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

Percentage Accurate: 95.7% → 97.7%

Time: 14.5s

Alternatives: 23

Speedup: 0.5×

• 35.9% 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: 95.7% 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: 97.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate--l+ N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate--l- N/A

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

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

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

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

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

      11. sub-neg N/A

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

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

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

      13. metadata-eval N/A

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

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

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

      15. sub-neg N/A

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

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

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

      17. metadata-eval 100.0

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

   4. Applied egg-rr 100.0%

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

   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. 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

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval 82.3

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

   5. Simplified 82.3%

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

4. Final simplification 99.2%

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

Alternative 2: 90.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, b, x - \mathsf{fma}\left(y + -1, z, \left(t + -1\right) \cdot a\right)\right)\\ \mathbf{if}\;a \leq -4.9 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma y b (- x (fma (+ y -1.0) z (* (+ t -1.0) a))))))
   (if (<= a -4.9e-5)
     t_1
     (if (<= a 1.3e+95) (fma b (+ y (+ t -2.0)) (fma z (- 1.0 y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, b, (x - fma((y + -1.0), z, ((t + -1.0) * a))));
	double tmp;
	if (a <= -4.9e-5) {
		tmp = t_1;
	} else if (a <= 1.3e+95) {
		tmp = fma(b, (y + (t + -2.0)), fma(z, (1.0 - y), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, b, Float64(x - fma(Float64(y + -1.0), z, Float64(Float64(t + -1.0) * a))))
	tmp = 0.0
	if (a <= -4.9e-5)
		tmp = t_1;
	elseif (a <= 1.3e+95)
		tmp = fma(b, Float64(y + Float64(t + -2.0)), fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * b + N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.9e-5], t$95$1, If[LessEqual[a, 1.3e+95], N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.9e-5 or 1.29999999999999995e95 < a

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate--l+ N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate--l- N/A

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

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

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

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

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

      11. sub-neg N/A

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

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

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

      13. metadata-eval N/A

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

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

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

      15. sub-neg N/A

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

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

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

      17. metadata-eval 95.1

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

   4. Applied egg-rr 95.1%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 90.4%

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

   if -4.9e-5 < a < 1.29999999999999995e95

   1. Initial program 96.7%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

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

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. sub-neg N/A

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

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

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(\left(y - 1\right)\right)}, x\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, \mathsf{neg}\left(\color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), x\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, \mathsf{neg}\left(\left(y + \color{blue}{-1}\right)\right), x\right)\right) \]

      18. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, \mathsf{neg}\left(\color{blue}{\left(-1 + y\right)}\right), x\right)\right) \]

      19. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(y\right)\right)}, x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, \color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right), x\right)\right) \]

      21. sub-neg N/A

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

      22. --lowering--.f64 94.5

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

   5. Simplified 94.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 57.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, 1 - y, x\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- 1.0 y) x)) (t_2 (* t (- b a))))
   (if (<= t -1.45e+34)
     t_2
     (if (<= t 3.8e-195)
       t_1
       (if (<= t 3.1e+27)
         (fma b (+ y -2.0) x)
         (if (<= t 1.95e+89) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (1.0 - y), x);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.45e+34) {
		tmp = t_2;
	} else if (t <= 3.8e-195) {
		tmp = t_1;
	} else if (t <= 3.1e+27) {
		tmp = fma(b, (y + -2.0), x);
	} else if (t <= 1.95e+89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(1.0 - y), x)
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.45e+34)
		tmp = t_2;
	elseif (t <= 3.8e-195)
		tmp = t_1;
	elseif (t <= 3.1e+27)
		tmp = fma(b, Float64(y + -2.0), x);
	elseif (t <= 1.95e+89)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e+34], t$95$2, If[LessEqual[t, 3.8e-195], t$95$1, If[LessEqual[t, 3.1e+27], N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.95e+89], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4500000000000001e34 or 1.95000000000000005e89 < t

   1. Initial program 92.3%

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

   3. Taylor expanded in t around inf

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

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

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

      2. --lowering--.f64 74.8

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

   5. Simplified 74.8%

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

   if -1.4500000000000001e34 < t < 3.80000000000000013e-195 or 3.09999999999999996e27 < t < 1.95000000000000005e89

   1. Initial program 96.3%

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

   3. Taylor expanded in 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. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

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

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 76.2%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(0 - y\right)} + 1\right) + x \]

      5. associate-+l- N/A

         \[\leadsto z \cdot \color{blue}{\left(0 - \left(y - 1\right)\right)} + x \]

      6. neg-sub0 N/A

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

      7. mul-1-neg N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. neg-sub0 N/A

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, x\right) \]

      11. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\left(0 - y\right) + 1}, x\right) \]

      12. neg-sub0 N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 62.0

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

   8. Simplified 62.0%

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

   if 3.80000000000000013e-195 < t < 3.09999999999999996e27

   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

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

   5. Simplified 66.0%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, y - 2, x\right)} \]

      3. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

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

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

      5. metadata-eval 64.2

         \[\leadsto \mathsf{fma}\left(b, y + \color{blue}{-2}, x\right) \]

   8. Simplified 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + -2, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 58.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 1 - t, x\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-299}:\\ \;\;\;\;\mathsf{fma}\left(b, t + -2, x\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (- 1.0 t) x)) (t_2 (* y (- b z))))
   (if (<= y -6.2e+84)
     t_2
     (if (<= y -5.5e-10)
       t_1
       (if (<= y 6e-299) (fma b (+ t -2.0) x) (if (<= y 2.8e+28) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (1.0 - t), x);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -6.2e+84) {
		tmp = t_2;
	} else if (y <= -5.5e-10) {
		tmp = t_1;
	} else if (y <= 6e-299) {
		tmp = fma(b, (t + -2.0), x);
	} else if (y <= 2.8e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(1.0 - t), x)
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -6.2e+84)
		tmp = t_2;
	elseif (y <= -5.5e-10)
		tmp = t_1;
	elseif (y <= 6e-299)
		tmp = fma(b, Float64(t + -2.0), x);
	elseif (y <= 2.8e+28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+84], t$95$2, If[LessEqual[y, -5.5e-10], t$95$1, If[LessEqual[y, 6e-299], N[(b * N[(t + -2.0), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 2.8e+28], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.20000000000000006e84 or 2.8000000000000001e28 < 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

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

      2. --lowering--.f64 72.9

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

   5. Simplified 72.9%

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

   if -6.20000000000000006e84 < y < -5.4999999999999996e-10 or 5.99999999999999969e-299 < y < 2.8000000000000001e28

   1. Initial program 97.6%

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

   3. Taylor expanded in 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. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

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

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 78.2%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - t\right)} + 1\right) + x \]

      5. associate-+l- N/A

         \[\leadsto a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)} + x \]

      6. neg-sub0 N/A

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

      7. mul-1-neg N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, x\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, x\right) \]

      11. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, x\right) \]

      12. neg-sub0 N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

      15. --lowering--.f64 60.4

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

   8. Simplified 60.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, x\right)} \]

   if -5.4999999999999996e-10 < y < 5.99999999999999969e-299

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 64.0%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, t - 2, x\right)} \]

      3. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

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

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

      5. metadata-eval 64.0

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{-2}, x\right) \]

   8. Simplified 64.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t + -2, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 87.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + -2\right)\\ t_2 := \mathsf{fma}\left(b, t\_1, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{if}\;z \leq -64000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(b, t\_1, \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t -2.0))) (t_2 (fma b t_1 (fma z (- 1.0 y) x))))
   (if (<= z -64000.0)
     t_2
     (if (<= z 6.7e+66) (fma b t_1 (fma a (- 1.0 t) x)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + -2.0);
	double t_2 = fma(b, t_1, fma(z, (1.0 - y), x));
	double tmp;
	if (z <= -64000.0) {
		tmp = t_2;
	} else if (z <= 6.7e+66) {
		tmp = fma(b, t_1, fma(a, (1.0 - t), x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + -2.0))
	t_2 = fma(b, t_1, fma(z, Float64(1.0 - y), x))
	tmp = 0.0
	if (z <= -64000.0)
		tmp = t_2;
	elseif (z <= 6.7e+66)
		tmp = fma(b, t_1, fma(a, Float64(1.0 - t), x));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -64000.0], t$95$2, If[LessEqual[z, 6.7e+66], N[(b * t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -64000 or 6.69999999999999969e66 < z

   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 a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

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

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. sub-neg N/A

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

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

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(\left(y - 1\right)\right)}, x\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, \mathsf{neg}\left(\color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), x\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, \mathsf{neg}\left(\left(y + \color{blue}{-1}\right)\right), x\right)\right) \]

      18. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, \mathsf{neg}\left(\color{blue}{\left(-1 + y\right)}\right), x\right)\right) \]

      19. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(y\right)\right)}, x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(z, \color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right), x\right)\right) \]

      21. sub-neg N/A

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

      22. --lowering--.f64 85.3

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

   5. Simplified 85.3%

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

   if -64000 < z < 6.69999999999999969e66

   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 z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

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

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. sub-neg N/A

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

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

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x\right)\right) \]

      21. sub-neg N/A

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

      22. --lowering--.f64 95.6

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

   5. Simplified 95.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 87.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+69}:\\ \;\;\;\;\mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (- 1.0 t) (fma z (- 1.0 y) x))))
   (if (<= z -3.8e+105)
     t_1
     (if (<= z 4e+69) (fma b (+ y (+ t -2.0)) (fma a (- 1.0 t) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	double tmp;
	if (z <= -3.8e+105) {
		tmp = t_1;
	} else if (z <= 4e+69) {
		tmp = fma(b, (y + (t + -2.0)), fma(a, (1.0 - t), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x))
	tmp = 0.0
	if (z <= -3.8e+105)
		tmp = t_1;
	elseif (z <= 4e+69)
		tmp = fma(b, Float64(y + Float64(t + -2.0)), fma(a, Float64(1.0 - t), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+105], t$95$1, If[LessEqual[z, 4e+69], N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8e105 or 4.0000000000000003e69 < z

   1. Initial program 91.4%

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

   3. Taylor expanded in 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. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

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

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 80.0%

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

   if -3.8e105 < z < 4.0000000000000003e69

   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 z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

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

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. sub-neg N/A

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

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

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x\right)\right) \]

      21. sub-neg N/A

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

      22. --lowering--.f64 93.0

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

   5. Simplified 93.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-246}:\\ \;\;\;\;\mathsf{fma}\left(b, t, x\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(b, -2, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -3.8e+57)
     t_1
     (if (<= y 4.3e-246)
       (fma b t x)
       (if (<= y 1.15e-49)
         (* t (- b a))
         (if (<= y 8.2e+15) (fma b -2.0 x) 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 <= -3.8e+57) {
		tmp = t_1;
	} else if (y <= 4.3e-246) {
		tmp = fma(b, t, x);
	} else if (y <= 1.15e-49) {
		tmp = t * (b - a);
	} else if (y <= 8.2e+15) {
		tmp = fma(b, -2.0, x);
	} 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 <= -3.8e+57)
		tmp = t_1;
	elseif (y <= 4.3e-246)
		tmp = fma(b, t, x);
	elseif (y <= 1.15e-49)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 8.2e+15)
		tmp = fma(b, -2.0, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+57], t$95$1, If[LessEqual[y, 4.3e-246], N[(b * t + x), $MachinePrecision], If[LessEqual[y, 1.15e-49], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+15], N[(b * -2.0 + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.7999999999999999e57 or 8.2e15 < y

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 71.3

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

   5. Simplified 71.3%

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

   if -3.7999999999999999e57 < y < 4.29999999999999992e-246

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 58.9%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, t - 2, x\right)} \]

      3. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

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

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

      5. metadata-eval 56.7

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{-2}, x\right) \]

   8. Simplified 56.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t + -2, x\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{t}, x\right) \]
   10. Step-by-step derivation

   11. Simplified 44.6%

       \[\leadsto \mathsf{fma}\left(b, \color{blue}{t}, x\right) \]

   if 4.29999999999999992e-246 < y < 1.15e-49

   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 t around inf

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

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

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

      2. --lowering--.f64 48.7

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

   5. Simplified 48.7%

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

   if 1.15e-49 < y < 8.2e15

   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

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

   5. Simplified 58.1%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, t - 2, x\right)} \]

      3. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

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

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

      5. metadata-eval 59.6

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{-2}, x\right) \]

   8. Simplified 59.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t + -2, x\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + -2 \cdot b} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{-2 \cdot b + x} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{b \cdot -2} + x \]

       3. accelerator-lowering-fma.f64 59.5

          \[\leadsto \color{blue}{\mathsf{fma}\left(b, -2, x\right)} \]

   11. Simplified 59.5%

       \[\leadsto \color{blue}{\mathsf{fma}\left(b, -2, x\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 84.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(y, -z, z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.9e+116)
   (+ x (* (- (+ y t) 2.0) b))
   (if (<= b 6.6e+35)
     (fma a (- 1.0 t) (fma z (- 1.0 y) x))
     (fma (+ y (+ t -2.0)) b (fma y (- z) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.9e+116) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (b <= 6.6e+35) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = fma((y + (t + -2.0)), b, fma(y, -z, z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.9e+116)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (b <= 6.6e+35)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = fma(Float64(y + Float64(t + -2.0)), b, fma(y, Float64(-z), z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.9e+116], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.6e+35], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b + N[(y * (-z) + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8999999999999999e116

   1. Initial program 86.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 85.4%

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

   if -1.8999999999999999e116 < b < 6.6000000000000003e35

   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. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

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

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 84.6%

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

   if 6.6000000000000003e35 < b

   1. Initial program 92.5%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate--l+ N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate--l- N/A

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

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

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

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

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

      11. sub-neg N/A

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

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

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

      13. metadata-eval N/A

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

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

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

      15. sub-neg N/A

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

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

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

      17. metadata-eval 92.5

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

   4. Applied egg-rr 92.5%

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

   5. Taylor expanded in z around inf

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

      1. distribute-rgt-out-- N/A

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

      2. *-lft-identity N/A

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

      3. unsub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

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

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

      8. mul-1-neg N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(y, \color{blue}{\mathsf{neg}\left(z\right)}, z\right)\right) \]

      11. neg-lowering-neg.f64 83.7

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

   7. Simplified 83.7%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\mathsf{fma}\left(y, -z, z\right)}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 84.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5.1 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -5.1e+110)
     t_1
     (if (<= b 1.1e+33) (fma a (- 1.0 t) (fma z (- 1.0 y) x)) 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 <= -5.1e+110) {
		tmp = t_1;
	} else if (b <= 1.1e+33) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} 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 <= -5.1e+110)
		tmp = t_1;
	elseif (b <= 1.1e+33)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return 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, -5.1e+110], t$95$1, If[LessEqual[b, 1.1e+33], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.1000000000000002e110 or 1.09999999999999997e33 < b

   1. Initial program 90.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 80.4%

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

   if -5.1000000000000002e110 < b < 1.09999999999999997e33

   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. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

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

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 84.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 26.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+58}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-163}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-101}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.85e+58)
   (* y b)
   (if (<= y -4.4e-163)
     x
     (if (<= y 2.3e-101) z (if (<= y 5.8e+15) x (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.85e+58) {
		tmp = y * b;
	} else if (y <= -4.4e-163) {
		tmp = x;
	} else if (y <= 2.3e-101) {
		tmp = z;
	} else if (y <= 5.8e+15) {
		tmp = x;
	} 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 <= (-1.85d+58)) then
        tmp = y * b
    else if (y <= (-4.4d-163)) then
        tmp = x
    else if (y <= 2.3d-101) then
        tmp = z
    else if (y <= 5.8d+15) then
        tmp = x
    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 <= -1.85e+58) {
		tmp = y * b;
	} else if (y <= -4.4e-163) {
		tmp = x;
	} else if (y <= 2.3e-101) {
		tmp = z;
	} else if (y <= 5.8e+15) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.85e+58:
		tmp = y * b
	elif y <= -4.4e-163:
		tmp = x
	elif y <= 2.3e-101:
		tmp = z
	elif y <= 5.8e+15:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.85e+58)
		tmp = Float64(y * b);
	elseif (y <= -4.4e-163)
		tmp = x;
	elseif (y <= 2.3e-101)
		tmp = z;
	elseif (y <= 5.8e+15)
		tmp = x;
	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 <= -1.85e+58)
		tmp = y * b;
	elseif (y <= -4.4e-163)
		tmp = x;
	elseif (y <= 2.3e-101)
		tmp = z;
	elseif (y <= 5.8e+15)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.85e+58], N[(y * b), $MachinePrecision], If[LessEqual[y, -4.4e-163], x, If[LessEqual[y, 2.3e-101], z, If[LessEqual[y, 5.8e+15], x, N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8500000000000001e58 or 5.8e15 < y

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 71.3

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

   5. Simplified 71.3%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot b} \]

      2. *-lowering-*.f64 40.4

         \[\leadsto \color{blue}{y \cdot b} \]

   8. Simplified 40.4%

      \[\leadsto \color{blue}{y \cdot b} \]

   if -1.8500000000000001e58 < y < -4.40000000000000022e-163 or 2.2999999999999999e-101 < y < 5.8e15

   1. Initial program 93.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 33.5%

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

   if -4.40000000000000022e-163 < y < 2.2999999999999999e-101

   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 z around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. *-lft-identity N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

         \[\leadsto \color{blue}{z - y \cdot z} \]

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

         \[\leadsto \color{blue}{z - y \cdot z} \]

      9. *-lowering-*.f64 27.4

         \[\leadsto z - \color{blue}{y \cdot z} \]

   5. Simplified 27.4%

      \[\leadsto \color{blue}{z - y \cdot z} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 27.4%

      \[\leadsto \color{blue}{z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 78.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+91}:\\ \;\;\;\;a + \left(z + \mathsf{fma}\left(y, b - z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.4e+85)
     t_1
     (if (<= t 2.5e+91) (+ a (+ z (fma y (- b z) x))) 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 <= -1.4e+85) {
		tmp = t_1;
	} else if (t <= 2.5e+91) {
		tmp = a + (z + fma(y, (b - z), x));
	} 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 <= -1.4e+85)
		tmp = t_1;
	elseif (t <= 2.5e+91)
		tmp = Float64(a + Float64(z + fma(y, Float64(b - z), x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+85], t$95$1, If[LessEqual[t, 2.5e+91], N[(a + N[(z + N[(y * N[(b - z), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e85 or 2.5000000000000001e91 < t

   1. Initial program 92.5%

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

   3. Taylor expanded in t around inf

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

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

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

      2. --lowering--.f64 78.6

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

   5. Simplified 78.6%

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

   if -1.4e85 < t < 2.5000000000000001e91

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate--l+ N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate--l- N/A

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

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

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

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

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

      11. sub-neg N/A

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

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

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

      13. metadata-eval N/A

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

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

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

      15. sub-neg N/A

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

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

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

      17. metadata-eval 98.3

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 85.9%

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

   8. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

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

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

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

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

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

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

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

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

      13. neg-sub0 N/A

          \[\leadsto a + \left(\left(x + b \cdot y\right) + z \cdot \color{blue}{\left(0 - \left(y - 1\right)\right)}\right) \]

      14. associate-+l- N/A

          \[\leadsto a + \left(\left(x + b \cdot y\right) + z \cdot \color{blue}{\left(\left(0 - y\right) + 1\right)}\right) \]

      15. neg-sub0 N/A

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

      16. distribute-rgt-in N/A

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

      17. mul-1-neg N/A

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

      18. associate-*r* N/A

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

      19. *-lft-identity N/A

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

   10. Simplified 84.0%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+91}:\\ \;\;\;\;a + \left(z + \mathsf{fma}\left(y, b - z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+31}:\\ \;\;\;\;x + \mathsf{fma}\left(z, 1 - y, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -6.4e+100)
     t_1
     (if (<= b 1.02e+31) (+ x (fma z (- 1.0 y) 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 <= -6.4e+100) {
		tmp = t_1;
	} else if (b <= 1.02e+31) {
		tmp = x + fma(z, (1.0 - y), 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 <= -6.4e+100)
		tmp = t_1;
	elseif (b <= 1.02e+31)
		tmp = Float64(x + fma(z, Float64(1.0 - y), a));
	else
		tmp = t_1;
	end
	return 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, -6.4e+100], t$95$1, If[LessEqual[b, 1.02e+31], N[(x + N[(z * N[(1.0 - y), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.3999999999999998e100 or 1.02000000000000007e31 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 79.8%

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

   if -6.3999999999999998e100 < b < 1.02000000000000007e31

   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. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

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

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 84.9%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. neg-sub0 N/A

         \[\leadsto x + \left(z \cdot \left(\color{blue}{\left(0 - y\right)} + 1\right) + a\right) \]

      6. associate-+l- N/A

         \[\leadsto x + \left(z \cdot \color{blue}{\left(0 - \left(y - 1\right)\right)} + a\right) \]

      7. neg-sub0 N/A

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

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

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

      9. remove-double-neg N/A

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

      10. mul-1-neg N/A

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

      11. distribute-neg-in N/A

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

      12. +-commutative N/A

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

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

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   8. Simplified 64.7%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(z, 1 - y, a\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 67.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+86}:\\ \;\;\;\;x + \mathsf{fma}\left(z, 1 - y, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.25e+35)
     t_1
     (if (<= t 4.1e+86) (+ x (fma z (- 1.0 y) a)) 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 <= -1.25e+35) {
		tmp = t_1;
	} else if (t <= 4.1e+86) {
		tmp = x + fma(z, (1.0 - y), a);
	} 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 <= -1.25e+35)
		tmp = t_1;
	elseif (t <= 4.1e+86)
		tmp = Float64(x + fma(z, Float64(1.0 - y), a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+35], t$95$1, If[LessEqual[t, 4.1e+86], N[(x + N[(z * N[(1.0 - y), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25000000000000005e35 or 4.0999999999999999e86 < t

   1. Initial program 92.3%

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

   3. Taylor expanded in t around inf

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

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

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

      2. --lowering--.f64 74.8

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

   5. Simplified 74.8%

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

   if -1.25000000000000005e35 < t < 4.0999999999999999e86

   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 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. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

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

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 68.6%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. neg-sub0 N/A

         \[\leadsto x + \left(z \cdot \left(\color{blue}{\left(0 - y\right)} + 1\right) + a\right) \]

      6. associate-+l- N/A

         \[\leadsto x + \left(z \cdot \color{blue}{\left(0 - \left(y - 1\right)\right)} + a\right) \]

      7. neg-sub0 N/A

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

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

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

      9. remove-double-neg N/A

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

      10. mul-1-neg N/A

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

      11. distribute-neg-in N/A

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

      12. +-commutative N/A

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

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

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   8. Simplified 65.8%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(z, 1 - y, a\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 58.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -7.2e+82) t_1 (if (<= y 1.15e+31) (fma a (- 1.0 t) x) 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 <= -7.2e+82) {
		tmp = t_1;
	} else if (y <= 1.15e+31) {
		tmp = fma(a, (1.0 - t), x);
	} 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 <= -7.2e+82)
		tmp = t_1;
	elseif (y <= 1.15e+31)
		tmp = fma(a, Float64(1.0 - t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+82], t$95$1, If[LessEqual[y, 1.15e+31], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.20000000000000028e82 or 1.15e31 < 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

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

      2. --lowering--.f64 72.9

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

   5. Simplified 72.9%

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

   if -7.20000000000000028e82 < y < 1.15e31

   1. Initial program 97.2%

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

   3. Taylor expanded in b around 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. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

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

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 69.0%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. neg-sub0 N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - t\right)} + 1\right) + x \]

      5. associate-+l- N/A

         \[\leadsto a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)} + x \]

      6. neg-sub0 N/A

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

      7. mul-1-neg N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, x\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, x\right) \]

      11. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, x\right) \]

      12. neg-sub0 N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

      15. --lowering--.f64 51.0

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

   8. Simplified 51.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 51.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -95:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5400000000000:\\ \;\;\;\;\mathsf{fma}\left(y, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -95.0) t_1 (if (<= t 5400000000000.0) (fma y b a) 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 <= -95.0) {
		tmp = t_1;
	} else if (t <= 5400000000000.0) {
		tmp = fma(y, b, a);
	} 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 <= -95.0)
		tmp = t_1;
	elseif (t <= 5400000000000.0)
		tmp = fma(y, b, a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -95.0], t$95$1, If[LessEqual[t, 5400000000000.0], N[(y * b + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -95 or 5.4e12 < 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

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

      2. --lowering--.f64 66.2

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

   5. Simplified 66.2%

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

   if -95 < t < 5.4e12

   1. Initial program 97.9%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate--l+ N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate--l- N/A

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

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

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

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

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

      11. sub-neg N/A

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

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

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

      13. metadata-eval N/A

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

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

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

      15. sub-neg N/A

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

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

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

      17. metadata-eval 97.9

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

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 86.1%

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

   8. Taylor expanded in a around inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto \mathsf{fma}\left(y, b, \color{blue}{a \cdot 1 - a \cdot t}\right) \]

      2. *-rgt-identity N/A

         \[\leadsto \mathsf{fma}\left(y, b, \color{blue}{a} - a \cdot t\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, b, \color{blue}{a - a \cdot t}\right) \]

      4. *-lowering-*.f64 38.7

         \[\leadsto \mathsf{fma}\left(y, b, a - \color{blue}{a \cdot t}\right) \]

   10. Simplified 38.7%

       \[\leadsto \mathsf{fma}\left(y, b, \color{blue}{a - a \cdot t}\right) \]

   11. Taylor expanded in t around 0

       \[\leadsto \color{blue}{a + b \cdot y} \]
   12. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{b \cdot y + a} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{y \cdot b} + a \]

       3. accelerator-lowering-fma.f64 38.3

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, b, a\right)} \]

   13. Simplified 38.3%

       \[\leadsto \color{blue}{\mathsf{fma}\left(y, b, a\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 39.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(y, b, a\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(b, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1e+55) (fma y b a) (if (<= y 3.7e+110) (fma b t x) (* y (- z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1e+55) {
		tmp = fma(y, b, a);
	} else if (y <= 3.7e+110) {
		tmp = fma(b, t, x);
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1e+55)
		tmp = fma(y, b, a);
	elseif (y <= 3.7e+110)
		tmp = fma(b, t, x);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1e+55], N[(y * b + a), $MachinePrecision], If[LessEqual[y, 3.7e+110], N[(b * t + x), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000001e55

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate--l+ N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate--l- N/A

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

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

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

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

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

      11. sub-neg N/A

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

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

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

      13. metadata-eval N/A

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

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

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

      15. sub-neg N/A

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

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

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

      17. metadata-eval 94.0

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

   4. Applied egg-rr 94.0%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 92.0%

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

   8. Taylor expanded in a around inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto \mathsf{fma}\left(y, b, \color{blue}{a \cdot 1 - a \cdot t}\right) \]

      2. *-rgt-identity N/A

         \[\leadsto \mathsf{fma}\left(y, b, \color{blue}{a} - a \cdot t\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, b, \color{blue}{a - a \cdot t}\right) \]

      4. *-lowering-*.f64 59.1

         \[\leadsto \mathsf{fma}\left(y, b, a - \color{blue}{a \cdot t}\right) \]

   10. Simplified 59.1%

       \[\leadsto \mathsf{fma}\left(y, b, \color{blue}{a - a \cdot t}\right) \]

   11. Taylor expanded in t around 0

       \[\leadsto \color{blue}{a + b \cdot y} \]
   12. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{b \cdot y + a} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{y \cdot b} + a \]

       3. accelerator-lowering-fma.f64 51.2

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, b, a\right)} \]

   13. Simplified 51.2%

       \[\leadsto \color{blue}{\mathsf{fma}\left(y, b, a\right)} \]

   if -1.00000000000000001e55 < y < 3.70000000000000012e110

   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 x around inf

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

   5. Simplified 53.6%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, t - 2, x\right)} \]

      3. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

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

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

      5. metadata-eval 49.5

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{-2}, x\right) \]

   8. Simplified 49.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t + -2, x\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{t}, x\right) \]
   10. Step-by-step derivation

   11. Simplified 39.8%

       \[\leadsto \mathsf{fma}\left(b, \color{blue}{t}, x\right) \]

   if 3.70000000000000012e110 < y

   1. Initial program 95.7%

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

   3. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 74.4

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

   5. Simplified 74.4%

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

   6. Taylor expanded in b around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. neg-lowering-neg.f64 53.5

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

   8. Simplified 53.5%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(y, b, a\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(b, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(y, b, a\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(b, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.9e+55) (fma y b a) (if (<= y 4.6e+177) (fma b t x) (fma y b a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.9e+55) {
		tmp = fma(y, b, a);
	} else if (y <= 4.6e+177) {
		tmp = fma(b, t, x);
	} else {
		tmp = fma(y, b, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.9e+55)
		tmp = fma(y, b, a);
	elseif (y <= 4.6e+177)
		tmp = fma(b, t, x);
	else
		tmp = fma(y, b, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.9e+55], N[(y * b + a), $MachinePrecision], If[LessEqual[y, 4.6e+177], N[(b * t + x), $MachinePrecision], N[(y * b + a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8999999999999999e55 or 4.5999999999999998e177 < y

   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. Step-by-step derivation

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate--l+ N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate--l- N/A

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

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

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

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

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

      11. sub-neg N/A

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

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

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

      13. metadata-eval N/A

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

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

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

      15. sub-neg N/A

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

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

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

      17. metadata-eval 95.3

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 94.2%

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

   8. Taylor expanded in a around inf

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

      1. distribute-lft-out-- N/A

         \[\leadsto \mathsf{fma}\left(y, b, \color{blue}{a \cdot 1 - a \cdot t}\right) \]

      2. *-rgt-identity N/A

         \[\leadsto \mathsf{fma}\left(y, b, \color{blue}{a} - a \cdot t\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, b, \color{blue}{a - a \cdot t}\right) \]

      4. *-lowering-*.f64 57.7

         \[\leadsto \mathsf{fma}\left(y, b, a - \color{blue}{a \cdot t}\right) \]

   10. Simplified 57.7%

       \[\leadsto \mathsf{fma}\left(y, b, \color{blue}{a - a \cdot t}\right) \]

   11. Taylor expanded in t around 0

       \[\leadsto \color{blue}{a + b \cdot y} \]
   12. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{b \cdot y + a} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{y \cdot b} + a \]

       3. accelerator-lowering-fma.f64 49.7

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, b, a\right)} \]

   13. Simplified 49.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(y, b, a\right)} \]

   if -2.8999999999999999e55 < y < 4.5999999999999998e177

   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 x around inf

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, t - 2, x\right)} \]

      3. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

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

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

      5. metadata-eval 48.5

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{-2}, x\right) \]

   8. Simplified 48.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t + -2, x\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{t}, x\right) \]
   10. Step-by-step derivation

   11. Simplified 39.4%

       \[\leadsto \mathsf{fma}\left(b, \color{blue}{t}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 37.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+160}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(b, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.5e+160) (* y b) (if (<= y 9.5e+177) (fma b t x) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.5e+160) {
		tmp = y * b;
	} else if (y <= 9.5e+177) {
		tmp = fma(b, t, x);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.5e+160)
		tmp = Float64(y * b);
	elseif (y <= 9.5e+177)
		tmp = fma(b, t, x);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.5e+160], N[(y * b), $MachinePrecision], If[LessEqual[y, 9.5e+177], N[(b * t + x), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4999999999999999e160 or 9.49999999999999996e177 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 82.5

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

   5. Simplified 82.5%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot b} \]

      2. *-lowering-*.f64 52.2

         \[\leadsto \color{blue}{y \cdot b} \]

   8. Simplified 52.2%

      \[\leadsto \color{blue}{y \cdot b} \]

   if -1.4999999999999999e160 < y < 9.49999999999999996e177

   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 x around inf

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

   5. Simplified 51.5%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, t - 2, x\right)} \]

      3. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

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

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

      5. metadata-eval 46.6

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{-2}, x\right) \]

   8. Simplified 46.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t + -2, x\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{t}, x\right) \]
   10. Step-by-step derivation

   11. Simplified 38.5%

       \[\leadsto \mathsf{fma}\left(b, \color{blue}{t}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 32.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+57}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(b, -2, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.3e+57) (* y b) (if (<= y 1.05e+16) (fma b -2.0 x) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.3e+57) {
		tmp = y * b;
	} else if (y <= 1.05e+16) {
		tmp = fma(b, -2.0, x);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.3e+57)
		tmp = Float64(y * b);
	elseif (y <= 1.05e+16)
		tmp = fma(b, -2.0, x);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.3e+57], N[(y * b), $MachinePrecision], If[LessEqual[y, 1.05e+16], N[(b * -2.0 + x), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999999e57 or 1.05e16 < y

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 71.3

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

   5. Simplified 71.3%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot b} \]

      2. *-lowering-*.f64 40.4

         \[\leadsto \color{blue}{y \cdot b} \]

   8. Simplified 40.4%

      \[\leadsto \color{blue}{y \cdot b} \]

   if -2.2999999999999999e57 < y < 1.05e16

   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 x around inf

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

   5. Simplified 52.6%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, t - 2, x\right)} \]

      3. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

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

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, x\right) \]

      5. metadata-eval 51.5

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{-2}, x\right) \]

   8. Simplified 51.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t + -2, x\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + -2 \cdot b} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{-2 \cdot b + x} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{b \cdot -2} + x \]

       3. accelerator-lowering-fma.f64 33.7

          \[\leadsto \color{blue}{\mathsf{fma}\left(b, -2, x\right)} \]

   11. Simplified 33.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(b, -2, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 26.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+31}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.3e+31) (* t b) (if (<= t 6.2e+86) x (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.3e+31) {
		tmp = t * b;
	} else if (t <= 6.2e+86) {
		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 (t <= (-6.3d+31)) then
        tmp = t * b
    else if (t <= 6.2d+86) 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 (t <= -6.3e+31) {
		tmp = t * b;
	} else if (t <= 6.2e+86) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.3e+31:
		tmp = t * b
	elif t <= 6.2e+86:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.3e+31)
		tmp = Float64(t * b);
	elseif (t <= 6.2e+86)
		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 (t <= -6.3e+31)
		tmp = t * b;
	elseif (t <= 6.2e+86)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.3e+31], N[(t * b), $MachinePrecision], If[LessEqual[t, 6.2e+86], x, N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2999999999999998e31 or 6.2000000000000004e86 < t

   1. Initial program 92.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 50.8%

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

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 40.9

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

   8. Simplified 40.9%

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

   if -6.2999999999999998e31 < t < 6.2000000000000004e86

   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 x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 22.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 20.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{+118}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.3e+118) z (if (<= z 6.7e+127) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.3e+118) {
		tmp = z;
	} else if (z <= 6.7e+127) {
		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 <= (-7.3d+118)) then
        tmp = z
    else if (z <= 6.7d+127) 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 <= -7.3e+118) {
		tmp = z;
	} else if (z <= 6.7e+127) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.3e+118:
		tmp = z
	elif z <= 6.7e+127:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.3e+118)
		tmp = z;
	elseif (z <= 6.7e+127)
		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 <= -7.3e+118)
		tmp = z;
	elseif (z <= 6.7e+127)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.3e+118], z, If[LessEqual[z, 6.7e+127], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -7.3000000000000003e118 or 6.6999999999999995e127 < z

   1. Initial program 91.9%

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

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

      2. neg-mul-1 N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. *-lft-identity N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

         \[\leadsto \color{blue}{z - y \cdot z} \]

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

         \[\leadsto \color{blue}{z - y \cdot z} \]

      9. *-lowering-*.f64 60.6

         \[\leadsto z - \color{blue}{y \cdot z} \]

   5. Simplified 60.6%

      \[\leadsto \color{blue}{z - y \cdot z} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 29.2%

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

   if -7.3000000000000003e118 < z < 6.6999999999999995e127

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 22.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 20.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+171}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.65 \cdot 10^{-19}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.3e+171) x (if (<= x 3.65e-19) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.3e+171) {
		tmp = x;
	} else if (x <= 3.65e-19) {
		tmp = a;
	} else {
		tmp = x;
	}
	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 (x <= (-3.3d+171)) then
        tmp = x
    else if (x <= 3.65d-19) then
        tmp = a
    else
        tmp = x
    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 (x <= -3.3e+171) {
		tmp = x;
	} else if (x <= 3.65e-19) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.3e+171:
		tmp = x
	elif x <= 3.65e-19:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.3e+171)
		tmp = x;
	elseif (x <= 3.65e-19)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.3e+171)
		tmp = x;
	elseif (x <= 3.65e-19)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.3e+171], x, If[LessEqual[x, 3.65e-19], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.29999999999999991e171 or 3.6499999999999998e-19 < x

   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 x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 40.6%

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

   if -3.29999999999999991e171 < x < 3.6499999999999998e-19

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. neg-mul-1 N/A

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

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

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

      7. *-commutative N/A

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

      8. unsub-neg N/A

         \[\leadsto \color{blue}{a - a \cdot t} \]

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

         \[\leadsto \color{blue}{a - a \cdot t} \]

      10. *-commutative N/A

          \[\leadsto a - \color{blue}{t \cdot a} \]

      11. *-lowering-*.f64 26.2

          \[\leadsto a - \color{blue}{t \cdot a} \]

   5. Simplified 26.2%

      \[\leadsto \color{blue}{a - t \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a} \]
   7. Step-by-step derivation

   8. Simplified 10.3%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 11.2% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

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 = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 95.7%

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

3. Taylor expanded in a around inf

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

   1. sub-neg N/A

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

   2. neg-mul-1 N/A

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

   3. distribute-rgt-in N/A

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

   4. *-lft-identity N/A

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

   5. neg-mul-1 N/A

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

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

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

   7. *-commutative N/A

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

   8. unsub-neg N/A

      \[\leadsto \color{blue}{a - a \cdot t} \]

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

      \[\leadsto \color{blue}{a - a \cdot t} \]

   10. *-commutative N/A

       \[\leadsto a - \color{blue}{t \cdot a} \]

   11. *-lowering-*.f64 23.5

       \[\leadsto a - \color{blue}{t \cdot a} \]

5. Simplified 23.5%

   \[\leadsto \color{blue}{a - t \cdot a} \]

6. Taylor expanded in t around 0

   \[\leadsto \color{blue}{a} \]
7. Step-by-step derivation

8. Simplified 8.7%

   \[\leadsto \color{blue}{a} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024198 
(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)))