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

Percentage Accurate: 94.8% → 97.8%

Time: 12.4s

Alternatives: 22

Speedup: 0.5×

• 36.3% 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: 94.8% 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: 97.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. mul-1-neg 100.0%

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

      10. remove-double-neg 100.0%

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

      11. distribute-lft-neg-in 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

      15. sub-neg 100.0%

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

      16. *-commutative 100.0%

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

   5. Simplified 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 61.6%

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

4. Final simplification 98.0%

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

Alternative 2: 97.2% 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 94.9%

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

   1. +-commutative 94.9%

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

   2. fma-define 97.2%

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

   3. associate--l+ 97.2%

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

   4. sub-neg 97.2%

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

   5. metadata-eval 97.2%

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

   6. sub-neg 97.2%

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

   7. associate-+l- 97.2%

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

   8. fmm-def 98.0%

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

   9. sub-neg 98.0%

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

   10. metadata-eval 98.0%

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

   11. remove-double-neg 98.0%

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

   12. sub-neg 98.0%

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

   13. metadata-eval 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 3: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+251}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+19}:\\ \;\;\;\;x + \left(t\_1 - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t \leq 0.00027:\\ \;\;\;\;\left(a + \left(b \cdot \left(y + -2\right) + \left(x + z\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= t -1.6e+251)
     (* t (- b a))
     (if (<= t -1.35e+19)
       (+ x (- t_1 (* z (+ y -1.0))))
       (if (<= t 0.00027)
         (- (+ a (+ (* b (+ y -2.0)) (+ x z))) (* y z))
         (+ (+ x (* b (- (+ y t) 2.0))) 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 (t <= -1.6e+251) {
		tmp = t * (b - a);
	} else if (t <= -1.35e+19) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else if (t <= 0.00027) {
		tmp = (a + ((b * (y + -2.0)) + (x + z))) - (y * z);
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + 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 (t <= (-1.6d+251)) then
        tmp = t * (b - a)
    else if (t <= (-1.35d+19)) then
        tmp = x + (t_1 - (z * (y + (-1.0d0))))
    else if (t <= 0.00027d0) then
        tmp = (a + ((b * (y + (-2.0d0))) + (x + z))) - (y * z)
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + 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 (t <= -1.6e+251) {
		tmp = t * (b - a);
	} else if (t <= -1.35e+19) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else if (t <= 0.00027) {
		tmp = (a + ((b * (y + -2.0)) + (x + z))) - (y * z);
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if t <= -1.6e+251:
		tmp = t * (b - a)
	elif t <= -1.35e+19:
		tmp = x + (t_1 - (z * (y + -1.0)))
	elif t <= 0.00027:
		tmp = (a + ((b * (y + -2.0)) + (x + z))) - (y * z)
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + 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 (t <= -1.6e+251)
		tmp = Float64(t * Float64(b - a));
	elseif (t <= -1.35e+19)
		tmp = Float64(x + Float64(t_1 - Float64(z * Float64(y + -1.0))));
	elseif (t <= 0.00027)
		tmp = Float64(Float64(a + Float64(Float64(b * Float64(y + -2.0)) + Float64(x + z))) - Float64(y * z));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + 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 (t <= -1.6e+251)
		tmp = t * (b - a);
	elseif (t <= -1.35e+19)
		tmp = x + (t_1 - (z * (y + -1.0)));
	elseif (t <= 0.00027)
		tmp = (a + ((b * (y + -2.0)) + (x + z))) - (y * z);
	else
		tmp = (x + (b * ((y + t) - 2.0))) + 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[t, -1.6e+251], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e+19], N[(x + N[(t$95$1 - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00027], N[(N[(a + N[(N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.5999999999999999e251

   1. Initial program 72.7%

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

   3. Taylor expanded in t around inf 81.9%

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

   if -1.5999999999999999e251 < t < -1.35e19

   1. Initial program 90.7%

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

   3. Taylor expanded in b around 0 82.5%

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

   if -1.35e19 < t < 2.70000000000000003e-4

   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 y around 0 97.9%

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

      1. sub-neg 97.9%

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

      2. mul-1-neg 97.9%

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

      3. unsub-neg 97.9%

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

      4. *-commutative 97.9%

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

      5. sub-neg 97.9%

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

      6. metadata-eval 97.9%

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

      7. *-commutative 97.9%

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

      8. distribute-neg-in 97.9%

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

      9. mul-1-neg 97.9%

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

      10. remove-double-neg 97.9%

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

      11. distribute-lft-neg-in 97.9%

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

      12. +-commutative 97.9%

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

      13. distribute-neg-in 97.9%

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

      14. metadata-eval 97.9%

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

      15. sub-neg 97.9%

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

      16. *-commutative 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in t around 0 97.4%

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

      1. associate-+r+ 97.4%

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

      2. +-commutative 97.4%

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

      3. sub-neg 97.4%

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

      4. metadata-eval 97.4%

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

   8. Simplified 97.4%

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

   if 2.70000000000000003e-4 < t

   1. Initial program 94.9%

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

   3. Taylor expanded in z around 0 86.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+251}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+19}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t \leq 0.00027:\\ \;\;\;\;\left(a + \left(b \cdot \left(y + -2\right) + \left(x + z\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+122}:\\ \;\;\;\;\left(a + \left(b \cdot \left(y + -2\right) + \left(x + z\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.15e+251)
     t_1
     (if (<= t -5.8e+19)
       (+ x (- (* a (- 1.0 t)) (* z (+ y -1.0))))
       (if (<= t 4.6e+122)
         (- (+ a (+ (* b (+ y -2.0)) (+ x z))) (* y z))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.15e+251) {
		tmp = t_1;
	} else if (t <= -5.8e+19) {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	} else if (t <= 4.6e+122) {
		tmp = (a + ((b * (y + -2.0)) + (x + z))) - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-1.15d+251)) then
        tmp = t_1
    else if (t <= (-5.8d+19)) then
        tmp = x + ((a * (1.0d0 - t)) - (z * (y + (-1.0d0))))
    else if (t <= 4.6d+122) then
        tmp = (a + ((b * (y + (-2.0d0))) + (x + z))) - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.15e+251) {
		tmp = t_1;
	} else if (t <= -5.8e+19) {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	} else if (t <= 4.6e+122) {
		tmp = (a + ((b * (y + -2.0)) + (x + z))) - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.15e+251:
		tmp = t_1
	elif t <= -5.8e+19:
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)))
	elif t <= 4.6e+122:
		tmp = (a + ((b * (y + -2.0)) + (x + z))) - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.15e+251)
		tmp = t_1;
	elseif (t <= -5.8e+19)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(z * Float64(y + -1.0))));
	elseif (t <= 4.6e+122)
		tmp = Float64(Float64(a + Float64(Float64(b * Float64(y + -2.0)) + Float64(x + z))) - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.15e+251)
		tmp = t_1;
	elseif (t <= -5.8e+19)
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	elseif (t <= 4.6e+122)
		tmp = (a + ((b * (y + -2.0)) + (x + z))) - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+251], t$95$1, If[LessEqual[t, -5.8e+19], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+122], N[(N[(a + N[(N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.14999999999999994e251 or 4.6000000000000001e122 < t

   1. Initial program 87.5%

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

   3. Taylor expanded in t around inf 82.1%

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

   if -1.14999999999999994e251 < t < -5.8e19

   1. Initial program 90.7%

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

   3. Taylor expanded in b around 0 82.5%

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

   if -5.8e19 < t < 4.6000000000000001e122

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 98.2%

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

      1. sub-neg 98.2%

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

      2. mul-1-neg 98.2%

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

      3. unsub-neg 98.2%

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

      4. *-commutative 98.2%

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

      5. sub-neg 98.2%

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

      6. metadata-eval 98.2%

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

      7. *-commutative 98.2%

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

      8. distribute-neg-in 98.2%

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

      9. mul-1-neg 98.2%

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

      10. remove-double-neg 98.2%

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

      11. distribute-lft-neg-in 98.2%

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

      12. +-commutative 98.2%

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

      13. distribute-neg-in 98.2%

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

      14. metadata-eval 98.2%

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

      15. sub-neg 98.2%

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

      16. *-commutative 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in t around 0 93.0%

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

      1. associate-+r+ 93.0%

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

      2. +-commutative 93.0%

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

      3. sub-neg 93.0%

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

      4. metadata-eval 93.0%

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

   8. Simplified 93.0%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+251}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+122}:\\ \;\;\;\;\left(a + \left(b \cdot \left(y + -2\right) + \left(x + z\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+18} \lor \neg \left(b \leq 3.4 \cdot 10^{-47}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1e+18) (not (<= b 3.4e-47)))
   (+ (+ x (* b (- (+ y t) 2.0))) (* z (- 1.0 y)))
   (+ x (- (* a (- 1.0 t)) (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1e+18) || !(b <= 3.4e-47)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	} else {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1d+18)) .or. (.not. (b <= 3.4d-47))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (z * (1.0d0 - y))
    else
        tmp = x + ((a * (1.0d0 - t)) - (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1e+18) || !(b <= 3.4e-47)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	} else {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1e+18) or not (b <= 3.4e-47):
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y))
	else:
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1e+18) || !(b <= 3.4e-47))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1e+18) || ~((b <= 3.4e-47)))
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	else
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1e+18], N[Not[LessEqual[b, 3.4e-47]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1e18 or 3.4000000000000002e-47 < b

   1. Initial program 90.8%

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

   3. Taylor expanded in a around 0 86.0%

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

   if -1e18 < b < 3.4000000000000002e-47

   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 95.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+18} \lor \neg \left(b \leq 3.4 \cdot 10^{-47}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+15}:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+37}:\\ \;\;\;\;z + \left(x + \left(t + -2\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -9.2e+92)
     t_1
     (if (<= y -7.5e+15)
       (+ a (+ x (* b (- y 2.0))))
       (if (<= y 7.5e+37) (+ z (+ x (* (+ t -2.0) b))) 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 <= -9.2e+92) {
		tmp = t_1;
	} else if (y <= -7.5e+15) {
		tmp = a + (x + (b * (y - 2.0)));
	} else if (y <= 7.5e+37) {
		tmp = z + (x + ((t + -2.0) * b));
	} 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 <= (-9.2d+92)) then
        tmp = t_1
    else if (y <= (-7.5d+15)) then
        tmp = a + (x + (b * (y - 2.0d0)))
    else if (y <= 7.5d+37) then
        tmp = z + (x + ((t + (-2.0d0)) * b))
    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 <= -9.2e+92) {
		tmp = t_1;
	} else if (y <= -7.5e+15) {
		tmp = a + (x + (b * (y - 2.0)));
	} else if (y <= 7.5e+37) {
		tmp = z + (x + ((t + -2.0) * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -9.2e+92:
		tmp = t_1
	elif y <= -7.5e+15:
		tmp = a + (x + (b * (y - 2.0)))
	elif y <= 7.5e+37:
		tmp = z + (x + ((t + -2.0) * b))
	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 <= -9.2e+92)
		tmp = t_1;
	elseif (y <= -7.5e+15)
		tmp = Float64(a + Float64(x + Float64(b * Float64(y - 2.0))));
	elseif (y <= 7.5e+37)
		tmp = Float64(z + Float64(x + Float64(Float64(t + -2.0) * b)));
	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 <= -9.2e+92)
		tmp = t_1;
	elseif (y <= -7.5e+15)
		tmp = a + (x + (b * (y - 2.0)));
	elseif (y <= 7.5e+37)
		tmp = z + (x + ((t + -2.0) * b));
	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, -9.2e+92], t$95$1, If[LessEqual[y, -7.5e+15], N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+37], N[(z + N[(x + N[(N[(t + -2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.19999999999999994e92 or 7.5000000000000003e37 < y

   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 y around inf 77.3%

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

   if -9.19999999999999994e92 < y < -7.5e15

   1. Initial program 94.7%

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

   3. Taylor expanded in y around 0 94.7%

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

      1. sub-neg 94.7%

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

      2. mul-1-neg 94.7%

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

      3. unsub-neg 94.7%

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

      4. *-commutative 94.7%

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

      5. sub-neg 94.7%

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

      6. metadata-eval 94.7%

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

      7. *-commutative 94.7%

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

      8. distribute-neg-in 94.7%

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

      9. mul-1-neg 94.7%

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

      10. remove-double-neg 94.7%

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

      11. distribute-lft-neg-in 94.7%

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

      12. +-commutative 94.7%

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

      13. distribute-neg-in 94.7%

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

      14. metadata-eval 94.7%

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

      15. sub-neg 94.7%

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

      16. *-commutative 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in t around 0 63.9%

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

      1. associate-+r+ 63.9%

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

      2. +-commutative 63.9%

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

      3. sub-neg 63.9%

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

      4. metadata-eval 63.9%

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

   8. Simplified 63.9%

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

   9. Taylor expanded in z around 0 58.9%

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

   if -7.5e15 < y < 7.5000000000000003e37

   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 a around 0 76.8%

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

   4. Taylor expanded in y around 0 74.5%

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

      1. sub-neg 74.5%

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

      2. sub-neg 74.5%

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

      3. metadata-eval 74.5%

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

      4. neg-mul-1 74.5%

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

      5. remove-double-neg 74.5%

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

   6. Simplified 74.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+15}:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+37}:\\ \;\;\;\;z + \left(x + \left(t + -2\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+133} \lor \neg \left(b \leq 1.62 \cdot 10^{+134}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + a \cdot \left(1 - t\right)\right)\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.5e+133) (not (<= b 1.62e+134)))
   (* b (- (+ y t) 2.0))
   (- (+ x (+ z (* a (- 1.0 t)))) (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+133) || !(b <= 1.62e+134)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = (x + (z + (a * (1.0 - t)))) - (y * 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 ((b <= (-7.5d+133)) .or. (.not. (b <= 1.62d+134))) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = (x + (z + (a * (1.0d0 - t)))) - (y * 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 ((b <= -7.5e+133) || !(b <= 1.62e+134)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.5e+133) or not (b <= 1.62e+134):
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.5e+133) || !(b <= 1.62e+134))
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = Float64(Float64(x + Float64(z + Float64(a * Float64(1.0 - t)))) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.5e+133) || ~((b <= 1.62e+134)))
		tmp = b * ((y + t) - 2.0);
	else
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.5e+133], N[Not[LessEqual[b, 1.62e+134]], $MachinePrecision]], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.49999999999999992e133 or 1.6199999999999999e134 < b

   1. Initial program 91.5%

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

   3. Taylor expanded in b around inf 88.1%

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

   if -7.49999999999999992e133 < b < 1.6199999999999999e134

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0 96.2%

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

      1. sub-neg 96.2%

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

      2. mul-1-neg 96.2%

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

      3. unsub-neg 96.2%

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

      4. *-commutative 96.2%

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

      5. sub-neg 96.2%

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

      6. metadata-eval 96.2%

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

      7. *-commutative 96.2%

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

      8. distribute-neg-in 96.2%

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

      9. mul-1-neg 96.2%

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

      10. remove-double-neg 96.2%

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

      11. distribute-lft-neg-in 96.2%

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

      12. +-commutative 96.2%

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

      13. distribute-neg-in 96.2%

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

      14. metadata-eval 96.2%

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

      15. sub-neg 96.2%

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

      16. *-commutative 96.2%

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

   5. Simplified 96.2%

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

   6. Taylor expanded in b around 0 85.8%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+133} \lor \neg \left(b \leq 1.62 \cdot 10^{+134}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + a \cdot \left(1 - t\right)\right)\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+133} \lor \neg \left(b \leq 1.85 \cdot 10^{+133}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8e+133) (not (<= b 1.85e+133)))
   (* b (- (+ y t) 2.0))
   (+ x (- (* a (- 1.0 t)) (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8e+133) || !(b <= 1.85e+133)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-8d+133)) .or. (.not. (b <= 1.85d+133))) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = x + ((a * (1.0d0 - t)) - (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8e+133) || !(b <= 1.85e+133)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -8e+133) or not (b <= 1.85e+133):
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8e+133) || !(b <= 1.85e+133))
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -8e+133) || ~((b <= 1.85e+133)))
		tmp = b * ((y + t) - 2.0);
	else
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8e+133], N[Not[LessEqual[b, 1.85e+133]], $MachinePrecision]], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.0000000000000002e133 or 1.85000000000000012e133 < b

   1. Initial program 91.5%

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

   3. Taylor expanded in b around inf 88.1%

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

   if -8.0000000000000002e133 < b < 1.85000000000000012e133

   1. Initial program 96.2%

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

   3. Taylor expanded in b around 0 85.8%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+133} \lor \neg \left(b \leq 1.85 \cdot 10^{+133}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 180000000:\\ \;\;\;\;z + \left(x + -2 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.2e+95)
     t_1
     (if (<= y -2e-30)
       (* t (- b a))
       (if (<= y 180000000.0) (+ z (+ x (* -2.0 b))) 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 <= -1.2e+95) {
		tmp = t_1;
	} else if (y <= -2e-30) {
		tmp = t * (b - a);
	} else if (y <= 180000000.0) {
		tmp = z + (x + (-2.0 * b));
	} 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 <= (-1.2d+95)) then
        tmp = t_1
    else if (y <= (-2d-30)) then
        tmp = t * (b - a)
    else if (y <= 180000000.0d0) then
        tmp = z + (x + ((-2.0d0) * b))
    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 <= -1.2e+95) {
		tmp = t_1;
	} else if (y <= -2e-30) {
		tmp = t * (b - a);
	} else if (y <= 180000000.0) {
		tmp = z + (x + (-2.0 * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.2e+95:
		tmp = t_1
	elif y <= -2e-30:
		tmp = t * (b - a)
	elif y <= 180000000.0:
		tmp = z + (x + (-2.0 * b))
	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 <= -1.2e+95)
		tmp = t_1;
	elseif (y <= -2e-30)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 180000000.0)
		tmp = Float64(z + Float64(x + Float64(-2.0 * b)));
	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 <= -1.2e+95)
		tmp = t_1;
	elseif (y <= -2e-30)
		tmp = t * (b - a);
	elseif (y <= 180000000.0)
		tmp = z + (x + (-2.0 * b));
	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, -1.2e+95], t$95$1, If[LessEqual[y, -2e-30], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 180000000.0], N[(z + N[(x + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e95 or 1.8e8 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 76.3%

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

   if -1.2e95 < y < -2e-30

   1. Initial program 96.8%

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

   3. Taylor expanded in t around inf 49.7%

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

   if -2e-30 < y < 1.8e8

   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 a around 0 77.9%

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

   4. Taylor expanded in y around 0 76.7%

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

      1. sub-neg 76.7%

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

      2. sub-neg 76.7%

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

      3. metadata-eval 76.7%

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

      4. neg-mul-1 76.7%

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

      5. remove-double-neg 76.7%

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

   6. Simplified 76.7%

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

   7. Taylor expanded in t around 0 60.4%

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

      1. *-commutative 60.4%

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

   9. Simplified 60.4%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 180000000:\\ \;\;\;\;z + \left(x + -2 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3.15 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+38}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -3.15e+88)
     t_1
     (if (<= y -5.5e-15)
       (* a (- 1.0 t))
       (if (<= y 1.46e+38) (+ x (* b (- t 2.0))) 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 <= -3.15e+88) {
		tmp = t_1;
	} else if (y <= -5.5e-15) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.46e+38) {
		tmp = x + (b * (t - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-3.15d+88)) then
        tmp = t_1
    else if (y <= (-5.5d-15)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 1.46d+38) then
        tmp = x + (b * (t - 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -3.15e+88) {
		tmp = t_1;
	} else if (y <= -5.5e-15) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.46e+38) {
		tmp = x + (b * (t - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -3.15e+88:
		tmp = t_1
	elif y <= -5.5e-15:
		tmp = a * (1.0 - t)
	elif y <= 1.46e+38:
		tmp = x + (b * (t - 2.0))
	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 <= -3.15e+88)
		tmp = t_1;
	elseif (y <= -5.5e-15)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 1.46e+38)
		tmp = Float64(x + Float64(b * Float64(t - 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -3.15e+88)
		tmp = t_1;
	elseif (y <= -5.5e-15)
		tmp = a * (1.0 - t);
	elseif (y <= 1.46e+38)
		tmp = x + (b * (t - 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.15e+88], t$95$1, If[LessEqual[y, -5.5e-15], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.46e+38], N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.15e88 or 1.46000000000000008e38 < y

   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 y around inf 77.3%

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

   if -3.15e88 < y < -5.5000000000000002e-15

   1. Initial program 96.5%

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

   3. Taylor expanded in a around inf 51.3%

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

   if -5.5000000000000002e-15 < y < 1.46000000000000008e38

   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 a around 0 78.2%

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

   4. Taylor expanded in y around 0 76.5%

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

      1. sub-neg 76.5%

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

      2. sub-neg 76.5%

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

      3. metadata-eval 76.5%

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

      4. neg-mul-1 76.5%

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

      5. remove-double-neg 76.5%

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

   6. Simplified 76.5%

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

   7. Taylor expanded in z around 0 56.1%

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

Alternative 11: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1720000000:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -9e+88)
     t_1
     (if (<= y -2.1e-51) (* t (- b a)) (if (<= y 1720000000.0) (+ x z) 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 <= -9e+88) {
		tmp = t_1;
	} else if (y <= -2.1e-51) {
		tmp = t * (b - a);
	} else if (y <= 1720000000.0) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-9d+88)) then
        tmp = t_1
    else if (y <= (-2.1d-51)) then
        tmp = t * (b - a)
    else if (y <= 1720000000.0d0) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -9e+88) {
		tmp = t_1;
	} else if (y <= -2.1e-51) {
		tmp = t * (b - a);
	} else if (y <= 1720000000.0) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -9e+88:
		tmp = t_1
	elif y <= -2.1e-51:
		tmp = t * (b - a)
	elif y <= 1720000000.0:
		tmp = x + z
	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 <= -9e+88)
		tmp = t_1;
	elseif (y <= -2.1e-51)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 1720000000.0)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -9e+88)
		tmp = t_1;
	elseif (y <= -2.1e-51)
		tmp = t * (b - a);
	elseif (y <= 1720000000.0)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+88], t$95$1, If[LessEqual[y, -2.1e-51], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1720000000.0], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9e88 or 1.72e9 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 76.3%

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

   if -9e88 < y < -2.10000000000000002e-51

   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 inf 49.8%

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

   if -2.10000000000000002e-51 < y < 1.72e9

   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 a around 0 78.8%

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

   4. Taylor expanded in b around 0 48.3%

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

   5. Taylor expanded in y around 0 47.1%

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

      1. sub-neg 47.1%

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

      2. neg-mul-1 47.1%

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

      3. remove-double-neg 47.1%

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

   7. Simplified 47.1%

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

Alternative 12: 68.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+18} \lor \neg \left(b \leq 1.6 \cdot 10^{+134}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + a\right)\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.4e+18) (not (<= b 1.6e+134)))
   (* b (- (+ y t) 2.0))
   (- (+ x (+ z a)) (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.4e+18) || !(b <= 1.6e+134)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = (x + (z + a)) - (y * 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 ((b <= (-3.4d+18)) .or. (.not. (b <= 1.6d+134))) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = (x + (z + a)) - (y * 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 ((b <= -3.4e+18) || !(b <= 1.6e+134)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = (x + (z + a)) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.4e+18) or not (b <= 1.6e+134):
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = (x + (z + a)) - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.4e+18) || !(b <= 1.6e+134))
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = Float64(Float64(x + Float64(z + a)) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.4e+18) || ~((b <= 1.6e+134)))
		tmp = b * ((y + t) - 2.0);
	else
		tmp = (x + (z + a)) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.4e+18], N[Not[LessEqual[b, 1.6e+134]], $MachinePrecision]], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.4e18 or 1.6e134 < b

   1. Initial program 89.1%

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

   3. Taylor expanded in b around inf 80.1%

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

   if -3.4e18 < b < 1.6e134

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 98.1%

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

      1. sub-neg 98.1%

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

      2. mul-1-neg 98.1%

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

      3. unsub-neg 98.1%

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

      4. *-commutative 98.1%

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

      5. sub-neg 98.1%

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

      6. metadata-eval 98.1%

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

      7. *-commutative 98.1%

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

      8. distribute-neg-in 98.1%

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

      9. mul-1-neg 98.1%

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

      10. remove-double-neg 98.1%

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

      11. distribute-lft-neg-in 98.1%

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

      12. +-commutative 98.1%

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

      13. distribute-neg-in 98.1%

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

      14. metadata-eval 98.1%

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

      15. sub-neg 98.1%

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

      16. *-commutative 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in b around 0 89.2%

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

   7. Taylor expanded in t around 0 71.6%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+18} \lor \neg \left(b \leq 1.6 \cdot 10^{+134}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + a\right)\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2850000000:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -1.4e+100)
     t_1
     (if (<= y -5e-48) (* t (- b a)) (if (<= y 2850000000.0) (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -1.4e+100) {
		tmp = t_1;
	} else if (y <= -5e-48) {
		tmp = t * (b - a);
	} else if (y <= 2850000000.0) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-1.4d+100)) then
        tmp = t_1
    else if (y <= (-5d-48)) then
        tmp = t * (b - a)
    else if (y <= 2850000000.0d0) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -1.4e+100) {
		tmp = t_1;
	} else if (y <= -5e-48) {
		tmp = t * (b - a);
	} else if (y <= 2850000000.0) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -1.4e+100:
		tmp = t_1
	elif y <= -5e-48:
		tmp = t * (b - a)
	elif y <= 2850000000.0:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -1.4e+100)
		tmp = t_1;
	elseif (y <= -5e-48)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 2850000000.0)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -1.4e+100)
		tmp = t_1;
	elseif (y <= -5e-48)
		tmp = t * (b - a);
	elseif (y <= 2850000000.0)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -1.4e+100], t$95$1, If[LessEqual[y, -5e-48], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2850000000.0], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3999999999999999e100 or 2.85e9 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 76.3%

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

   4. Taylor expanded in b around 0 46.9%

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

      1. neg-mul-1 46.9%

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

   6. Simplified 46.9%

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

   if -1.3999999999999999e100 < y < -4.9999999999999999e-48

   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 inf 49.8%

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

   if -4.9999999999999999e-48 < y < 2.85e9

   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 a around 0 78.8%

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

   4. Taylor expanded in b around 0 48.3%

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

   5. Taylor expanded in y around 0 47.1%

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

      1. sub-neg 47.1%

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

      2. neg-mul-1 47.1%

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

      3. remove-double-neg 47.1%

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

   7. Simplified 47.1%

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

Alternative 14: 39.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-14}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 430000000000:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -1.06e+90)
     t_1
     (if (<= y -3.1e-14)
       (* a (- 1.0 t))
       (if (<= y 430000000000.0) (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -1.06e+90) {
		tmp = t_1;
	} else if (y <= -3.1e-14) {
		tmp = a * (1.0 - t);
	} else if (y <= 430000000000.0) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-1.06d+90)) then
        tmp = t_1
    else if (y <= (-3.1d-14)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 430000000000.0d0) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -1.06e+90) {
		tmp = t_1;
	} else if (y <= -3.1e-14) {
		tmp = a * (1.0 - t);
	} else if (y <= 430000000000.0) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -1.06e+90:
		tmp = t_1
	elif y <= -3.1e-14:
		tmp = a * (1.0 - t)
	elif y <= 430000000000.0:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -1.06e+90)
		tmp = t_1;
	elseif (y <= -3.1e-14)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 430000000000.0)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -1.06e+90)
		tmp = t_1;
	elseif (y <= -3.1e-14)
		tmp = a * (1.0 - t);
	elseif (y <= 430000000000.0)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -1.06e+90], t$95$1, If[LessEqual[y, -3.1e-14], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 430000000000.0], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.06e90 or 4.3e11 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 76.3%

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

   4. Taylor expanded in b around 0 46.9%

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

      1. neg-mul-1 46.9%

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

   6. Simplified 46.9%

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

   if -1.06e90 < y < -3.10000000000000004e-14

   1. Initial program 96.5%

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

   3. Taylor expanded in a around inf 51.3%

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

   if -3.10000000000000004e-14 < y < 4.3e11

   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 a around 0 78.4%

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

   4. Taylor expanded in b around 0 47.4%

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

   5. Taylor expanded in y around 0 46.2%

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

      1. sub-neg 46.2%

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

      2. neg-mul-1 46.2%

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

      3. remove-double-neg 46.2%

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

   7. Simplified 46.2%

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

Alternative 15: 38.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 410000000000:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -4.3e+91)
     t_1
     (if (<= y -2.9e-15) (* t (- a)) (if (<= y 410000000000.0) (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -4.3e+91) {
		tmp = t_1;
	} else if (y <= -2.9e-15) {
		tmp = t * -a;
	} else if (y <= 410000000000.0) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-4.3d+91)) then
        tmp = t_1
    else if (y <= (-2.9d-15)) then
        tmp = t * -a
    else if (y <= 410000000000.0d0) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -4.3e+91) {
		tmp = t_1;
	} else if (y <= -2.9e-15) {
		tmp = t * -a;
	} else if (y <= 410000000000.0) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -4.3e+91:
		tmp = t_1
	elif y <= -2.9e-15:
		tmp = t * -a
	elif y <= 410000000000.0:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -4.3e+91)
		tmp = t_1;
	elseif (y <= -2.9e-15)
		tmp = Float64(t * Float64(-a));
	elseif (y <= 410000000000.0)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -4.3e+91)
		tmp = t_1;
	elseif (y <= -2.9e-15)
		tmp = t * -a;
	elseif (y <= 410000000000.0)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -4.3e+91], t$95$1, If[LessEqual[y, -2.9e-15], N[(t * (-a)), $MachinePrecision], If[LessEqual[y, 410000000000.0], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3000000000000001e91 or 4.1e11 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 76.3%

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

   4. Taylor expanded in b around 0 46.9%

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

      1. neg-mul-1 46.9%

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

   6. Simplified 46.9%

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

   if -4.3000000000000001e91 < y < -2.90000000000000019e-15

   1. Initial program 96.5%

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

   3. Taylor expanded in t around inf 49.6%

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

   4. Taylor expanded in b around 0 32.5%

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

      1. neg-mul-1 32.5%

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

   6. Simplified 32.5%

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

   if -2.90000000000000019e-15 < y < 4.1e11

   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 a around 0 78.4%

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

   4. Taylor expanded in b around 0 47.4%

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

   5. Taylor expanded in y around 0 46.2%

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

      1. sub-neg 46.2%

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

      2. neg-mul-1 46.2%

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

      3. remove-double-neg 46.2%

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

   7. Simplified 46.2%

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

Alternative 16: 68.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{-9}:\\ \;\;\;\;t\_1 - y \cdot z\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+133}:\\ \;\;\;\;\left(x + \left(z + a\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -6e-9)
     (- t_1 (* y z))
     (if (<= b 1.9e+133) (- (+ x (+ z a)) (* y z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -6e-9) {
		tmp = t_1 - (y * z);
	} else if (b <= 1.9e+133) {
		tmp = (x + (z + a)) - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-6d-9)) then
        tmp = t_1 - (y * z)
    else if (b <= 1.9d+133) then
        tmp = (x + (z + a)) - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -6e-9) {
		tmp = t_1 - (y * z);
	} else if (b <= 1.9e+133) {
		tmp = (x + (z + a)) - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -6e-9:
		tmp = t_1 - (y * z)
	elif b <= 1.9e+133:
		tmp = (x + (z + a)) - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -6e-9)
		tmp = Float64(t_1 - Float64(y * z));
	elseif (b <= 1.9e+133)
		tmp = Float64(Float64(x + Float64(z + a)) - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -6e-9)
		tmp = t_1 - (y * z);
	elseif (b <= 1.9e+133)
		tmp = (x + (z + a)) - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e-9], N[(t$95$1 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e+133], N[(N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.99999999999999996e-9

   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 y around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. *-commutative 73.4%

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

      3. distribute-lft-neg-in 73.4%

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

   5. Simplified 73.4%

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

   if -5.99999999999999996e-9 < b < 1.9000000000000001e133

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 98.1%

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

      1. sub-neg 98.1%

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

      2. mul-1-neg 98.1%

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

      3. unsub-neg 98.1%

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

      4. *-commutative 98.1%

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

      5. sub-neg 98.1%

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

      6. metadata-eval 98.1%

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

      7. *-commutative 98.1%

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

      8. distribute-neg-in 98.1%

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

      9. mul-1-neg 98.1%

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

      10. remove-double-neg 98.1%

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

      11. distribute-lft-neg-in 98.1%

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

      12. +-commutative 98.1%

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

      13. distribute-neg-in 98.1%

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

      14. metadata-eval 98.1%

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

      15. sub-neg 98.1%

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

      16. *-commutative 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in b around 0 89.6%

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

   7. Taylor expanded in t around 0 72.5%

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

   if 1.9000000000000001e133 < b

   1. Initial program 90.3%

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

   3. Taylor expanded in b around inf 93.6%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+133}:\\ \;\;\;\;\left(x + \left(z + a\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 61.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+18} \lor \neg \left(b \leq 1.6 \cdot 10^{+133}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.4e+18) (not (<= b 1.6e+133)))
   (* b (- (+ y t) 2.0))
   (- x (* z (+ y -1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.4e+18) || !(b <= 1.6e+133)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x - (z * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.4d+18)) .or. (.not. (b <= 1.6d+133))) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = x - (z * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.4e+18) || !(b <= 1.6e+133)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x - (z * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.4e+18) or not (b <= 1.6e+133):
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = x - (z * (y + -1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.4e+18) || !(b <= 1.6e+133))
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = Float64(x - Float64(z * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.4e+18) || ~((b <= 1.6e+133)))
		tmp = b * ((y + t) - 2.0);
	else
		tmp = x - (z * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.4e+18], N[Not[LessEqual[b, 1.6e+133]], $MachinePrecision]], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.4e18 or 1.59999999999999999e133 < b

   1. Initial program 89.1%

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

   3. Taylor expanded in b around inf 80.1%

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

   if -3.4e18 < b < 1.59999999999999999e133

   1. Initial program 98.1%

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

   3. Taylor expanded in a around 0 70.0%

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

   4. Taylor expanded in b around 0 61.0%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+18} \lor \neg \left(b \leq 1.6 \cdot 10^{+133}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1660000 \lor \neg \left(y \leq 4.1 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1660000.0) (not (<= y 4.1e+93))) (* y b) (+ x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1660000.0) || !(y <= 4.1e+93)) {
		tmp = y * b;
	} else {
		tmp = x + 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 ((y <= (-1660000.0d0)) .or. (.not. (y <= 4.1d+93))) then
        tmp = y * b
    else
        tmp = x + 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 ((y <= -1660000.0) || !(y <= 4.1e+93)) {
		tmp = y * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1660000.0) or not (y <= 4.1e+93):
		tmp = y * b
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1660000.0) || !(y <= 4.1e+93))
		tmp = Float64(y * b);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1660000.0) || ~((y <= 4.1e+93)))
		tmp = y * b;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1660000.0], N[Not[LessEqual[y, 4.1e+93]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.66e6 or 4.1000000000000001e93 < y

   1. Initial program 89.9%

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

   3. Taylor expanded in y around inf 73.3%

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

   4. Taylor expanded in b around inf 42.6%

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

      1. *-commutative 42.6%

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

   6. Simplified 42.6%

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

   if -1.66e6 < y < 4.1000000000000001e93

   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 a around 0 75.2%

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

   4. Taylor expanded in b around 0 47.4%

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

   5. Taylor expanded in y around 0 40.2%

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

      1. sub-neg 40.2%

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

      2. neg-mul-1 40.2%

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

      3. remove-double-neg 40.2%

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

   7. Simplified 40.2%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1660000 \lor \neg \left(y \leq 4.1 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 26.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{-11} \lor \neg \left(b \leq 2.6 \cdot 10^{+28}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.5e-11) (not (<= b 2.6e+28))) (* y b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.5e-11) || !(b <= 2.6e+28)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.5d-11)) .or. (.not. (b <= 2.6d+28))) then
        tmp = y * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.5e-11) || !(b <= 2.6e+28)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.5e-11) or not (b <= 2.6e+28):
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.5e-11) || !(b <= 2.6e+28))
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.5e-11) || ~((b <= 2.6e+28)))
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.5e-11], N[Not[LessEqual[b, 2.6e+28]], $MachinePrecision]], N[(y * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -3.50000000000000019e-11 or 2.6000000000000002e28 < b

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 46.4%

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

   4. Taylor expanded in b around inf 37.7%

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

      1. *-commutative 37.7%

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

   6. Simplified 37.7%

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

   if -3.50000000000000019e-11 < b < 2.6000000000000002e28

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 27.7%

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

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{-11} \lor \neg \left(b \leq 2.6 \cdot 10^{+28}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+16} \lor \neg \left(b \leq 1.6 \cdot 10^{+133}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.2e+16) (not (<= b 1.6e+133))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.2e+16) || !(b <= 1.6e+133)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.2d+16)) .or. (.not. (b <= 1.6d+133))) then
        tmp = t * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.2e+16) || !(b <= 1.6e+133)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.2e+16) or not (b <= 1.6e+133):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.2e+16) || !(b <= 1.6e+133))
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.2e+16) || ~((b <= 1.6e+133)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.2e+16], N[Not[LessEqual[b, 1.6e+133]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -6.2e16 or 1.59999999999999999e133 < b

   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 t around inf 37.1%

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

   4. Taylor expanded in b around inf 31.6%

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

      1. *-commutative 31.6%

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

   6. Simplified 31.6%

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

   if -6.2e16 < b < 1.59999999999999999e133

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 24.5%

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

4. Final simplification 27.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+16} \lor \neg \left(b \leq 1.6 \cdot 10^{+133}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 21.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+49}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.7e+49) a (if (<= a 4.3e+85) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.7e+49) {
		tmp = a;
	} else if (a <= 4.3e+85) {
		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 <= (-3.7d+49)) then
        tmp = a
    else if (a <= 4.3d+85) 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 <= -3.7e+49) {
		tmp = a;
	} else if (a <= 4.3e+85) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.7e+49:
		tmp = a
	elif a <= 4.3e+85:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.7e+49)
		tmp = a;
	elseif (a <= 4.3e+85)
		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 <= -3.7e+49)
		tmp = a;
	elseif (a <= 4.3e+85)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.7e+49], a, If[LessEqual[a, 4.3e+85], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -3.70000000000000018e49 or 4.2999999999999999e85 < a

   1. Initial program 91.7%

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

   3. Taylor expanded in y around 0 91.7%

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

      1. sub-neg 91.7%

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

      2. mul-1-neg 91.7%

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

      3. unsub-neg 91.7%

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

      4. *-commutative 91.7%

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

      5. sub-neg 91.7%

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

      6. metadata-eval 91.7%

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

      7. *-commutative 91.7%

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

      8. distribute-neg-in 91.7%

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

      9. mul-1-neg 91.7%

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

      10. remove-double-neg 91.7%

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

      11. distribute-lft-neg-in 91.7%

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

      12. +-commutative 91.7%

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

      13. distribute-neg-in 91.7%

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

      14. metadata-eval 91.7%

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

      15. sub-neg 91.7%

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

      16. *-commutative 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in t around 0 62.8%

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

      1. associate-+r+ 62.8%

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

      2. +-commutative 62.8%

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

      3. sub-neg 62.8%

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

      4. metadata-eval 62.8%

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

   8. Simplified 62.8%

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

   9. Taylor expanded in a around inf 20.5%

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

   if -3.70000000000000018e49 < a < 4.2999999999999999e85

   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 x around inf 23.8%

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

Alternative 22: 10.7% 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 94.9%

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

3. Taylor expanded in y around 0 94.9%

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

   1. sub-neg 94.9%

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

   2. mul-1-neg 94.9%

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

   3. unsub-neg 94.9%

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

   4. *-commutative 94.9%

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

   5. sub-neg 94.9%

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

   6. metadata-eval 94.9%

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

   7. *-commutative 94.9%

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

   8. distribute-neg-in 94.9%

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

   9. mul-1-neg 94.9%

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

   10. remove-double-neg 94.9%

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

   11. distribute-lft-neg-in 94.9%

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

   12. +-commutative 94.9%

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

   13. distribute-neg-in 94.9%

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

   14. metadata-eval 94.9%

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

   15. sub-neg 94.9%

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

   16. *-commutative 94.9%

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

5. Simplified 94.9%

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

6. Taylor expanded in t around 0 72.5%

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

   1. associate-+r+ 72.5%

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

   2. +-commutative 72.5%

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

   3. sub-neg 72.5%

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

   4. metadata-eval 72.5%

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

8. Simplified 72.5%

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

9. Taylor expanded in a around inf 9.6%

   \[\leadsto \color{blue}{a} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024185 
(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)))