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

Percentage Accurate: 94.6% → 97.4%

Time: 21.4s

Alternatives: 32

Speedup: 0.5×

• 37.2% 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: 94.6% 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: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Step-by-step derivation

   1. +-commutative 96.1%

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

   2. fma-def 98.0%

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

   3. associate--l+ 98.0%

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

   4. sub-neg 98.0%

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

   5. metadata-eval 98.0%

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

   6. sub-neg 98.0%

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

   7. associate-+l- 98.0%

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

   8. fma-neg 99.6%

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

   9. sub-neg 99.6%

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

   10. metadata-eval 99.6%

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

   11. remove-double-neg 99.6%

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

   12. sub-neg 99.6%

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

   13. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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 100.0%

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

      2. associate--l- 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. fma-udef 100.0%

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

      8. associate-+r- 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-+r+ 100.0%

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

      12. *-commutative 100.0%

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

      13. associate-+r+ 100.0%

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

      14. +-commutative 100.0%

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

      15. associate-+l+ 100.0%

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

   4. Applied egg-rr 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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 0 50.0%

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

      1. +-commutative 50.0%

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

      2. sub-neg 50.0%

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

      3. metadata-eval 50.0%

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

      4. *-commutative 50.0%

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

      5. fma-def 90.0%

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

      6. *-commutative 90.0%

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

      7. sub-neg 90.0%

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

      8. metadata-eval 90.0%

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

   5. Applied egg-rr 90.0%

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

4. Final simplification 99.6%

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

Alternative 3: 97.4% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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 0 50.0%

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

      1. +-commutative 50.0%

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

      2. sub-neg 50.0%

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

      3. metadata-eval 50.0%

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

      4. *-commutative 50.0%

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

      5. fma-def 90.0%

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

      6. *-commutative 90.0%

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

      7. sub-neg 90.0%

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

      8. metadata-eval 90.0%

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

   5. Applied egg-rr 90.0%

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

4. Final simplification 99.6%

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

Alternative 4: 97.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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 y around inf 80.5%

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

4. Final simplification 99.2%

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

Alternative 5: 56.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := a + b \cdot \left(y - 2\right)\\ t_3 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.95 \cdot 10^{+41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (+ a (* b (- y 2.0)))) (t_3 (* t (- b a))))
   (if (<= t -2.95e+41)
     t_3
     (if (<= t -1.7e-52)
       t_1
       (if (<= t -3.4e-108)
         t_2
         (if (<= t -7e-174)
           t_1
           (if (<= t -5.2e-246)
             t_2
             (if (<= t -2e-278) t_1 (if (<= t 8.6e+16) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = a + (b * (y - 2.0));
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -2.95e+41) {
		tmp = t_3;
	} else if (t <= -1.7e-52) {
		tmp = t_1;
	} else if (t <= -3.4e-108) {
		tmp = t_2;
	} else if (t <= -7e-174) {
		tmp = t_1;
	} else if (t <= -5.2e-246) {
		tmp = t_2;
	} else if (t <= -2e-278) {
		tmp = t_1;
	} else if (t <= 8.6e+16) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = a + (b * (y - 2.0d0))
    t_3 = t * (b - a)
    if (t <= (-2.95d+41)) then
        tmp = t_3
    else if (t <= (-1.7d-52)) then
        tmp = t_1
    else if (t <= (-3.4d-108)) then
        tmp = t_2
    else if (t <= (-7d-174)) then
        tmp = t_1
    else if (t <= (-5.2d-246)) then
        tmp = t_2
    else if (t <= (-2d-278)) then
        tmp = t_1
    else if (t <= 8.6d+16) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = a + (b * (y - 2.0));
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -2.95e+41) {
		tmp = t_3;
	} else if (t <= -1.7e-52) {
		tmp = t_1;
	} else if (t <= -3.4e-108) {
		tmp = t_2;
	} else if (t <= -7e-174) {
		tmp = t_1;
	} else if (t <= -5.2e-246) {
		tmp = t_2;
	} else if (t <= -2e-278) {
		tmp = t_1;
	} else if (t <= 8.6e+16) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = a + (b * (y - 2.0))
	t_3 = t * (b - a)
	tmp = 0
	if t <= -2.95e+41:
		tmp = t_3
	elif t <= -1.7e-52:
		tmp = t_1
	elif t <= -3.4e-108:
		tmp = t_2
	elif t <= -7e-174:
		tmp = t_1
	elif t <= -5.2e-246:
		tmp = t_2
	elif t <= -2e-278:
		tmp = t_1
	elif t <= 8.6e+16:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(a + Float64(b * Float64(y - 2.0)))
	t_3 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.95e+41)
		tmp = t_3;
	elseif (t <= -1.7e-52)
		tmp = t_1;
	elseif (t <= -3.4e-108)
		tmp = t_2;
	elseif (t <= -7e-174)
		tmp = t_1;
	elseif (t <= -5.2e-246)
		tmp = t_2;
	elseif (t <= -2e-278)
		tmp = t_1;
	elseif (t <= 8.6e+16)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = a + (b * (y - 2.0));
	t_3 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.95e+41)
		tmp = t_3;
	elseif (t <= -1.7e-52)
		tmp = t_1;
	elseif (t <= -3.4e-108)
		tmp = t_2;
	elseif (t <= -7e-174)
		tmp = t_1;
	elseif (t <= -5.2e-246)
		tmp = t_2;
	elseif (t <= -2e-278)
		tmp = t_1;
	elseif (t <= 8.6e+16)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.95e+41], t$95$3, If[LessEqual[t, -1.7e-52], t$95$1, If[LessEqual[t, -3.4e-108], t$95$2, If[LessEqual[t, -7e-174], t$95$1, If[LessEqual[t, -5.2e-246], t$95$2, If[LessEqual[t, -2e-278], t$95$1, If[LessEqual[t, 8.6e+16], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.95e41 or 8.6e16 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf 68.3%

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

   if -2.95e41 < t < -1.70000000000000009e-52 or -3.40000000000000002e-108 < t < -6.99999999999999975e-174 or -5.1999999999999997e-246 < t < -1.99999999999999988e-278

   1. Initial program 97.8%

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

   3. Taylor expanded in b around 0 89.6%

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

   4. Taylor expanded in y around inf 68.7%

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

      1. *-commutative 68.7%

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

   6. Simplified 68.7%

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

   if -1.70000000000000009e-52 < t < -3.40000000000000002e-108 or -6.99999999999999975e-174 < t < -5.1999999999999997e-246 or -1.99999999999999988e-278 < t < 8.6e16

   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 t around 0 96.7%

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

   4. Taylor expanded in a around 0 96.7%

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

   5. Taylor expanded in z around 0 71.6%

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

   6. Taylor expanded in x around 0 55.2%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-52}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-108}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-174}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-246}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-278}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+16}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-288}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.0215:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+91}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* a (- 1.0 t)))))
        (t_2 (* y (- b z)))
        (t_3 (+ x (+ z (* (+ t -2.0) b)))))
   (if (<= y -7.5e+93)
     t_2
     (if (<= y -5e-206)
       t_1
       (if (<= y -2.7e-288)
         t_3
         (if (<= y 3.4e-28)
           t_1
           (if (<= y 0.0215)
             t_3
             (if (<= y 1.2e+91) (+ (+ x a) (* z (- 1.0 y))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = y * (b - z);
	double t_3 = x + (z + ((t + -2.0) * b));
	double tmp;
	if (y <= -7.5e+93) {
		tmp = t_2;
	} else if (y <= -5e-206) {
		tmp = t_1;
	} else if (y <= -2.7e-288) {
		tmp = t_3;
	} else if (y <= 3.4e-28) {
		tmp = t_1;
	} else if (y <= 0.0215) {
		tmp = t_3;
	} else if (y <= 1.2e+91) {
		tmp = (x + a) + (z * (1.0 - y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z + (a * (1.0d0 - t)))
    t_2 = y * (b - z)
    t_3 = x + (z + ((t + (-2.0d0)) * b))
    if (y <= (-7.5d+93)) then
        tmp = t_2
    else if (y <= (-5d-206)) then
        tmp = t_1
    else if (y <= (-2.7d-288)) then
        tmp = t_3
    else if (y <= 3.4d-28) then
        tmp = t_1
    else if (y <= 0.0215d0) then
        tmp = t_3
    else if (y <= 1.2d+91) then
        tmp = (x + a) + (z * (1.0d0 - y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = y * (b - z);
	double t_3 = x + (z + ((t + -2.0) * b));
	double tmp;
	if (y <= -7.5e+93) {
		tmp = t_2;
	} else if (y <= -5e-206) {
		tmp = t_1;
	} else if (y <= -2.7e-288) {
		tmp = t_3;
	} else if (y <= 3.4e-28) {
		tmp = t_1;
	} else if (y <= 0.0215) {
		tmp = t_3;
	} else if (y <= 1.2e+91) {
		tmp = (x + a) + (z * (1.0 - y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a * (1.0 - t)))
	t_2 = y * (b - z)
	t_3 = x + (z + ((t + -2.0) * b))
	tmp = 0
	if y <= -7.5e+93:
		tmp = t_2
	elif y <= -5e-206:
		tmp = t_1
	elif y <= -2.7e-288:
		tmp = t_3
	elif y <= 3.4e-28:
		tmp = t_1
	elif y <= 0.0215:
		tmp = t_3
	elif y <= 1.2e+91:
		tmp = (x + a) + (z * (1.0 - y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(x + Float64(z + Float64(Float64(t + -2.0) * b)))
	tmp = 0.0
	if (y <= -7.5e+93)
		tmp = t_2;
	elseif (y <= -5e-206)
		tmp = t_1;
	elseif (y <= -2.7e-288)
		tmp = t_3;
	elseif (y <= 3.4e-28)
		tmp = t_1;
	elseif (y <= 0.0215)
		tmp = t_3;
	elseif (y <= 1.2e+91)
		tmp = Float64(Float64(x + a) + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + (a * (1.0 - t)));
	t_2 = y * (b - z);
	t_3 = x + (z + ((t + -2.0) * b));
	tmp = 0.0;
	if (y <= -7.5e+93)
		tmp = t_2;
	elseif (y <= -5e-206)
		tmp = t_1;
	elseif (y <= -2.7e-288)
		tmp = t_3;
	elseif (y <= 3.4e-28)
		tmp = t_1;
	elseif (y <= 0.0215)
		tmp = t_3;
	elseif (y <= 1.2e+91)
		tmp = (x + a) + (z * (1.0 - y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z + N[(N[(t + -2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+93], t$95$2, If[LessEqual[y, -5e-206], t$95$1, If[LessEqual[y, -2.7e-288], t$95$3, If[LessEqual[y, 3.4e-28], t$95$1, If[LessEqual[y, 0.0215], t$95$3, If[LessEqual[y, 1.2e+91], N[(N[(x + a), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.5000000000000002e93 or 1.19999999999999991e91 < y

   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 y around inf 81.8%

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

   if -7.5000000000000002e93 < y < -5e-206 or -2.7000000000000001e-288 < y < 3.4000000000000001e-28

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0 76.6%

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

   4. Taylor expanded in y around 0 73.2%

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

      1. +-commutative 73.2%

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

      2. sub-neg 73.2%

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

      3. metadata-eval 73.2%

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

      4. *-commutative 73.2%

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

      5. mul-1-neg 73.2%

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

      6. unsub-neg 73.2%

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

      7. *-commutative 73.2%

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

   6. Simplified 73.2%

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

   if -5e-206 < y < -2.7000000000000001e-288 or 3.4000000000000001e-28 < y < 0.021499999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 88.4%

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

   4. Taylor expanded in y around 0 85.5%

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

      1. associate--l+ 85.5%

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

      2. sub-neg 85.5%

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

      3. metadata-eval 85.5%

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

      4. neg-mul-1 85.5%

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

   6. Simplified 85.5%

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

   if 0.021499999999999998 < y < 1.19999999999999991e91

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 90.6%

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

   4. Taylor expanded in a around 0 90.6%

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

   5. Taylor expanded in b around 0 79.2%

      \[\leadsto \color{blue}{\left(a + x\right) - z \cdot \left(y - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-206}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-288}:\\ \;\;\;\;x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-28}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 0.0215:\\ \;\;\;\;x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+91}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + t_2\\ \mathbf{if}\;b \leq -1.12 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-50}:\\ \;\;\;\;t_2 - y \cdot z\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y)))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (+ x t_2)))
   (if (<= b -1.12e+139)
     t_3
     (if (<= b -1.75e+21)
       t_1
       (if (<= b -4.1e-50) (- t_2 (* y z)) (if (<= b 2.35e+79) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + t_2;
	double tmp;
	if (b <= -1.12e+139) {
		tmp = t_3;
	} else if (b <= -1.75e+21) {
		tmp = t_1;
	} else if (b <= -4.1e-50) {
		tmp = t_2 - (y * z);
	} else if (b <= 2.35e+79) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = x + t_2
    if (b <= (-1.12d+139)) then
        tmp = t_3
    else if (b <= (-1.75d+21)) then
        tmp = t_1
    else if (b <= (-4.1d-50)) then
        tmp = t_2 - (y * z)
    else if (b <= 2.35d+79) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + t_2;
	double tmp;
	if (b <= -1.12e+139) {
		tmp = t_3;
	} else if (b <= -1.75e+21) {
		tmp = t_1;
	} else if (b <= -4.1e-50) {
		tmp = t_2 - (y * z);
	} else if (b <= 2.35e+79) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	t_2 = b * ((y + t) - 2.0)
	t_3 = x + t_2
	tmp = 0
	if b <= -1.12e+139:
		tmp = t_3
	elif b <= -1.75e+21:
		tmp = t_1
	elif b <= -4.1e-50:
		tmp = t_2 - (y * z)
	elif b <= 2.35e+79:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(x + t_2)
	tmp = 0.0
	if (b <= -1.12e+139)
		tmp = t_3;
	elseif (b <= -1.75e+21)
		tmp = t_1;
	elseif (b <= -4.1e-50)
		tmp = Float64(t_2 - Float64(y * z));
	elseif (b <= 2.35e+79)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	t_2 = b * ((y + t) - 2.0);
	t_3 = x + t_2;
	tmp = 0.0;
	if (b <= -1.12e+139)
		tmp = t_3;
	elseif (b <= -1.75e+21)
		tmp = t_1;
	elseif (b <= -4.1e-50)
		tmp = t_2 - (y * z);
	elseif (b <= 2.35e+79)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + t$95$2), $MachinePrecision]}, If[LessEqual[b, -1.12e+139], t$95$3, If[LessEqual[b, -1.75e+21], t$95$1, If[LessEqual[b, -4.1e-50], N[(t$95$2 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.35e+79], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.12e139 or 2.35000000000000011e79 < b

   1. Initial program 91.1%

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

   3. Taylor expanded in a around 0 85.4%

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

   4. Taylor expanded in z around 0 81.7%

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

   if -1.12e139 < b < -1.75e21 or -4.09999999999999985e-50 < b < 2.35000000000000011e79

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0 86.6%

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

   if -1.75e21 < b < -4.09999999999999985e-50

   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 y around inf 85.1%

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

      1. mul-1-neg 85.1%

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

      2. *-commutative 85.1%

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

      3. distribute-rgt-neg-in 85.1%

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

   5. Simplified 85.1%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{+139}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+21}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-50}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+79}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := \left(a + \left(x + b \cdot \left(y - 2\right)\right)\right) + t_2\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+53}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+131}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+159}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_1 + t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (* z (- 1.0 y)))
        (t_3 (+ (+ a (+ x (* b (- y 2.0)))) t_2)))
   (if (<= z -2.3e+26)
     t_3
     (if (<= z 1.85e+53)
       (+ (+ x (* b (- (+ y t) 2.0))) t_1)
       (if (<= z 8e+131)
         t_3
         (if (<= z 2.05e+159) (* t (- b a)) (+ x (+ t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double t_3 = (a + (x + (b * (y - 2.0)))) + t_2;
	double tmp;
	if (z <= -2.3e+26) {
		tmp = t_3;
	} else if (z <= 1.85e+53) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else if (z <= 8e+131) {
		tmp = t_3;
	} else if (z <= 2.05e+159) {
		tmp = t * (b - a);
	} else {
		tmp = x + (t_1 + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = z * (1.0d0 - y)
    t_3 = (a + (x + (b * (y - 2.0d0)))) + t_2
    if (z <= (-2.3d+26)) then
        tmp = t_3
    else if (z <= 1.85d+53) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else if (z <= 8d+131) then
        tmp = t_3
    else if (z <= 2.05d+159) then
        tmp = t * (b - a)
    else
        tmp = x + (t_1 + t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double t_3 = (a + (x + (b * (y - 2.0)))) + t_2;
	double tmp;
	if (z <= -2.3e+26) {
		tmp = t_3;
	} else if (z <= 1.85e+53) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else if (z <= 8e+131) {
		tmp = t_3;
	} else if (z <= 2.05e+159) {
		tmp = t * (b - a);
	} else {
		tmp = x + (t_1 + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = z * (1.0 - y)
	t_3 = (a + (x + (b * (y - 2.0)))) + t_2
	tmp = 0
	if z <= -2.3e+26:
		tmp = t_3
	elif z <= 1.85e+53:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	elif z <= 8e+131:
		tmp = t_3
	elif z <= 2.05e+159:
		tmp = t * (b - a)
	else:
		tmp = x + (t_1 + t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(z * Float64(1.0 - y))
	t_3 = Float64(Float64(a + Float64(x + Float64(b * Float64(y - 2.0)))) + t_2)
	tmp = 0.0
	if (z <= -2.3e+26)
		tmp = t_3;
	elseif (z <= 1.85e+53)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	elseif (z <= 8e+131)
		tmp = t_3;
	elseif (z <= 2.05e+159)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + Float64(t_1 + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = z * (1.0 - y);
	t_3 = (a + (x + (b * (y - 2.0)))) + t_2;
	tmp = 0.0;
	if (z <= -2.3e+26)
		tmp = t_3;
	elseif (z <= 1.85e+53)
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	elseif (z <= 8e+131)
		tmp = t_3;
	elseif (z <= 2.05e+159)
		tmp = t * (b - a);
	else
		tmp = x + (t_1 + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[z, -2.3e+26], t$95$3, If[LessEqual[z, 1.85e+53], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 8e+131], t$95$3, If[LessEqual[z, 2.05e+159], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3000000000000001e26 or 1.85e53 < z < 7.9999999999999993e131

   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 t around 0 87.9%

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

   4. Taylor expanded in a around 0 87.9%

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

   if -2.3000000000000001e26 < z < 1.85e53

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 96.2%

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

   if 7.9999999999999993e131 < z < 2.05000000000000007e159

   1. Initial program 42.6%

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

   3. Taylor expanded in t around inf 85.8%

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

   if 2.05000000000000007e159 < z

   1. Initial program 93.5%

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

   3. Taylor expanded in b around 0 93.1%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+26}:\\ \;\;\;\;\left(a + \left(x + b \cdot \left(y - 2\right)\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+53}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+131}:\\ \;\;\;\;\left(a + \left(x + b \cdot \left(y - 2\right)\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+159}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 26.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+95}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-238}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-245}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-153}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 44000000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+86}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.2e+95)
   (* y b)
   (if (<= y -1.6e-147)
     x
     (if (<= y -5.2e-238)
       z
       (if (<= y 1.05e-245)
         (* t b)
         (if (<= y 3.9e-153)
           z
           (if (<= y 7.4e-90)
             x
             (if (<= y 44000000.0)
               (* t b)
               (if (<= y 4.9e+86) a (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.2e+95) {
		tmp = y * b;
	} else if (y <= -1.6e-147) {
		tmp = x;
	} else if (y <= -5.2e-238) {
		tmp = z;
	} else if (y <= 1.05e-245) {
		tmp = t * b;
	} else if (y <= 3.9e-153) {
		tmp = z;
	} else if (y <= 7.4e-90) {
		tmp = x;
	} else if (y <= 44000000.0) {
		tmp = t * b;
	} else if (y <= 4.9e+86) {
		tmp = a;
	} 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 <= (-9.2d+95)) then
        tmp = y * b
    else if (y <= (-1.6d-147)) then
        tmp = x
    else if (y <= (-5.2d-238)) then
        tmp = z
    else if (y <= 1.05d-245) then
        tmp = t * b
    else if (y <= 3.9d-153) then
        tmp = z
    else if (y <= 7.4d-90) then
        tmp = x
    else if (y <= 44000000.0d0) then
        tmp = t * b
    else if (y <= 4.9d+86) then
        tmp = a
    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 <= -9.2e+95) {
		tmp = y * b;
	} else if (y <= -1.6e-147) {
		tmp = x;
	} else if (y <= -5.2e-238) {
		tmp = z;
	} else if (y <= 1.05e-245) {
		tmp = t * b;
	} else if (y <= 3.9e-153) {
		tmp = z;
	} else if (y <= 7.4e-90) {
		tmp = x;
	} else if (y <= 44000000.0) {
		tmp = t * b;
	} else if (y <= 4.9e+86) {
		tmp = a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.2e+95:
		tmp = y * b
	elif y <= -1.6e-147:
		tmp = x
	elif y <= -5.2e-238:
		tmp = z
	elif y <= 1.05e-245:
		tmp = t * b
	elif y <= 3.9e-153:
		tmp = z
	elif y <= 7.4e-90:
		tmp = x
	elif y <= 44000000.0:
		tmp = t * b
	elif y <= 4.9e+86:
		tmp = a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.2e+95)
		tmp = Float64(y * b);
	elseif (y <= -1.6e-147)
		tmp = x;
	elseif (y <= -5.2e-238)
		tmp = z;
	elseif (y <= 1.05e-245)
		tmp = Float64(t * b);
	elseif (y <= 3.9e-153)
		tmp = z;
	elseif (y <= 7.4e-90)
		tmp = x;
	elseif (y <= 44000000.0)
		tmp = Float64(t * b);
	elseif (y <= 4.9e+86)
		tmp = a;
	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 <= -9.2e+95)
		tmp = y * b;
	elseif (y <= -1.6e-147)
		tmp = x;
	elseif (y <= -5.2e-238)
		tmp = z;
	elseif (y <= 1.05e-245)
		tmp = t * b;
	elseif (y <= 3.9e-153)
		tmp = z;
	elseif (y <= 7.4e-90)
		tmp = x;
	elseif (y <= 44000000.0)
		tmp = t * b;
	elseif (y <= 4.9e+86)
		tmp = a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.2e+95], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.6e-147], x, If[LessEqual[y, -5.2e-238], z, If[LessEqual[y, 1.05e-245], N[(t * b), $MachinePrecision], If[LessEqual[y, 3.9e-153], z, If[LessEqual[y, 7.4e-90], x, If[LessEqual[y, 44000000.0], N[(t * b), $MachinePrecision], If[LessEqual[y, 4.9e+86], a, N[(y * b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.19999999999999989e95 or 4.8999999999999999e86 < y

   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 b around inf 43.2%

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

   4. Taylor expanded in y around inf 43.2%

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

   if -9.19999999999999989e95 < y < -1.5999999999999999e-147 or 3.9000000000000002e-153 < y < 7.40000000000000035e-90

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 32.6%

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

   if -1.5999999999999999e-147 < y < -5.2000000000000002e-238 or 1.05000000000000005e-245 < y < 3.9000000000000002e-153

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 34.4%

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

   4. Taylor expanded in y around 0 34.4%

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

   if -5.2000000000000002e-238 < y < 1.05000000000000005e-245 or 7.40000000000000035e-90 < y < 4.4e7

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 72.5%

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

   4. Taylor expanded in t around inf 32.6%

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

   if 4.4e7 < y < 4.8999999999999999e86

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 90.1%

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

   4. Taylor expanded in a around inf 31.5%

      \[\leadsto \color{blue}{a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+95}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-238}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-245}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-153}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 44000000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+86}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -1.52 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-112}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-93}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))) (t_2 (* a (- 1.0 t))))
   (if (<= a -2.2e+131)
     t_2
     (if (<= a -4.8e+54)
       (* y (- z))
       (if (<= a -1.52e-33)
         (* b (- y 2.0))
         (if (<= a -6.6e-112)
           (+ x a)
           (if (<= a 3.7e-171)
             t_1
             (if (<= a 8.5e-93) (+ x a) (if (<= a 2.1e-13) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -2.2e+131) {
		tmp = t_2;
	} else if (a <= -4.8e+54) {
		tmp = y * -z;
	} else if (a <= -1.52e-33) {
		tmp = b * (y - 2.0);
	} else if (a <= -6.6e-112) {
		tmp = x + a;
	} else if (a <= 3.7e-171) {
		tmp = t_1;
	} else if (a <= 8.5e-93) {
		tmp = x + a;
	} else if (a <= 2.1e-13) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    t_2 = a * (1.0d0 - t)
    if (a <= (-2.2d+131)) then
        tmp = t_2
    else if (a <= (-4.8d+54)) then
        tmp = y * -z
    else if (a <= (-1.52d-33)) then
        tmp = b * (y - 2.0d0)
    else if (a <= (-6.6d-112)) then
        tmp = x + a
    else if (a <= 3.7d-171) then
        tmp = t_1
    else if (a <= 8.5d-93) then
        tmp = x + a
    else if (a <= 2.1d-13) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -2.2e+131) {
		tmp = t_2;
	} else if (a <= -4.8e+54) {
		tmp = y * -z;
	} else if (a <= -1.52e-33) {
		tmp = b * (y - 2.0);
	} else if (a <= -6.6e-112) {
		tmp = x + a;
	} else if (a <= 3.7e-171) {
		tmp = t_1;
	} else if (a <= 8.5e-93) {
		tmp = x + a;
	} else if (a <= 2.1e-13) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -2.2e+131:
		tmp = t_2
	elif a <= -4.8e+54:
		tmp = y * -z
	elif a <= -1.52e-33:
		tmp = b * (y - 2.0)
	elif a <= -6.6e-112:
		tmp = x + a
	elif a <= 3.7e-171:
		tmp = t_1
	elif a <= 8.5e-93:
		tmp = x + a
	elif a <= 2.1e-13:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -2.2e+131)
		tmp = t_2;
	elseif (a <= -4.8e+54)
		tmp = Float64(y * Float64(-z));
	elseif (a <= -1.52e-33)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (a <= -6.6e-112)
		tmp = Float64(x + a);
	elseif (a <= 3.7e-171)
		tmp = t_1;
	elseif (a <= 8.5e-93)
		tmp = Float64(x + a);
	elseif (a <= 2.1e-13)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -2.2e+131)
		tmp = t_2;
	elseif (a <= -4.8e+54)
		tmp = y * -z;
	elseif (a <= -1.52e-33)
		tmp = b * (y - 2.0);
	elseif (a <= -6.6e-112)
		tmp = x + a;
	elseif (a <= 3.7e-171)
		tmp = t_1;
	elseif (a <= 8.5e-93)
		tmp = x + a;
	elseif (a <= 2.1e-13)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e+131], t$95$2, If[LessEqual[a, -4.8e+54], N[(y * (-z)), $MachinePrecision], If[LessEqual[a, -1.52e-33], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.6e-112], N[(x + a), $MachinePrecision], If[LessEqual[a, 3.7e-171], t$95$1, If[LessEqual[a, 8.5e-93], N[(x + a), $MachinePrecision], If[LessEqual[a, 2.1e-13], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.1999999999999999e131 or 2.09999999999999989e-13 < a

   1. Initial program 94.2%

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

   3. Taylor expanded in a around inf 63.5%

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

   if -2.1999999999999999e131 < a < -4.79999999999999997e54

   1. Initial program 90.9%

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

   3. Taylor expanded in z around inf 73.2%

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

   4. Taylor expanded in y around inf 57.0%

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

      1. mul-1-neg 57.0%

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

      2. *-commutative 57.0%

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

      3. distribute-rgt-neg-in 57.0%

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

   6. Simplified 57.0%

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

   if -4.79999999999999997e54 < a < -1.52e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 42.9%

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

   4. Taylor expanded in t around 0 42.0%

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

   if -1.52e-33 < a < -6.6000000000000002e-112 or 3.70000000000000012e-171 < a < 8.5000000000000007e-93

   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 t around 0 88.9%

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

   4. Taylor expanded in a around 0 88.9%

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

   5. Taylor expanded in z around 0 57.2%

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

   6. Taylor expanded in b around 0 43.1%

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

   if -6.6000000000000002e-112 < a < 3.70000000000000012e-171 or 8.5000000000000007e-93 < a < 2.09999999999999989e-13

   1. Initial program 97.7%

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

   3. Taylor expanded in b around inf 49.9%

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

   4. Taylor expanded in y around 0 33.9%

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+131}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -1.52 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-112}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-171}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-93}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := b \cdot \left(y - 2\right)\\ t_4 := a + t_3\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-108}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-203}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+37}:\\ \;\;\;\;x + t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z)))
        (t_2 (* t (- b a)))
        (t_3 (* b (- y 2.0)))
        (t_4 (+ a t_3)))
   (if (<= t -1.05e+41)
     t_2
     (if (<= t -4e-52)
       t_1
       (if (<= t -2.8e-108)
         t_4
         (if (<= t -4.5e-174)
           t_1
           (if (<= t 8.5e-203) t_4 (if (<= t 4.2e+37) (+ x t_3) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = t * (b - a);
	double t_3 = b * (y - 2.0);
	double t_4 = a + t_3;
	double tmp;
	if (t <= -1.05e+41) {
		tmp = t_2;
	} else if (t <= -4e-52) {
		tmp = t_1;
	} else if (t <= -2.8e-108) {
		tmp = t_4;
	} else if (t <= -4.5e-174) {
		tmp = t_1;
	} else if (t <= 8.5e-203) {
		tmp = t_4;
	} else if (t <= 4.2e+37) {
		tmp = x + t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = t * (b - a)
    t_3 = b * (y - 2.0d0)
    t_4 = a + t_3
    if (t <= (-1.05d+41)) then
        tmp = t_2
    else if (t <= (-4d-52)) then
        tmp = t_1
    else if (t <= (-2.8d-108)) then
        tmp = t_4
    else if (t <= (-4.5d-174)) then
        tmp = t_1
    else if (t <= 8.5d-203) then
        tmp = t_4
    else if (t <= 4.2d+37) then
        tmp = x + t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = t * (b - a);
	double t_3 = b * (y - 2.0);
	double t_4 = a + t_3;
	double tmp;
	if (t <= -1.05e+41) {
		tmp = t_2;
	} else if (t <= -4e-52) {
		tmp = t_1;
	} else if (t <= -2.8e-108) {
		tmp = t_4;
	} else if (t <= -4.5e-174) {
		tmp = t_1;
	} else if (t <= 8.5e-203) {
		tmp = t_4;
	} else if (t <= 4.2e+37) {
		tmp = x + t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = t * (b - a)
	t_3 = b * (y - 2.0)
	t_4 = a + t_3
	tmp = 0
	if t <= -1.05e+41:
		tmp = t_2
	elif t <= -4e-52:
		tmp = t_1
	elif t <= -2.8e-108:
		tmp = t_4
	elif t <= -4.5e-174:
		tmp = t_1
	elif t <= 8.5e-203:
		tmp = t_4
	elif t <= 4.2e+37:
		tmp = x + t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(t * Float64(b - a))
	t_3 = Float64(b * Float64(y - 2.0))
	t_4 = Float64(a + t_3)
	tmp = 0.0
	if (t <= -1.05e+41)
		tmp = t_2;
	elseif (t <= -4e-52)
		tmp = t_1;
	elseif (t <= -2.8e-108)
		tmp = t_4;
	elseif (t <= -4.5e-174)
		tmp = t_1;
	elseif (t <= 8.5e-203)
		tmp = t_4;
	elseif (t <= 4.2e+37)
		tmp = Float64(x + t_3);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = t * (b - a);
	t_3 = b * (y - 2.0);
	t_4 = a + t_3;
	tmp = 0.0;
	if (t <= -1.05e+41)
		tmp = t_2;
	elseif (t <= -4e-52)
		tmp = t_1;
	elseif (t <= -2.8e-108)
		tmp = t_4;
	elseif (t <= -4.5e-174)
		tmp = t_1;
	elseif (t <= 8.5e-203)
		tmp = t_4;
	elseif (t <= 4.2e+37)
		tmp = x + t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a + t$95$3), $MachinePrecision]}, If[LessEqual[t, -1.05e+41], t$95$2, If[LessEqual[t, -4e-52], t$95$1, If[LessEqual[t, -2.8e-108], t$95$4, If[LessEqual[t, -4.5e-174], t$95$1, If[LessEqual[t, 8.5e-203], t$95$4, If[LessEqual[t, 4.2e+37], N[(x + t$95$3), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.05e41 or 4.2000000000000002e37 < t

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf 70.4%

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

   if -1.05e41 < t < -4e-52 or -2.8e-108 < t < -4.49999999999999964e-174

   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 88.4%

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

   4. Taylor expanded in y around inf 64.9%

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

      1. *-commutative 64.9%

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

   6. Simplified 64.9%

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

   if -4e-52 < t < -2.8e-108 or -4.49999999999999964e-174 < t < 8.50000000000000031e-203

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0 98.5%

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

   4. Taylor expanded in a around 0 98.5%

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

   5. Taylor expanded in z around 0 69.2%

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

   6. Taylor expanded in x around 0 57.6%

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

   if 8.50000000000000031e-203 < t < 4.2000000000000002e37

   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 t around 0 91.6%

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

   4. Taylor expanded in a around 0 91.6%

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

   5. Taylor expanded in z around 0 67.5%

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

   6. Taylor expanded in a around 0 55.3%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-52}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-108}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-174}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-203}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+37}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := x + \left(z + a\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-236}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (* y (- b z))) (t_3 (+ x (+ z a))))
   (if (<= y -3.5e+93)
     t_2
     (if (<= y -7.8e-113)
       t_1
       (if (<= y -1.45e-236)
         t_3
         (if (<= y 1.02e-231)
           t_1
           (if (<= y 2.9e-152) t_3 (if (<= y 5e+85) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = y * (b - z);
	double t_3 = x + (z + a);
	double tmp;
	if (y <= -3.5e+93) {
		tmp = t_2;
	} else if (y <= -7.8e-113) {
		tmp = t_1;
	} else if (y <= -1.45e-236) {
		tmp = t_3;
	} else if (y <= 1.02e-231) {
		tmp = t_1;
	} else if (y <= 2.9e-152) {
		tmp = t_3;
	} else if (y <= 5e+85) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = y * (b - z)
    t_3 = x + (z + a)
    if (y <= (-3.5d+93)) then
        tmp = t_2
    else if (y <= (-7.8d-113)) then
        tmp = t_1
    else if (y <= (-1.45d-236)) then
        tmp = t_3
    else if (y <= 1.02d-231) then
        tmp = t_1
    else if (y <= 2.9d-152) then
        tmp = t_3
    else if (y <= 5d+85) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = y * (b - z);
	double t_3 = x + (z + a);
	double tmp;
	if (y <= -3.5e+93) {
		tmp = t_2;
	} else if (y <= -7.8e-113) {
		tmp = t_1;
	} else if (y <= -1.45e-236) {
		tmp = t_3;
	} else if (y <= 1.02e-231) {
		tmp = t_1;
	} else if (y <= 2.9e-152) {
		tmp = t_3;
	} else if (y <= 5e+85) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = y * (b - z)
	t_3 = x + (z + a)
	tmp = 0
	if y <= -3.5e+93:
		tmp = t_2
	elif y <= -7.8e-113:
		tmp = t_1
	elif y <= -1.45e-236:
		tmp = t_3
	elif y <= 1.02e-231:
		tmp = t_1
	elif y <= 2.9e-152:
		tmp = t_3
	elif y <= 5e+85:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(x + Float64(z + a))
	tmp = 0.0
	if (y <= -3.5e+93)
		tmp = t_2;
	elseif (y <= -7.8e-113)
		tmp = t_1;
	elseif (y <= -1.45e-236)
		tmp = t_3;
	elseif (y <= 1.02e-231)
		tmp = t_1;
	elseif (y <= 2.9e-152)
		tmp = t_3;
	elseif (y <= 5e+85)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = y * (b - z);
	t_3 = x + (z + a);
	tmp = 0.0;
	if (y <= -3.5e+93)
		tmp = t_2;
	elseif (y <= -7.8e-113)
		tmp = t_1;
	elseif (y <= -1.45e-236)
		tmp = t_3;
	elseif (y <= 1.02e-231)
		tmp = t_1;
	elseif (y <= 2.9e-152)
		tmp = t_3;
	elseif (y <= 5e+85)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+93], t$95$2, If[LessEqual[y, -7.8e-113], t$95$1, If[LessEqual[y, -1.45e-236], t$95$3, If[LessEqual[y, 1.02e-231], t$95$1, If[LessEqual[y, 2.9e-152], t$95$3, If[LessEqual[y, 5e+85], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.49999999999999998e93 or 5.0000000000000001e85 < y

   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 y around inf 81.8%

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

   if -3.49999999999999998e93 < y < -7.7999999999999997e-113 or -1.45e-236 < y < 1.02000000000000006e-231 or 2.9000000000000001e-152 < y < 5.0000000000000001e85

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0 71.3%

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

   4. Taylor expanded in a around inf 55.6%

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

   if -7.7999999999999997e-113 < y < -1.45e-236 or 1.02000000000000006e-231 < y < 2.9000000000000001e-152

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 77.2%

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

   4. Taylor expanded in t around 0 66.8%

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

   5. Taylor expanded in y around 0 66.8%

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

      1. mul-1-neg 66.8%

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

   7. Simplified 66.8%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-113}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-236}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-231}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-152}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+85}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-50}:\\ \;\;\;\;\left(a + b \cdot \left(y - 2\right)\right) + t_2\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+76}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))) (t_2 (* z (- 1.0 y))))
   (if (<= b -2.6e+73)
     t_1
     (if (<= b -4.1e-50)
       (+ (+ a (* b (- y 2.0))) t_2)
       (if (<= b 7.5e+76) (+ x (+ (* a (- 1.0 t)) t_2)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double t_2 = z * (1.0 - y);
	double tmp;
	if (b <= -2.6e+73) {
		tmp = t_1;
	} else if (b <= -4.1e-50) {
		tmp = (a + (b * (y - 2.0))) + t_2;
	} else if (b <= 7.5e+76) {
		tmp = x + ((a * (1.0 - t)) + t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    t_2 = z * (1.0d0 - y)
    if (b <= (-2.6d+73)) then
        tmp = t_1
    else if (b <= (-4.1d-50)) then
        tmp = (a + (b * (y - 2.0d0))) + t_2
    else if (b <= 7.5d+76) then
        tmp = x + ((a * (1.0d0 - t)) + t_2)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double t_2 = z * (1.0 - y);
	double tmp;
	if (b <= -2.6e+73) {
		tmp = t_1;
	} else if (b <= -4.1e-50) {
		tmp = (a + (b * (y - 2.0))) + t_2;
	} else if (b <= 7.5e+76) {
		tmp = x + ((a * (1.0 - t)) + t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	t_2 = z * (1.0 - y)
	tmp = 0
	if b <= -2.6e+73:
		tmp = t_1
	elif b <= -4.1e-50:
		tmp = (a + (b * (y - 2.0))) + t_2
	elif b <= 7.5e+76:
		tmp = x + ((a * (1.0 - t)) + t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_2 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -2.6e+73)
		tmp = t_1;
	elseif (b <= -4.1e-50)
		tmp = Float64(Float64(a + Float64(b * Float64(y - 2.0))) + t_2);
	elseif (b <= 7.5e+76)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + t_2));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	t_2 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -2.6e+73)
		tmp = t_1;
	elseif (b <= -4.1e-50)
		tmp = (a + (b * (y - 2.0))) + t_2;
	elseif (b <= 7.5e+76)
		tmp = x + ((a * (1.0 - t)) + t_2);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.6e+73], t$95$1, If[LessEqual[b, -4.1e-50], N[(N[(a + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[b, 7.5e+76], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6000000000000001e73 or 7.4999999999999995e76 < b

   1. Initial program 92.0%

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

   3. Taylor expanded in a around 0 85.3%

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

   4. Taylor expanded in z around 0 79.8%

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

   if -2.6000000000000001e73 < b < -4.09999999999999985e-50

   1. Initial program 96.4%

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

   3. Taylor expanded in t around 0 89.6%

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

   4. Taylor expanded in a around 0 89.6%

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

   5. Taylor expanded in x around 0 85.9%

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

   if -4.09999999999999985e-50 < b < 7.4999999999999995e76

   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 b around 0 88.2%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+73}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-50}:\\ \;\;\;\;\left(a + b \cdot \left(y - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+76}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 83.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 320000000000:\\ \;\;\;\;\left(a + \left(x + b \cdot \left(y - 2\right)\right)\right) + t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+169}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* t (- b a))))
   (if (<= t -4.3e+42)
     t_2
     (if (<= t 320000000000.0)
       (+ (+ a (+ x (* b (- y 2.0)))) t_1)
       (if (<= t 1.7e+169) (+ x (+ (* a (- 1.0 t)) t_1)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.3e+42) {
		tmp = t_2;
	} else if (t <= 320000000000.0) {
		tmp = (a + (x + (b * (y - 2.0)))) + t_1;
	} else if (t <= 1.7e+169) {
		tmp = x + ((a * (1.0 - t)) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = t * (b - a)
    if (t <= (-4.3d+42)) then
        tmp = t_2
    else if (t <= 320000000000.0d0) then
        tmp = (a + (x + (b * (y - 2.0d0)))) + t_1
    else if (t <= 1.7d+169) then
        tmp = x + ((a * (1.0d0 - t)) + t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.3e+42) {
		tmp = t_2;
	} else if (t <= 320000000000.0) {
		tmp = (a + (x + (b * (y - 2.0)))) + t_1;
	} else if (t <= 1.7e+169) {
		tmp = x + ((a * (1.0 - t)) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -4.3e+42:
		tmp = t_2
	elif t <= 320000000000.0:
		tmp = (a + (x + (b * (y - 2.0)))) + t_1
	elif t <= 1.7e+169:
		tmp = x + ((a * (1.0 - t)) + t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.3e+42)
		tmp = t_2;
	elseif (t <= 320000000000.0)
		tmp = Float64(Float64(a + Float64(x + Float64(b * Float64(y - 2.0)))) + t_1);
	elseif (t <= 1.7e+169)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.3e+42)
		tmp = t_2;
	elseif (t <= 320000000000.0)
		tmp = (a + (x + (b * (y - 2.0)))) + t_1;
	elseif (t <= 1.7e+169)
		tmp = x + ((a * (1.0 - t)) + t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e+42], t$95$2, If[LessEqual[t, 320000000000.0], N[(N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 1.7e+169], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2999999999999998e42 or 1.70000000000000014e169 < t

   1. Initial program 94.3%

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

   3. Taylor expanded in t around inf 76.5%

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

   if -4.2999999999999998e42 < t < 3.2e11

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0 96.0%

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

   4. Taylor expanded in a around 0 96.0%

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

   if 3.2e11 < t < 1.70000000000000014e169

   1. Initial program 93.7%

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

   3. Taylor expanded in b around 0 81.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 320000000000:\\ \;\;\;\;\left(a + \left(x + b \cdot \left(y - 2\right)\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+169}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 83.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{+134}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-17}:\\ \;\;\;\;t_2 + t_3\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_1 + t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (* z (- 1.0 y))))
   (if (<= a -8.6e+134)
     (+ t_2 t_1)
     (if (<= a 3.5e-17) (+ t_2 t_3) (+ x (+ t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (a <= -8.6e+134) {
		tmp = t_2 + t_1;
	} else if (a <= 3.5e-17) {
		tmp = t_2 + t_3;
	} else {
		tmp = x + (t_1 + t_3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = z * (1.0d0 - y)
    if (a <= (-8.6d+134)) then
        tmp = t_2 + t_1
    else if (a <= 3.5d-17) then
        tmp = t_2 + t_3
    else
        tmp = x + (t_1 + t_3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (a <= -8.6e+134) {
		tmp = t_2 + t_1;
	} else if (a <= 3.5e-17) {
		tmp = t_2 + t_3;
	} else {
		tmp = x + (t_1 + t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = z * (1.0 - y)
	tmp = 0
	if a <= -8.6e+134:
		tmp = t_2 + t_1
	elif a <= 3.5e-17:
		tmp = t_2 + t_3
	else:
		tmp = x + (t_1 + t_3)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (a <= -8.6e+134)
		tmp = Float64(t_2 + t_1);
	elseif (a <= 3.5e-17)
		tmp = Float64(t_2 + t_3);
	else
		tmp = Float64(x + Float64(t_1 + t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (a <= -8.6e+134)
		tmp = t_2 + t_1;
	elseif (a <= 3.5e-17)
		tmp = t_2 + t_3;
	else
		tmp = x + (t_1 + t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.6e+134], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[a, 3.5e-17], N[(t$95$2 + t$95$3), $MachinePrecision], N[(x + N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.6000000000000001e134

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 91.9%

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

   if -8.6000000000000001e134 < a < 3.5000000000000002e-17

   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 a around 0 94.4%

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

   if 3.5000000000000002e-17 < a

   1. Initial program 94.3%

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

   3. Taylor expanded in b around 0 80.8%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+134}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-17}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 84.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;a \leq -9 \cdot 10^{+133}:\\ \;\;\;\;t_1 + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-13}:\\ \;\;\;\;t_1 + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= a -9e+133)
     (+ t_1 (* a (- 1.0 t)))
     (if (<= a 3e-13)
       (+ t_1 (* z (- 1.0 y)))
       (+ a (+ x (+ (* b (- y 2.0)) (* t (- b a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (a <= -9e+133) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (a <= 3e-13) {
		tmp = t_1 + (z * (1.0 - y));
	} else {
		tmp = a + (x + ((b * (y - 2.0)) + (t * (b - a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if (a <= (-9d+133)) then
        tmp = t_1 + (a * (1.0d0 - t))
    else if (a <= 3d-13) then
        tmp = t_1 + (z * (1.0d0 - y))
    else
        tmp = a + (x + ((b * (y - 2.0d0)) + (t * (b - a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (a <= -9e+133) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (a <= 3e-13) {
		tmp = t_1 + (z * (1.0 - y));
	} else {
		tmp = a + (x + ((b * (y - 2.0)) + (t * (b - a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if a <= -9e+133:
		tmp = t_1 + (a * (1.0 - t))
	elif a <= 3e-13:
		tmp = t_1 + (z * (1.0 - y))
	else:
		tmp = a + (x + ((b * (y - 2.0)) + (t * (b - a))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (a <= -9e+133)
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	elseif (a <= 3e-13)
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(a + Float64(x + Float64(Float64(b * Float64(y - 2.0)) + Float64(t * Float64(b - a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (a <= -9e+133)
		tmp = t_1 + (a * (1.0 - t));
	elseif (a <= 3e-13)
		tmp = t_1 + (z * (1.0 - y));
	else
		tmp = a + (x + ((b * (y - 2.0)) + (t * (b - a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+133], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e-13], N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(x + N[(N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.9999999999999997e133

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 91.9%

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

   if -8.9999999999999997e133 < a < 2.99999999999999984e-13

   1. Initial program 97.4%

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

   3. Taylor expanded in a around 0 94.5%

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

   if 2.99999999999999984e-13 < a

   1. Initial program 94.2%

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

   3. Taylor expanded in t around 0 95.6%

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

   4. Taylor expanded in z around 0 81.3%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+133}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-13}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-190}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.75:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -1.45e+41)
     t_2
     (if (<= t -1.5e-52)
       (* y (- z))
       (if (<= t -4.6e-82)
         t_1
         (if (<= t -2.45e-190)
           (+ x a)
           (if (<= t -5.5e-282) t_1 (if (<= t 0.75) (+ x a) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.45e+41) {
		tmp = t_2;
	} else if (t <= -1.5e-52) {
		tmp = y * -z;
	} else if (t <= -4.6e-82) {
		tmp = t_1;
	} else if (t <= -2.45e-190) {
		tmp = x + a;
	} else if (t <= -5.5e-282) {
		tmp = t_1;
	} else if (t <= 0.75) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-1.45d+41)) then
        tmp = t_2
    else if (t <= (-1.5d-52)) then
        tmp = y * -z
    else if (t <= (-4.6d-82)) then
        tmp = t_1
    else if (t <= (-2.45d-190)) then
        tmp = x + a
    else if (t <= (-5.5d-282)) then
        tmp = t_1
    else if (t <= 0.75d0) then
        tmp = x + a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.45e+41) {
		tmp = t_2;
	} else if (t <= -1.5e-52) {
		tmp = y * -z;
	} else if (t <= -4.6e-82) {
		tmp = t_1;
	} else if (t <= -2.45e-190) {
		tmp = x + a;
	} else if (t <= -5.5e-282) {
		tmp = t_1;
	} else if (t <= 0.75) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -1.45e+41:
		tmp = t_2
	elif t <= -1.5e-52:
		tmp = y * -z
	elif t <= -4.6e-82:
		tmp = t_1
	elif t <= -2.45e-190:
		tmp = x + a
	elif t <= -5.5e-282:
		tmp = t_1
	elif t <= 0.75:
		tmp = x + a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.45e+41)
		tmp = t_2;
	elseif (t <= -1.5e-52)
		tmp = Float64(y * Float64(-z));
	elseif (t <= -4.6e-82)
		tmp = t_1;
	elseif (t <= -2.45e-190)
		tmp = Float64(x + a);
	elseif (t <= -5.5e-282)
		tmp = t_1;
	elseif (t <= 0.75)
		tmp = Float64(x + a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.45e+41)
		tmp = t_2;
	elseif (t <= -1.5e-52)
		tmp = y * -z;
	elseif (t <= -4.6e-82)
		tmp = t_1;
	elseif (t <= -2.45e-190)
		tmp = x + a;
	elseif (t <= -5.5e-282)
		tmp = t_1;
	elseif (t <= 0.75)
		tmp = x + a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e+41], t$95$2, If[LessEqual[t, -1.5e-52], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, -4.6e-82], t$95$1, If[LessEqual[t, -2.45e-190], N[(x + a), $MachinePrecision], If[LessEqual[t, -5.5e-282], t$95$1, If[LessEqual[t, 0.75], N[(x + a), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.44999999999999994e41 or 0.75 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf 66.4%

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

   if -1.44999999999999994e41 < t < -1.5e-52

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf 46.8%

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

   4. Taylor expanded in y around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. *-commutative 40.3%

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

      3. distribute-rgt-neg-in 40.3%

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

   6. Simplified 40.3%

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

   if -1.5e-52 < t < -4.59999999999999994e-82 or -2.4499999999999999e-190 < t < -5.5000000000000001e-282

   1. Initial program 96.6%

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

   3. Taylor expanded in b around inf 56.6%

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

   4. Taylor expanded in t around 0 56.6%

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

   if -4.59999999999999994e-82 < t < -2.4499999999999999e-190 or -5.5000000000000001e-282 < t < 0.75

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0 97.3%

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

   4. Taylor expanded in a around 0 97.3%

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

   5. Taylor expanded in z around 0 70.6%

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

   6. Taylor expanded in b around 0 46.4%

      \[\leadsto \color{blue}{a + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-190}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-282}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 0.75:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-29}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-198}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 1600:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+62}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -3.4e+98)
     t_1
     (if (<= y -1.8e-29)
       (- x (* y z))
       (if (<= y -4.2e-119)
         (* b (- t 2.0))
         (if (<= y -2.5e-198)
           (+ x a)
           (if (<= y 1600.0)
             (* t (- b a))
             (if (<= y 4.2e+62) (+ x a) 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 <= -3.4e+98) {
		tmp = t_1;
	} else if (y <= -1.8e-29) {
		tmp = x - (y * z);
	} else if (y <= -4.2e-119) {
		tmp = b * (t - 2.0);
	} else if (y <= -2.5e-198) {
		tmp = x + a;
	} else if (y <= 1600.0) {
		tmp = t * (b - a);
	} else if (y <= 4.2e+62) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-3.4d+98)) then
        tmp = t_1
    else if (y <= (-1.8d-29)) then
        tmp = x - (y * z)
    else if (y <= (-4.2d-119)) then
        tmp = b * (t - 2.0d0)
    else if (y <= (-2.5d-198)) then
        tmp = x + a
    else if (y <= 1600.0d0) then
        tmp = t * (b - a)
    else if (y <= 4.2d+62) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -3.4e+98) {
		tmp = t_1;
	} else if (y <= -1.8e-29) {
		tmp = x - (y * z);
	} else if (y <= -4.2e-119) {
		tmp = b * (t - 2.0);
	} else if (y <= -2.5e-198) {
		tmp = x + a;
	} else if (y <= 1600.0) {
		tmp = t * (b - a);
	} else if (y <= 4.2e+62) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -3.4e+98:
		tmp = t_1
	elif y <= -1.8e-29:
		tmp = x - (y * z)
	elif y <= -4.2e-119:
		tmp = b * (t - 2.0)
	elif y <= -2.5e-198:
		tmp = x + a
	elif y <= 1600.0:
		tmp = t * (b - a)
	elif y <= 4.2e+62:
		tmp = x + a
	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 <= -3.4e+98)
		tmp = t_1;
	elseif (y <= -1.8e-29)
		tmp = Float64(x - Float64(y * z));
	elseif (y <= -4.2e-119)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= -2.5e-198)
		tmp = Float64(x + a);
	elseif (y <= 1600.0)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 4.2e+62)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -3.4e+98)
		tmp = t_1;
	elseif (y <= -1.8e-29)
		tmp = x - (y * z);
	elseif (y <= -4.2e-119)
		tmp = b * (t - 2.0);
	elseif (y <= -2.5e-198)
		tmp = x + a;
	elseif (y <= 1600.0)
		tmp = t * (b - a);
	elseif (y <= 4.2e+62)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+98], t$95$1, If[LessEqual[y, -1.8e-29], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-119], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-198], N[(x + a), $MachinePrecision], If[LessEqual[y, 1600.0], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+62], N[(x + a), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.39999999999999972e98 or 4.2e62 < y

   1. Initial program 91.2%

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

   3. Taylor expanded in y around inf 79.2%

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

   if -3.39999999999999972e98 < y < -1.79999999999999987e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 84.0%

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

   4. Taylor expanded in y around inf 52.2%

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

      1. *-commutative 52.2%

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

   6. Simplified 52.2%

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

   if -1.79999999999999987e-29 < y < -4.2e-119

   1. Initial program 89.8%

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

   3. Taylor expanded in b around inf 55.9%

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

   4. Taylor expanded in y around 0 55.9%

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

   if -4.2e-119 < y < -2.5e-198 or 1600 < y < 4.2e62

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 89.9%

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

   4. Taylor expanded in a around 0 89.9%

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

   5. Taylor expanded in z around 0 63.4%

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

   6. Taylor expanded in b around 0 57.3%

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

   if -2.5e-198 < y < 1600

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 46.1%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-29}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-198}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 1600:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+62}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ t_2 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-80}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-200}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-5}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))) (t_2 (* t (- a))))
   (if (<= t -1.3e+45)
     t_2
     (if (<= t -7.5e-62)
       t_1
       (if (<= t -1.65e-80)
         (* y b)
         (if (<= t -2.8e-200)
           (+ x a)
           (if (<= t -6.8e-280) t_1 (if (<= t 1.4e-5) (+ x a) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double t_2 = t * -a;
	double tmp;
	if (t <= -1.3e+45) {
		tmp = t_2;
	} else if (t <= -7.5e-62) {
		tmp = t_1;
	} else if (t <= -1.65e-80) {
		tmp = y * b;
	} else if (t <= -2.8e-200) {
		tmp = x + a;
	} else if (t <= -6.8e-280) {
		tmp = t_1;
	} else if (t <= 1.4e-5) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * -z
    t_2 = t * -a
    if (t <= (-1.3d+45)) then
        tmp = t_2
    else if (t <= (-7.5d-62)) then
        tmp = t_1
    else if (t <= (-1.65d-80)) then
        tmp = y * b
    else if (t <= (-2.8d-200)) then
        tmp = x + a
    else if (t <= (-6.8d-280)) then
        tmp = t_1
    else if (t <= 1.4d-5) then
        tmp = x + a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double t_2 = t * -a;
	double tmp;
	if (t <= -1.3e+45) {
		tmp = t_2;
	} else if (t <= -7.5e-62) {
		tmp = t_1;
	} else if (t <= -1.65e-80) {
		tmp = y * b;
	} else if (t <= -2.8e-200) {
		tmp = x + a;
	} else if (t <= -6.8e-280) {
		tmp = t_1;
	} else if (t <= 1.4e-5) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	t_2 = t * -a
	tmp = 0
	if t <= -1.3e+45:
		tmp = t_2
	elif t <= -7.5e-62:
		tmp = t_1
	elif t <= -1.65e-80:
		tmp = y * b
	elif t <= -2.8e-200:
		tmp = x + a
	elif t <= -6.8e-280:
		tmp = t_1
	elif t <= 1.4e-5:
		tmp = x + a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	t_2 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -1.3e+45)
		tmp = t_2;
	elseif (t <= -7.5e-62)
		tmp = t_1;
	elseif (t <= -1.65e-80)
		tmp = Float64(y * b);
	elseif (t <= -2.8e-200)
		tmp = Float64(x + a);
	elseif (t <= -6.8e-280)
		tmp = t_1;
	elseif (t <= 1.4e-5)
		tmp = Float64(x + a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	t_2 = t * -a;
	tmp = 0.0;
	if (t <= -1.3e+45)
		tmp = t_2;
	elseif (t <= -7.5e-62)
		tmp = t_1;
	elseif (t <= -1.65e-80)
		tmp = y * b;
	elseif (t <= -2.8e-200)
		tmp = x + a;
	elseif (t <= -6.8e-280)
		tmp = t_1;
	elseif (t <= 1.4e-5)
		tmp = x + a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -1.3e+45], t$95$2, If[LessEqual[t, -7.5e-62], t$95$1, If[LessEqual[t, -1.65e-80], N[(y * b), $MachinePrecision], If[LessEqual[t, -2.8e-200], N[(x + a), $MachinePrecision], If[LessEqual[t, -6.8e-280], t$95$1, If[LessEqual[t, 1.4e-5], N[(x + a), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.30000000000000004e45 or 1.39999999999999998e-5 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in b around 0 64.8%

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

   4. Taylor expanded in t around inf 43.0%

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

      1. associate-*r* 43.0%

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

      2. mul-1-neg 43.0%

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

   6. Simplified 43.0%

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

   if -1.30000000000000004e45 < t < -7.5000000000000003e-62 or -2.80000000000000007e-200 < t < -6.7999999999999995e-280

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 43.3%

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

   4. Taylor expanded in y around inf 36.8%

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

      1. mul-1-neg 36.8%

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

      2. *-commutative 36.8%

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

      3. distribute-rgt-neg-in 36.8%

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

   6. Simplified 36.8%

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

   if -7.5000000000000003e-62 < t < -1.65e-80

   1. Initial program 83.3%

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

   3. Taylor expanded in b around inf 85.3%

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

   4. Taylor expanded in y around inf 69.3%

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

   if -1.65e-80 < t < -2.80000000000000007e-200 or -6.7999999999999995e-280 < t < 1.39999999999999998e-5

   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. Taylor expanded in t around 0 97.9%

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

   4. Taylor expanded in a around 0 97.9%

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

   5. Taylor expanded in z around 0 70.8%

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

   6. Taylor expanded in b around 0 45.5%

      \[\leadsto \color{blue}{a + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-80}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-200}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-5}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 3.65 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-92}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))) (t_2 (* a (- 1.0 t))))
   (if (<= a -2.3e+131)
     t_2
     (if (<= a -5e-115)
       (* y (- z))
       (if (<= a 3.65e-171)
         t_1
         (if (<= a 2.6e-92) (+ x a) (if (<= a 1.5e-13) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -2.3e+131) {
		tmp = t_2;
	} else if (a <= -5e-115) {
		tmp = y * -z;
	} else if (a <= 3.65e-171) {
		tmp = t_1;
	} else if (a <= 2.6e-92) {
		tmp = x + a;
	} else if (a <= 1.5e-13) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    t_2 = a * (1.0d0 - t)
    if (a <= (-2.3d+131)) then
        tmp = t_2
    else if (a <= (-5d-115)) then
        tmp = y * -z
    else if (a <= 3.65d-171) then
        tmp = t_1
    else if (a <= 2.6d-92) then
        tmp = x + a
    else if (a <= 1.5d-13) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -2.3e+131) {
		tmp = t_2;
	} else if (a <= -5e-115) {
		tmp = y * -z;
	} else if (a <= 3.65e-171) {
		tmp = t_1;
	} else if (a <= 2.6e-92) {
		tmp = x + a;
	} else if (a <= 1.5e-13) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -2.3e+131:
		tmp = t_2
	elif a <= -5e-115:
		tmp = y * -z
	elif a <= 3.65e-171:
		tmp = t_1
	elif a <= 2.6e-92:
		tmp = x + a
	elif a <= 1.5e-13:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -2.3e+131)
		tmp = t_2;
	elseif (a <= -5e-115)
		tmp = Float64(y * Float64(-z));
	elseif (a <= 3.65e-171)
		tmp = t_1;
	elseif (a <= 2.6e-92)
		tmp = Float64(x + a);
	elseif (a <= 1.5e-13)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -2.3e+131)
		tmp = t_2;
	elseif (a <= -5e-115)
		tmp = y * -z;
	elseif (a <= 3.65e-171)
		tmp = t_1;
	elseif (a <= 2.6e-92)
		tmp = x + a;
	elseif (a <= 1.5e-13)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e+131], t$95$2, If[LessEqual[a, -5e-115], N[(y * (-z)), $MachinePrecision], If[LessEqual[a, 3.65e-171], t$95$1, If[LessEqual[a, 2.6e-92], N[(x + a), $MachinePrecision], If[LessEqual[a, 1.5e-13], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.29999999999999992e131 or 1.49999999999999992e-13 < a

   1. Initial program 94.2%

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

   3. Taylor expanded in a around inf 63.5%

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

   if -2.29999999999999992e131 < a < -5.0000000000000003e-115

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 48.1%

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

   4. Taylor expanded in y around inf 30.6%

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

      1. mul-1-neg 30.6%

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

      2. *-commutative 30.6%

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

      3. distribute-rgt-neg-in 30.6%

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

   6. Simplified 30.6%

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

   if -5.0000000000000003e-115 < a < 3.65000000000000008e-171 or 2.6e-92 < a < 1.49999999999999992e-13

   1. Initial program 97.7%

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

   3. Taylor expanded in b around inf 49.2%

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

   4. Taylor expanded in y around 0 35.0%

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

   if 3.65000000000000008e-171 < a < 2.6e-92

   1. Initial program 93.3%

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

   3. Taylor expanded in t around 0 80.9%

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

   4. Taylor expanded in a around 0 80.9%

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

   5. Taylor expanded in z around 0 58.1%

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

   6. Taylor expanded in b around 0 50.9%

      \[\leadsto \color{blue}{a + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+131}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 3.65 \cdot 10^{-171}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-92}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 59.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00068:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (* y (- b z))))
   (if (<= y -7e+93)
     t_2
     (if (<= y 3.5e-28)
       t_1
       (if (<= y 0.00068) (* b (- t 2.0)) (if (<= y 1e+89) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -7e+93) {
		tmp = t_2;
	} else if (y <= 3.5e-28) {
		tmp = t_1;
	} else if (y <= 0.00068) {
		tmp = b * (t - 2.0);
	} else if (y <= 1e+89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = y * (b - z)
    if (y <= (-7d+93)) then
        tmp = t_2
    else if (y <= 3.5d-28) then
        tmp = t_1
    else if (y <= 0.00068d0) then
        tmp = b * (t - 2.0d0)
    else if (y <= 1d+89) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -7e+93) {
		tmp = t_2;
	} else if (y <= 3.5e-28) {
		tmp = t_1;
	} else if (y <= 0.00068) {
		tmp = b * (t - 2.0);
	} else if (y <= 1e+89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -7e+93:
		tmp = t_2
	elif y <= 3.5e-28:
		tmp = t_1
	elif y <= 0.00068:
		tmp = b * (t - 2.0)
	elif y <= 1e+89:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -7e+93)
		tmp = t_2;
	elseif (y <= 3.5e-28)
		tmp = t_1;
	elseif (y <= 0.00068)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 1e+89)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -7e+93)
		tmp = t_2;
	elseif (y <= 3.5e-28)
		tmp = t_1;
	elseif (y <= 0.00068)
		tmp = b * (t - 2.0);
	elseif (y <= 1e+89)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+93], t$95$2, If[LessEqual[y, 3.5e-28], t$95$1, If[LessEqual[y, 0.00068], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+89], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.99999999999999996e93 or 9.99999999999999995e88 < y

   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 y around inf 81.8%

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

   if -6.99999999999999996e93 < y < 3.5e-28 or 6.8e-4 < y < 9.99999999999999995e88

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 75.1%

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

   4. Taylor expanded in a around inf 54.4%

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

   if 3.5e-28 < y < 6.8e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 72.0%

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

   4. Taylor expanded in y around 0 72.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-28}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 0.00068:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 10^{+89}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 66.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-52}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+38}:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.55e+41)
     t_1
     (if (<= t -5.4e-52)
       (- x (* y z))
       (if (<= t 7.2e+38) (+ a (+ x (* b (- y 2.0)))) 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 <= -1.55e+41) {
		tmp = t_1;
	} else if (t <= -5.4e-52) {
		tmp = x - (y * z);
	} else if (t <= 7.2e+38) {
		tmp = a + (x + (b * (y - 2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-1.55d+41)) then
        tmp = t_1
    else if (t <= (-5.4d-52)) then
        tmp = x - (y * z)
    else if (t <= 7.2d+38) then
        tmp = a + (x + (b * (y - 2.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.55e+41) {
		tmp = t_1;
	} else if (t <= -5.4e-52) {
		tmp = x - (y * z);
	} else if (t <= 7.2e+38) {
		tmp = a + (x + (b * (y - 2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.55e+41:
		tmp = t_1
	elif t <= -5.4e-52:
		tmp = x - (y * z)
	elif t <= 7.2e+38:
		tmp = a + (x + (b * (y - 2.0)))
	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 <= -1.55e+41)
		tmp = t_1;
	elseif (t <= -5.4e-52)
		tmp = Float64(x - Float64(y * z));
	elseif (t <= 7.2e+38)
		tmp = Float64(a + Float64(x + Float64(b * Float64(y - 2.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.55e+41)
		tmp = t_1;
	elseif (t <= -5.4e-52)
		tmp = x - (y * z);
	elseif (t <= 7.2e+38)
		tmp = a + (x + (b * (y - 2.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+41], t$95$1, If[LessEqual[t, -5.4e-52], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+38], N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55e41 or 7.19999999999999938e38 < t

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf 70.4%

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

   if -1.55e41 < t < -5.40000000000000019e-52

   1. Initial program 96.6%

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

   3. Taylor expanded in b around 0 83.7%

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

   4. Taylor expanded in y around inf 63.7%

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

      1. *-commutative 63.7%

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

   6. Simplified 63.7%

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

   if -5.40000000000000019e-52 < t < 7.19999999999999938e38

   1. Initial program 97.7%

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

   3. Taylor expanded in t around 0 95.8%

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

   4. Taylor expanded in a around 0 95.8%

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

   5. Taylor expanded in z around 0 68.2%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-52}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+38}:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 67.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-28}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+88}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -3.8e+93)
     t_1
     (if (<= y 3.5e-28)
       (+ x (+ z (* a (- 1.0 t))))
       (if (<= y 3.5e+88) (+ (+ x a) (* z (- 1.0 y))) 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+93) {
		tmp = t_1;
	} else if (y <= 3.5e-28) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (y <= 3.5e+88) {
		tmp = (x + a) + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-3.8d+93)) then
        tmp = t_1
    else if (y <= 3.5d-28) then
        tmp = x + (z + (a * (1.0d0 - t)))
    else if (y <= 3.5d+88) then
        tmp = (x + a) + (z * (1.0d0 - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -3.8e+93) {
		tmp = t_1;
	} else if (y <= 3.5e-28) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (y <= 3.5e+88) {
		tmp = (x + a) + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -3.8e+93:
		tmp = t_1
	elif y <= 3.5e-28:
		tmp = x + (z + (a * (1.0 - t)))
	elif y <= 3.5e+88:
		tmp = (x + a) + (z * (1.0 - y))
	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+93)
		tmp = t_1;
	elseif (y <= 3.5e-28)
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	elseif (y <= 3.5e+88)
		tmp = Float64(Float64(x + a) + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -3.8e+93)
		tmp = t_1;
	elseif (y <= 3.5e-28)
		tmp = x + (z + (a * (1.0 - t)));
	elseif (y <= 3.5e+88)
		tmp = (x + a) + (z * (1.0 - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+93], t$95$1, If[LessEqual[y, 3.5e-28], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+88], N[(N[(x + a), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999998e93 or 3.4999999999999998e88 < y

   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 y around inf 81.8%

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

   if -3.7999999999999998e93 < y < 3.5e-28

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0 73.7%

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

   4. Taylor expanded in y around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. sub-neg 70.7%

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

      3. metadata-eval 70.7%

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

      4. *-commutative 70.7%

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

      5. mul-1-neg 70.7%

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

      6. unsub-neg 70.7%

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

      7. *-commutative 70.7%

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

   6. Simplified 70.7%

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

   if 3.5e-28 < y < 3.4999999999999998e88

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 82.3%

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

   4. Taylor expanded in a around 0 82.3%

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

   5. Taylor expanded in b around 0 66.4%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-28}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+88}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 50.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4.05 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-198}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 26000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+62}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -4.05e+46)
     t_1
     (if (<= y -3e-198)
       (+ x a)
       (if (<= y 26000.0) (* t (- b a)) (if (<= y 4.2e+62) (+ x a) 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 <= -4.05e+46) {
		tmp = t_1;
	} else if (y <= -3e-198) {
		tmp = x + a;
	} else if (y <= 26000.0) {
		tmp = t * (b - a);
	} else if (y <= 4.2e+62) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-4.05d+46)) then
        tmp = t_1
    else if (y <= (-3d-198)) then
        tmp = x + a
    else if (y <= 26000.0d0) then
        tmp = t * (b - a)
    else if (y <= 4.2d+62) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4.05e+46) {
		tmp = t_1;
	} else if (y <= -3e-198) {
		tmp = x + a;
	} else if (y <= 26000.0) {
		tmp = t * (b - a);
	} else if (y <= 4.2e+62) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -4.05e+46:
		tmp = t_1
	elif y <= -3e-198:
		tmp = x + a
	elif y <= 26000.0:
		tmp = t * (b - a)
	elif y <= 4.2e+62:
		tmp = x + a
	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 <= -4.05e+46)
		tmp = t_1;
	elseif (y <= -3e-198)
		tmp = Float64(x + a);
	elseif (y <= 26000.0)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 4.2e+62)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -4.05e+46)
		tmp = t_1;
	elseif (y <= -3e-198)
		tmp = x + a;
	elseif (y <= 26000.0)
		tmp = t * (b - a);
	elseif (y <= 4.2e+62)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.05e+46], t$95$1, If[LessEqual[y, -3e-198], N[(x + a), $MachinePrecision], If[LessEqual[y, 26000.0], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+62], N[(x + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.05000000000000024e46 or 4.2e62 < y

   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 y around inf 76.0%

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

   if -4.05000000000000024e46 < y < -3.0000000000000001e-198 or 26000 < y < 4.2e62

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0 78.7%

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

   4. Taylor expanded in a around 0 78.7%

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

   5. Taylor expanded in z around 0 55.7%

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

   6. Taylor expanded in b around 0 47.1%

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

   if -3.0000000000000001e-198 < y < 26000

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 46.1%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.05 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-198}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 26000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+62}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 67.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+95} \lor \neg \left(y \leq 1.5 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.2e+95) (not (<= y 1.5e+93)))
   (* y (- b z))
   (+ x (+ z (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+95) || !(y <= 1.5e+93)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (z + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.2d+95)) .or. (.not. (y <= 1.5d+93))) then
        tmp = y * (b - z)
    else
        tmp = x + (z + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+95) || !(y <= 1.5e+93)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (z + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.2e+95) or not (y <= 1.5e+93):
		tmp = y * (b - z)
	else:
		tmp = x + (z + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.2e+95) || !(y <= 1.5e+93))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.2e+95) || ~((y <= 1.5e+93)))
		tmp = y * (b - z);
	else
		tmp = x + (z + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.2e+95], N[Not[LessEqual[y, 1.5e+93]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2000000000000001e95 or 1.49999999999999989e93 < y

   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 y around inf 81.8%

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

   if -3.2000000000000001e95 < y < 1.49999999999999989e93

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 73.1%

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

   4. Taylor expanded in y around 0 67.2%

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

      1. +-commutative 67.2%

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

      2. sub-neg 67.2%

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

      3. metadata-eval 67.2%

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

      4. *-commutative 67.2%

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

      5. mul-1-neg 67.2%

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

      6. unsub-neg 67.2%

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

      7. *-commutative 67.2%

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

   6. Simplified 67.2%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+95} \lor \neg \left(y \leq 1.5 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 26.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-203}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.2e+32)
   (* t b)
   (if (<= t -7.5e-295) x (if (<= t 7.2e-203) a (if (<= t 1e+38) x (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.2e+32) {
		tmp = t * b;
	} else if (t <= -7.5e-295) {
		tmp = x;
	} else if (t <= 7.2e-203) {
		tmp = a;
	} else if (t <= 1e+38) {
		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 <= (-1.2d+32)) then
        tmp = t * b
    else if (t <= (-7.5d-295)) then
        tmp = x
    else if (t <= 7.2d-203) then
        tmp = a
    else if (t <= 1d+38) 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 <= -1.2e+32) {
		tmp = t * b;
	} else if (t <= -7.5e-295) {
		tmp = x;
	} else if (t <= 7.2e-203) {
		tmp = a;
	} else if (t <= 1e+38) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.2e+32:
		tmp = t * b
	elif t <= -7.5e-295:
		tmp = x
	elif t <= 7.2e-203:
		tmp = a
	elif t <= 1e+38:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.2e+32)
		tmp = Float64(t * b);
	elseif (t <= -7.5e-295)
		tmp = x;
	elseif (t <= 7.2e-203)
		tmp = a;
	elseif (t <= 1e+38)
		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 <= -1.2e+32)
		tmp = t * b;
	elseif (t <= -7.5e-295)
		tmp = x;
	elseif (t <= 7.2e-203)
		tmp = a;
	elseif (t <= 1e+38)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.2e+32], N[(t * b), $MachinePrecision], If[LessEqual[t, -7.5e-295], x, If[LessEqual[t, 7.2e-203], a, If[LessEqual[t, 1e+38], x, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.19999999999999996e32 or 9.99999999999999977e37 < t

   1. Initial program 93.8%

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

   3. Taylor expanded in a around 0 64.9%

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

   4. Taylor expanded in t around inf 33.8%

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

   if -1.19999999999999996e32 < t < -7.4999999999999997e-295 or 7.19999999999999958e-203 < t < 9.99999999999999977e37

   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 21.8%

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

   if -7.4999999999999997e-295 < t < 7.19999999999999958e-203

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in a around inf 40.4%

      \[\leadsto \color{blue}{a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-203}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 31.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+263}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+99}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-162}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+128}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8e+263)
   (* y b)
   (if (<= b -6.6e+99)
     (* t b)
     (if (<= b -2.6e-162) (* y (- z)) (if (<= b 3.6e+128) (+ x a) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8e+263) {
		tmp = y * b;
	} else if (b <= -6.6e+99) {
		tmp = t * b;
	} else if (b <= -2.6e-162) {
		tmp = y * -z;
	} else if (b <= 3.6e+128) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8d+263)) then
        tmp = y * b
    else if (b <= (-6.6d+99)) then
        tmp = t * b
    else if (b <= (-2.6d-162)) then
        tmp = y * -z
    else if (b <= 3.6d+128) then
        tmp = x + a
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8e+263) {
		tmp = y * b;
	} else if (b <= -6.6e+99) {
		tmp = t * b;
	} else if (b <= -2.6e-162) {
		tmp = y * -z;
	} else if (b <= 3.6e+128) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8e+263:
		tmp = y * b
	elif b <= -6.6e+99:
		tmp = t * b
	elif b <= -2.6e-162:
		tmp = y * -z
	elif b <= 3.6e+128:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8e+263)
		tmp = Float64(y * b);
	elseif (b <= -6.6e+99)
		tmp = Float64(t * b);
	elseif (b <= -2.6e-162)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 3.6e+128)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8e+263)
		tmp = y * b;
	elseif (b <= -6.6e+99)
		tmp = t * b;
	elseif (b <= -2.6e-162)
		tmp = y * -z;
	elseif (b <= 3.6e+128)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8e+263], N[(y * b), $MachinePrecision], If[LessEqual[b, -6.6e+99], N[(t * b), $MachinePrecision], If[LessEqual[b, -2.6e-162], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 3.6e+128], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.00000000000000013e263 or 3.60000000000000027e128 < b

   1. Initial program 85.0%

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

   3. Taylor expanded in b around inf 81.3%

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

   4. Taylor expanded in y around inf 45.3%

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

   if -8.00000000000000013e263 < b < -6.5999999999999998e99

   1. Initial program 96.8%

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

   3. Taylor expanded in a around 0 89.7%

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

   4. Taylor expanded in t around inf 42.6%

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

   if -6.5999999999999998e99 < b < -2.6e-162

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 42.3%

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

   4. Taylor expanded in y around inf 33.5%

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

      1. mul-1-neg 33.5%

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

      2. *-commutative 33.5%

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

      3. distribute-rgt-neg-in 33.5%

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

   6. Simplified 33.5%

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

   if -2.6e-162 < b < 3.60000000000000027e128

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0 78.2%

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

   4. Taylor expanded in a around 0 78.2%

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

   5. Taylor expanded in z around 0 47.2%

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

   6. Taylor expanded in b around 0 35.9%

      \[\leadsto \color{blue}{a + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+263}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+99}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-162}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+128}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 35.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -2.65 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-17}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -2.65e+131)
     t_1
     (if (<= a -5.6e-246) (* y (- z)) (if (<= a 2.9e-17) (+ x a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -2.65e+131) {
		tmp = t_1;
	} else if (a <= -5.6e-246) {
		tmp = y * -z;
	} else if (a <= 2.9e-17) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-2.65d+131)) then
        tmp = t_1
    else if (a <= (-5.6d-246)) then
        tmp = y * -z
    else if (a <= 2.9d-17) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -2.65e+131) {
		tmp = t_1;
	} else if (a <= -5.6e-246) {
		tmp = y * -z;
	} else if (a <= 2.9e-17) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -2.65e+131:
		tmp = t_1
	elif a <= -5.6e-246:
		tmp = y * -z
	elif a <= 2.9e-17:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -2.65e+131)
		tmp = t_1;
	elseif (a <= -5.6e-246)
		tmp = Float64(y * Float64(-z));
	elseif (a <= 2.9e-17)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -2.65e+131)
		tmp = t_1;
	elseif (a <= -5.6e-246)
		tmp = y * -z;
	elseif (a <= 2.9e-17)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.65e+131], t$95$1, If[LessEqual[a, -5.6e-246], N[(y * (-z)), $MachinePrecision], If[LessEqual[a, 2.9e-17], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.6499999999999998e131 or 2.9000000000000003e-17 < a

   1. Initial program 94.3%

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

   3. Taylor expanded in a around inf 62.4%

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

   if -2.6499999999999998e131 < a < -5.5999999999999999e-246

   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 z around inf 43.7%

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

   4. Taylor expanded in y around inf 29.0%

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

      1. mul-1-neg 29.0%

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

      2. *-commutative 29.0%

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

      3. distribute-rgt-neg-in 29.0%

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

   6. Simplified 29.0%

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

   if -5.5999999999999999e-246 < a < 2.9000000000000003e-17

   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 t around 0 81.0%

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

   4. Taylor expanded in a around 0 81.0%

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

   5. Taylor expanded in z around 0 55.7%

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

   6. Taylor expanded in b around 0 30.6%

      \[\leadsto \color{blue}{a + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{+131}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-17}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 33.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+266}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -3.35 \cdot 10^{+100}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{+128}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.6e+266)
   (* y b)
   (if (<= b -3.35e+100) (* t b) (if (<= b 2.45e+128) (+ x a) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.6e+266) {
		tmp = y * b;
	} else if (b <= -3.35e+100) {
		tmp = t * b;
	} else if (b <= 2.45e+128) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.6d+266)) then
        tmp = y * b
    else if (b <= (-3.35d+100)) then
        tmp = t * b
    else if (b <= 2.45d+128) then
        tmp = x + a
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.6e+266) {
		tmp = y * b;
	} else if (b <= -3.35e+100) {
		tmp = t * b;
	} else if (b <= 2.45e+128) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.6e+266:
		tmp = y * b
	elif b <= -3.35e+100:
		tmp = t * b
	elif b <= 2.45e+128:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.6e+266)
		tmp = Float64(y * b);
	elseif (b <= -3.35e+100)
		tmp = Float64(t * b);
	elseif (b <= 2.45e+128)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.6e+266)
		tmp = y * b;
	elseif (b <= -3.35e+100)
		tmp = t * b;
	elseif (b <= 2.45e+128)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.6e+266], N[(y * b), $MachinePrecision], If[LessEqual[b, -3.35e+100], N[(t * b), $MachinePrecision], If[LessEqual[b, 2.45e+128], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.60000000000000014e266 or 2.45000000000000009e128 < b

   1. Initial program 85.0%

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

   3. Taylor expanded in b around inf 81.3%

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

   4. Taylor expanded in y around inf 45.3%

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

   if -2.60000000000000014e266 < b < -3.3499999999999998e100

   1. Initial program 96.8%

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

   3. Taylor expanded in a around 0 89.7%

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

   4. Taylor expanded in t around inf 42.6%

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

   if -3.3499999999999998e100 < b < 2.45000000000000009e128

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0 78.4%

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

   4. Taylor expanded in a around 0 78.4%

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

   5. Taylor expanded in z around 0 44.9%

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

   6. Taylor expanded in b around 0 31.6%

      \[\leadsto \color{blue}{a + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+266}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -3.35 \cdot 10^{+100}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{+128}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 20.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2250000:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2250000.0) a (if (<= a 1.5e-13) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2250000.0) {
		tmp = a;
	} else if (a <= 1.5e-13) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2250000.0d0)) then
        tmp = a
    else if (a <= 1.5d-13) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2250000.0) {
		tmp = a;
	} else if (a <= 1.5e-13) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2250000.0:
		tmp = a
	elif a <= 1.5e-13:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2250000.0)
		tmp = a;
	elseif (a <= 1.5e-13)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2250000.0)
		tmp = a;
	elseif (a <= 1.5e-13)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2250000.0], a, If[LessEqual[a, 1.5e-13], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -2.25e6 or 1.49999999999999992e-13 < a

   1. Initial program 94.3%

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

   3. Taylor expanded in t around 0 63.1%

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

   4. Taylor expanded in a around inf 21.1%

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

   if -2.25e6 < a < 1.49999999999999992e-13

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf 24.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2250000:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 20.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+152}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1e+152) z (if (<= z 2.25e+95) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1e+152) {
		tmp = z;
	} else if (z <= 2.25e+95) {
		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 <= (-1d+152)) then
        tmp = z
    else if (z <= 2.25d+95) 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 <= -1e+152) {
		tmp = z;
	} else if (z <= 2.25e+95) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1e+152:
		tmp = z
	elif z <= 2.25e+95:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1e+152)
		tmp = z;
	elseif (z <= 2.25e+95)
		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 <= -1e+152)
		tmp = z;
	elseif (z <= 2.25e+95)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1e+152], z, If[LessEqual[z, 2.25e+95], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1e152 or 2.25000000000000008e95 < z

   1. Initial program 89.2%

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

   3. Taylor expanded in z around inf 64.7%

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

   4. Taylor expanded in y around 0 25.5%

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

   if -1e152 < z < 2.25000000000000008e95

   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 22.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+152}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 10.8% accurate, 21.0× 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 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 t around 0 73.0%

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

4. Taylor expanded in a around inf 11.5%

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

5. Final simplification 11.5%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024011 
(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)))