 1.05e+96) (* t b) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e+40) {
		tmp = y * b;
	} else if (y <= 1.05e+96) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.5d+40)) then
        tmp = y * b
    else if (y <= 1.05d+96) then
        tmp = t * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e+40) {
		tmp = y * b;
	} else if (y <= 1.05e+96) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.5e+40:
		tmp = y * b
	elif y <= 1.05e+96:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.5e+40)
		tmp = Float64(y * b);
	elseif (y <= 1.05e+96)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.5e+40)
		tmp = y * b;
	elseif (y <= 1.05e+96)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.5e+40], N[(y * b), $MachinePrecision], If[LessEqual[y, 1.05e+96], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999999e40 or 1.0500000000000001e96 < y

   1. Initial program 93.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(b - z\right)}\right) \]

      2. --lowering--.f64 74.1%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 74.1%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{b} \]

      2. *-lowering-*.f64 41.9%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{b}\right) \]

   8. Simplified 41.9%

      \[\leadsto \color{blue}{y \cdot b} \]

   if -3.4999999999999999e40 < y < 1.0500000000000001e96

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(y, t\right), 2\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 49.9%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto t \cdot \color{blue}{b} \]

      2. *-lowering-*.f64 22.0%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{b}\right) \]

   8. Simplified 22.0%

      \[\leadsto \color{blue}{t \cdot b} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 26: 20.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+78}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+191}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.2e+78) z (if (<= z 3.8e+191) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.2e+78) {
		tmp = z;
	} else if (z <= 3.8e+191) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5.2d+78)) then
        tmp = z
    else if (z <= 3.8d+191) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.2e+78) {
		tmp = z;
	} else if (z <= 3.8e+191) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.2e+78:
		tmp = z
	elif z <= 3.8e+191:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.2e+78)
		tmp = z;
	elseif (z <= 3.8e+191)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.2e+78)
		tmp = z;
	elseif (z <= 3.8e+191)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.2e+78], z, If[LessEqual[z, 3.8e+191], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e78 or 3.7999999999999998e191 < z

   1. Initial program 91.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      2. neg-mul-1 N/A

         \[\leadsto z \cdot \left(1 + -1 \cdot \color{blue}{y}\right) \]

      3. +-commutative N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) \]

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + -1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto z \cdot \left(-1 \cdot \color{blue}{\left(y - 1\right)}\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 + \color{blue}{y}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(-1 \cdot -1 + \color{blue}{-1 \cdot y}\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \color{blue}{-1} \cdot y\right)\right) \]

      16. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(1 - \color{blue}{y}\right)\right) \]

      18. --lowering--.f64 69.5%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 69.5%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 29.5%

      \[\leadsto \color{blue}{z} \]

   if -5.2e78 < z < 3.7999999999999998e191

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 18.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 27: 15.4% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 96.4%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 14.5%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))