Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.4% → 96.3%

Time: 10.4s

Alternatives: 12

Speedup: 0.6×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+303}:\\ \;\;\;\;\frac{x \cdot \left(z \cdot t + y \cdot \left(z + -1\right)\right)}{z \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 -5e+303)
     (/ (* x (+ (* z t) (* y (+ z -1.0)))) (* z (+ z -1.0)))
     (* t_1 x))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -5e+303) {
		tmp = (x * ((z * t) + (y * (z + -1.0)))) / (z * (z + -1.0));
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / z) + (t / (z + (-1.0d0)))
    if (t_1 <= (-5d+303)) then
        tmp = (x * ((z * t) + (y * (z + (-1.0d0))))) / (z * (z + (-1.0d0)))
    else
        tmp = t_1 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -5e+303) {
		tmp = (x * ((z * t) + (y * (z + -1.0)))) / (z * (z + -1.0));
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if t_1 <= -5e+303:
		tmp = (x * ((z * t) + (y * (z + -1.0)))) / (z * (z + -1.0))
	else:
		tmp = t_1 * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t_1 <= -5e+303)
		tmp = Float64(Float64(x * Float64(Float64(z * t) + Float64(y * Float64(z + -1.0)))) / Float64(z * Float64(z + -1.0)));
	else
		tmp = Float64(t_1 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -5e+303)
		tmp = (x * ((z * t) + (y * (z + -1.0)))) / (z * (z + -1.0));
	else
		tmp = t_1 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+303], N[(N[(x * N[(N[(z * t), $MachinePrecision] + N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -4.9999999999999997e303

   1. Initial program 66.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 66.7%

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

      2. frac-sub 66.7%

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

      3. associate-*l/ 100.0%

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

   4. Applied egg-rr 100.0%

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

   if -4.9999999999999997e303 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 96.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -5 \cdot 10^{+303}:\\ \;\;\;\;\frac{x \cdot \left(z \cdot t + y \cdot \left(z + -1\right)\right)}{z \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 61.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-x\right)\\ t_2 := \frac{y \cdot x}{z}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-276}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- x))) (t_2 (/ (* y x) z)))
   (if (<= y -1.55e+40)
     t_2
     (if (<= y -1.75e-122)
       (* x (/ t z))
       (if (<= y -1.15e-150)
         t_1
         (if (<= y 4.8e-276) (/ (* t x) z) (if (<= y 1.1e-127) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -x;
	double t_2 = (y * x) / z;
	double tmp;
	if (y <= -1.55e+40) {
		tmp = t_2;
	} else if (y <= -1.75e-122) {
		tmp = x * (t / z);
	} else if (y <= -1.15e-150) {
		tmp = t_1;
	} else if (y <= 4.8e-276) {
		tmp = (t * x) / z;
	} else if (y <= 1.1e-127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * -x
    t_2 = (y * x) / z
    if (y <= (-1.55d+40)) then
        tmp = t_2
    else if (y <= (-1.75d-122)) then
        tmp = x * (t / z)
    else if (y <= (-1.15d-150)) then
        tmp = t_1
    else if (y <= 4.8d-276) then
        tmp = (t * x) / z
    else if (y <= 1.1d-127) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * -x;
	double t_2 = (y * x) / z;
	double tmp;
	if (y <= -1.55e+40) {
		tmp = t_2;
	} else if (y <= -1.75e-122) {
		tmp = x * (t / z);
	} else if (y <= -1.15e-150) {
		tmp = t_1;
	} else if (y <= 4.8e-276) {
		tmp = (t * x) / z;
	} else if (y <= 1.1e-127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -x
	t_2 = (y * x) / z
	tmp = 0
	if y <= -1.55e+40:
		tmp = t_2
	elif y <= -1.75e-122:
		tmp = x * (t / z)
	elif y <= -1.15e-150:
		tmp = t_1
	elif y <= 4.8e-276:
		tmp = (t * x) / z
	elif y <= 1.1e-127:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-x))
	t_2 = Float64(Float64(y * x) / z)
	tmp = 0.0
	if (y <= -1.55e+40)
		tmp = t_2;
	elseif (y <= -1.75e-122)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= -1.15e-150)
		tmp = t_1;
	elseif (y <= 4.8e-276)
		tmp = Float64(Float64(t * x) / z);
	elseif (y <= 1.1e-127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -x;
	t_2 = (y * x) / z;
	tmp = 0.0;
	if (y <= -1.55e+40)
		tmp = t_2;
	elseif (y <= -1.75e-122)
		tmp = x * (t / z);
	elseif (y <= -1.15e-150)
		tmp = t_1;
	elseif (y <= 4.8e-276)
		tmp = (t * x) / z;
	elseif (y <= 1.1e-127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-x)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -1.55e+40], t$95$2, If[LessEqual[y, -1.75e-122], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-150], t$95$1, If[LessEqual[y, 4.8e-276], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.1e-127], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.5499999999999999e40 or 1.1000000000000001e-127 < y

   1. Initial program 91.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.1%

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

   if -1.5499999999999999e40 < y < -1.7500000000000001e-122

   1. Initial program 99.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.8%

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

      1. *-commutative 72.8%

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

      2. remove-double-neg 72.8%

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

      3. cancel-sign-sub-inv 72.8%

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

      4. metadata-eval 72.8%

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

      5. *-lft-identity 72.8%

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

      6. distribute-neg-out 72.8%

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

      7. neg-mul-1 72.8%

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

      8. sub-neg 72.8%

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

      9. distribute-lft-neg-in 72.8%

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

      10. *-commutative 72.8%

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

      11. distribute-neg-frac 72.8%

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

      12. associate-/l* 86.0%

          \[\leadsto -\color{blue}{x \cdot \frac{-1 \cdot y - t}{z}} \]

      13. distribute-rgt-neg-in 86.0%

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

      14. distribute-neg-frac 86.0%

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

   5. Simplified 86.0%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   6. Taylor expanded in y around inf 68.9%

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

      1. times-frac 75.5%

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

      2. distribute-rgt1-in 75.5%

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

   8. Simplified 75.5%

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

   9. Taylor expanded in y around 0 44.2%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   10. Step-by-step derivation

       1. *-commutative 44.2%

          \[\leadsto \frac{\color{blue}{x \cdot t}}{z} \]

       2. associate-/l* 57.4%

          \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]

   11. Simplified 57.4%

       \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]

   if -1.7500000000000001e-122 < y < -1.15000000000000001e-150 or 4.79999999999999965e-276 < y < 1.1000000000000001e-127

   1. Initial program 99.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. distribute-neg-frac 99.9%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\frac{-t}{1 - z}} \cdot x \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x + \frac{-t}{1 - z} \cdot x} \]

   5. Taylor expanded in z around 0 76.7%

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

      1. +-commutative 76.7%

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

      2. associate-*r* 79.9%

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

      3. *-commutative 79.9%

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

      4. neg-mul-1 79.9%

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

      5. distribute-lft-neg-in 79.9%

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

      6. cancel-sign-sub-inv 79.9%

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

      7. *-commutative 79.9%

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

      8. associate-*r* 79.5%

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

      9. distribute-rgt-out-- 79.5%

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

   7. Simplified 79.5%

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

   8. Taylor expanded in y around 0 73.4%

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

      1. associate-*r* 73.4%

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

      2. neg-mul-1 73.4%

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

   10. Simplified 73.4%

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

   if -1.15000000000000001e-150 < y < 4.79999999999999965e-276

   1. Initial program 94.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 69.3%

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

      1. *-commutative 69.3%

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

      2. remove-double-neg 69.3%

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

      3. cancel-sign-sub-inv 69.3%

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

      4. metadata-eval 69.3%

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

      5. *-lft-identity 69.3%

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

      6. distribute-neg-out 69.3%

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

      7. neg-mul-1 69.3%

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

      8. sub-neg 69.3%

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

      9. distribute-lft-neg-in 69.3%

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

      10. *-commutative 69.3%

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

      11. distribute-neg-frac 69.3%

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

      12. associate-/l* 69.5%

          \[\leadsto -\color{blue}{x \cdot \frac{-1 \cdot y - t}{z}} \]

      13. distribute-rgt-neg-in 69.5%

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

      14. distribute-neg-frac 69.5%

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

   5. Simplified 69.5%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   6. Taylor expanded in t around 0 69.3%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z} + \frac{x \cdot y}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 60.9%

         \[\leadsto \color{blue}{t \cdot \frac{x}{z}} + \frac{x \cdot y}{z} \]

      2. *-commutative 60.9%

         \[\leadsto t \cdot \frac{x}{z} + \frac{\color{blue}{y \cdot x}}{z} \]

      3. associate-/l* 63.7%

         \[\leadsto t \cdot \frac{x}{z} + \color{blue}{y \cdot \frac{x}{z}} \]

      4. distribute-rgt-out 63.7%

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

      5. +-commutative 63.7%

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

   8. Simplified 63.7%

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

   9. Taylor expanded in y around 0 63.5%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+40}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-276}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -2.85 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+250} \lor \neg \left(t \leq 5.6 \cdot 10^{+298}\right):\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -2.85e+147)
     t_1
     (if (<= t 9.2e+146)
       (* (/ y z) x)
       (if (or (<= t 1.15e+250) (not (<= t 5.6e+298))) (* t (- x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -2.85e+147) {
		tmp = t_1;
	} else if (t <= 9.2e+146) {
		tmp = (y / z) * x;
	} else if ((t <= 1.15e+250) || !(t <= 5.6e+298)) {
		tmp = t * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-2.85d+147)) then
        tmp = t_1
    else if (t <= 9.2d+146) then
        tmp = (y / z) * x
    else if ((t <= 1.15d+250) .or. (.not. (t <= 5.6d+298))) then
        tmp = t * -x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -2.85e+147) {
		tmp = t_1;
	} else if (t <= 9.2e+146) {
		tmp = (y / z) * x;
	} else if ((t <= 1.15e+250) || !(t <= 5.6e+298)) {
		tmp = t * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -2.85e+147:
		tmp = t_1
	elif t <= 9.2e+146:
		tmp = (y / z) * x
	elif (t <= 1.15e+250) or not (t <= 5.6e+298):
		tmp = t * -x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -2.85e+147)
		tmp = t_1;
	elseif (t <= 9.2e+146)
		tmp = Float64(Float64(y / z) * x);
	elseif ((t <= 1.15e+250) || !(t <= 5.6e+298))
		tmp = Float64(t * Float64(-x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -2.85e+147)
		tmp = t_1;
	elseif (t <= 9.2e+146)
		tmp = (y / z) * x;
	elseif ((t <= 1.15e+250) || ~((t <= 5.6e+298)))
		tmp = t * -x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.85e+147], t$95$1, If[LessEqual[t, 9.2e+146], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[Or[LessEqual[t, 1.15e+250], N[Not[LessEqual[t, 5.6e+298]], $MachinePrecision]], N[(t * (-x)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.84999999999999996e147 or 1.1500000000000001e250 < t < 5.60000000000000033e298

   1. Initial program 95.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. remove-double-neg 51.5%

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

      3. cancel-sign-sub-inv 51.5%

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

      4. metadata-eval 51.5%

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

      5. *-lft-identity 51.5%

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

      6. distribute-neg-out 51.5%

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

      7. neg-mul-1 51.5%

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

      8. sub-neg 51.5%

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

      9. distribute-lft-neg-in 51.5%

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

      10. *-commutative 51.5%

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

      11. distribute-neg-frac 51.5%

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

      12. associate-/l* 69.3%

          \[\leadsto -\color{blue}{x \cdot \frac{-1 \cdot y - t}{z}} \]

      13. distribute-rgt-neg-in 69.3%

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

      14. distribute-neg-frac 69.3%

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

   5. Simplified 69.3%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   6. Taylor expanded in y around inf 47.0%

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

      1. times-frac 50.9%

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

      2. distribute-rgt1-in 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in y around 0 45.5%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   10. Step-by-step derivation

       1. *-commutative 45.5%

          \[\leadsto \frac{\color{blue}{x \cdot t}}{z} \]

       2. associate-/l* 65.3%

          \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]

   11. Simplified 65.3%

       \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]

   if -2.84999999999999996e147 < t < 9.20000000000000001e146

   1. Initial program 92.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.4%

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

      1. associate-*r/ 75.5%

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

   5. Simplified 75.5%

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

   if 9.20000000000000001e146 < t < 1.1500000000000001e250 or 5.60000000000000033e298 < t

   1. Initial program 96.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 96.4%

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

      2. distribute-rgt-in 92.6%

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

      3. distribute-neg-frac 92.6%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\frac{-t}{1 - z}} \cdot x \]

   4. Applied egg-rr 92.6%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x + \frac{-t}{1 - z} \cdot x} \]

   5. Taylor expanded in z around 0 62.8%

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

      1. +-commutative 62.8%

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

      2. associate-*r* 65.0%

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

      3. *-commutative 65.0%

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

      4. neg-mul-1 65.0%

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

      5. distribute-lft-neg-in 65.0%

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

      6. cancel-sign-sub-inv 65.0%

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

      7. *-commutative 65.0%

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

      8. associate-*r* 64.7%

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

      9. distribute-rgt-out-- 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in y around 0 51.4%

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

      1. associate-*r* 51.4%

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

      2. neg-mul-1 51.4%

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

   10. Simplified 51.4%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+146}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+250} \lor \neg \left(t \leq 5.6 \cdot 10^{+298}\right):\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+143}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+249}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+298}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -3.1e+146)
     t_1
     (if (<= t 4.4e+143)
       (* (/ y z) x)
       (if (<= t 2.2e+249)
         (* t (- x))
         (if (<= t 6.5e+298) t_1 (* y (/ x z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -3.1e+146) {
		tmp = t_1;
	} else if (t <= 4.4e+143) {
		tmp = (y / z) * x;
	} else if (t <= 2.2e+249) {
		tmp = t * -x;
	} else if (t <= 6.5e+298) {
		tmp = t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-3.1d+146)) then
        tmp = t_1
    else if (t <= 4.4d+143) then
        tmp = (y / z) * x
    else if (t <= 2.2d+249) then
        tmp = t * -x
    else if (t <= 6.5d+298) then
        tmp = t_1
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -3.1e+146) {
		tmp = t_1;
	} else if (t <= 4.4e+143) {
		tmp = (y / z) * x;
	} else if (t <= 2.2e+249) {
		tmp = t * -x;
	} else if (t <= 6.5e+298) {
		tmp = t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -3.1e+146:
		tmp = t_1
	elif t <= 4.4e+143:
		tmp = (y / z) * x
	elif t <= 2.2e+249:
		tmp = t * -x
	elif t <= 6.5e+298:
		tmp = t_1
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -3.1e+146)
		tmp = t_1;
	elseif (t <= 4.4e+143)
		tmp = Float64(Float64(y / z) * x);
	elseif (t <= 2.2e+249)
		tmp = Float64(t * Float64(-x));
	elseif (t <= 6.5e+298)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -3.1e+146)
		tmp = t_1;
	elseif (t <= 4.4e+143)
		tmp = (y / z) * x;
	elseif (t <= 2.2e+249)
		tmp = t * -x;
	elseif (t <= 6.5e+298)
		tmp = t_1;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+146], t$95$1, If[LessEqual[t, 4.4e+143], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 2.2e+249], N[(t * (-x)), $MachinePrecision], If[LessEqual[t, 6.5e+298], t$95$1, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.1000000000000002e146 or 2.1999999999999998e249 < t < 6.5e298

   1. Initial program 95.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. remove-double-neg 51.5%

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

      3. cancel-sign-sub-inv 51.5%

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

      4. metadata-eval 51.5%

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

      5. *-lft-identity 51.5%

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

      6. distribute-neg-out 51.5%

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

      7. neg-mul-1 51.5%

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

      8. sub-neg 51.5%

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

      9. distribute-lft-neg-in 51.5%

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

      10. *-commutative 51.5%

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

      11. distribute-neg-frac 51.5%

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

      12. associate-/l* 69.3%

          \[\leadsto -\color{blue}{x \cdot \frac{-1 \cdot y - t}{z}} \]

      13. distribute-rgt-neg-in 69.3%

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

      14. distribute-neg-frac 69.3%

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

   5. Simplified 69.3%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   6. Taylor expanded in y around inf 47.0%

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

      1. times-frac 50.9%

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

      2. distribute-rgt1-in 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in y around 0 45.5%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   10. Step-by-step derivation

       1. *-commutative 45.5%

          \[\leadsto \frac{\color{blue}{x \cdot t}}{z} \]

       2. associate-/l* 65.3%

          \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]

   11. Simplified 65.3%

       \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]

   if -3.1000000000000002e146 < t < 4.40000000000000028e143

   1. Initial program 92.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.4%

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

      1. associate-*r/ 75.5%

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

   5. Simplified 75.5%

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

   if 4.40000000000000028e143 < t < 2.1999999999999998e249

   1. Initial program 100.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 95.7%

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

      3. distribute-neg-frac 95.7%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\frac{-t}{1 - z}} \cdot x \]

   4. Applied egg-rr 95.7%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x + \frac{-t}{1 - z} \cdot x} \]

   5. Taylor expanded in z around 0 60.4%

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

      1. +-commutative 60.4%

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

      2. associate-*r* 60.5%

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

      3. *-commutative 60.5%

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

      4. neg-mul-1 60.5%

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

      5. distribute-lft-neg-in 60.5%

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

      6. cancel-sign-sub-inv 60.5%

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

      7. *-commutative 60.5%

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

      8. associate-*r* 60.2%

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

      9. distribute-rgt-out-- 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in y around 0 53.0%

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

      1. associate-*r* 53.0%

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

      2. neg-mul-1 53.0%

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

   10. Simplified 53.0%

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

   if 6.5e298 < t

   1. Initial program 68.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 68.7%

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

      2. frac-sub 68.7%

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

      3. associate-*l/ 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r/ 99.5%

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

      4. associate-/r* 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in y around inf 48.1%

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

      1. associate-*l/ 48.1%

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

      2. *-commutative 48.1%

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

   10. Simplified 48.1%

       \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+143}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+249}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+298}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -inf.0

   1. Initial program 64.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 64.2%

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

      2. frac-sub 64.2%

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

      3. associate-*l/ 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r/ 99.8%

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

      4. associate-/r* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around inf 99.9%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

   10. Simplified 99.8%

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

       1. clear-num 99.8%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{z}{x}}} \]

       2. un-div-inv 100.0%

          \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} \]

   12. Applied egg-rr 100.0%

       \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} \]

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 97.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 97.3%

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

Alternative 6: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= z -3.3e+226)
     t_1
     (if (<= z -6.5e+26)
       (* (/ y z) x)
       (if (<= z 4.8e+155) (* x (- (/ y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -3.3e+226) {
		tmp = t_1;
	} else if (z <= -6.5e+26) {
		tmp = (y / z) * x;
	} else if (z <= 4.8e+155) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (z <= (-3.3d+226)) then
        tmp = t_1
    else if (z <= (-6.5d+26)) then
        tmp = (y / z) * x
    else if (z <= 4.8d+155) then
        tmp = x * ((y / z) - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -3.3e+226) {
		tmp = t_1;
	} else if (z <= -6.5e+26) {
		tmp = (y / z) * x;
	} else if (z <= 4.8e+155) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if z <= -3.3e+226:
		tmp = t_1
	elif z <= -6.5e+26:
		tmp = (y / z) * x
	elif z <= 4.8e+155:
		tmp = x * ((y / z) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (z <= -3.3e+226)
		tmp = t_1;
	elseif (z <= -6.5e+26)
		tmp = Float64(Float64(y / z) * x);
	elseif (z <= 4.8e+155)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (z <= -3.3e+226)
		tmp = t_1;
	elseif (z <= -6.5e+26)
		tmp = (y / z) * x;
	elseif (z <= 4.8e+155)
		tmp = x * ((y / z) - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+226], t$95$1, If[LessEqual[z, -6.5e+26], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 4.8e+155], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.29999999999999978e226 or 4.80000000000000042e155 < z

   1. Initial program 94.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. remove-double-neg 76.7%

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

      3. cancel-sign-sub-inv 76.7%

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

      4. metadata-eval 76.7%

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

      5. *-lft-identity 76.7%

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

      6. distribute-neg-out 76.7%

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

      7. neg-mul-1 76.7%

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

      8. sub-neg 76.7%

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

      9. distribute-lft-neg-in 76.7%

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

      10. *-commutative 76.7%

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

      11. distribute-neg-frac 76.7%

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

      12. associate-/l* 94.1%

          \[\leadsto -\color{blue}{x \cdot \frac{-1 \cdot y - t}{z}} \]

      13. distribute-rgt-neg-in 94.1%

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

      14. distribute-neg-frac 94.1%

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

   5. Simplified 94.1%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   6. Taylor expanded in y around inf 68.1%

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

      1. times-frac 70.3%

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

      2. distribute-rgt1-in 70.3%

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

   8. Simplified 70.3%

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

   9. Taylor expanded in y around 0 54.9%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   10. Step-by-step derivation

       1. *-commutative 54.9%

          \[\leadsto \frac{\color{blue}{x \cdot t}}{z} \]

       2. associate-/l* 68.5%

          \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]

   11. Simplified 68.5%

       \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]

   if -3.29999999999999978e226 < z < -6.50000000000000022e26

   1. Initial program 99.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.7%

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

      1. associate-*r/ 72.6%

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

   5. Simplified 72.6%

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

   if -6.50000000000000022e26 < z < 4.80000000000000042e155

   1. Initial program 92.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 87.1%

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

      1. mul-1-neg 87.1%

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

      2. unsub-neg 87.1%

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

      3. div-sub 87.1%

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

      4. associate-/l* 87.2%

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

      5. *-inverses 87.2%

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

      6. *-rgt-identity 87.2%

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

   5. Simplified 87.2%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0)))
   (* x (/ (+ y t) z))
   (/ (* x (- y (* z t))) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = (x * (y - (z * t))) / z;
	}
	return tmp;
}

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = (x * (y - (z * t))) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = x * ((y + t) / z)
	else:
		tmp = (x * (y - (z * t))) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.0))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	else
		tmp = Float64(Float64(x * Float64(y - Float64(z * t))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.0)))
		tmp = x * ((y + t) / z);
	else
		tmp = (x * (y - (z * t))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 97.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 86.7%

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

      1. *-commutative 86.7%

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

      2. remove-double-neg 86.7%

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

      3. cancel-sign-sub-inv 86.7%

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

      4. metadata-eval 86.7%

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

      5. *-lft-identity 86.7%

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

      6. distribute-neg-out 86.7%

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

      7. neg-mul-1 86.7%

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

      8. sub-neg 86.7%

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

      9. distribute-lft-neg-in 86.7%

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

      10. *-commutative 86.7%

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

      11. distribute-neg-frac 86.7%

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

      12. associate-/l* 97.0%

          \[\leadsto -\color{blue}{x \cdot \frac{-1 \cdot y - t}{z}} \]

      13. distribute-rgt-neg-in 97.0%

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

      14. distribute-neg-frac 97.0%

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

   5. Simplified 97.0%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   if -1 < z < 1

   1. Initial program 90.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 90.2%

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

      2. distribute-rgt-in 87.3%

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

      3. distribute-neg-frac 87.3%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\frac{-t}{1 - z}} \cdot x \]

   4. Applied egg-rr 87.3%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x + \frac{-t}{1 - z} \cdot x} \]

   5. Taylor expanded in z around 0 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-*r* 93.3%

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

      3. *-commutative 93.3%

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

      4. neg-mul-1 93.3%

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

      5. distribute-lft-neg-in 93.3%

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

      6. cancel-sign-sub-inv 93.3%

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

      7. *-commutative 93.3%

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

      8. associate-*r* 94.7%

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

      9. distribute-rgt-out-- 96.2%

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

   7. Simplified 96.2%

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

4. Final simplification 96.6%

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

Alternative 8: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.0))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.0)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 97.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 86.7%

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

      1. *-commutative 86.7%

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

      2. remove-double-neg 86.7%

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

      3. cancel-sign-sub-inv 86.7%

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

      4. metadata-eval 86.7%

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

      5. *-lft-identity 86.7%

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

      6. distribute-neg-out 86.7%

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

      7. neg-mul-1 86.7%

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

      8. sub-neg 86.7%

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

      9. distribute-lft-neg-in 86.7%

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

      10. *-commutative 86.7%

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

      11. distribute-neg-frac 86.7%

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

      12. associate-/l* 97.0%

          \[\leadsto -\color{blue}{x \cdot \frac{-1 \cdot y - t}{z}} \]

      13. distribute-rgt-neg-in 97.0%

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

      14. distribute-neg-frac 97.0%

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

   5. Simplified 97.0%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   if -1 < z < 1

   1. Initial program 90.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 89.9%

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

      1. mul-1-neg 89.9%

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

      2. unsub-neg 89.9%

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

      3. div-sub 89.9%

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

      4. associate-/l* 90.0%

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

      5. *-inverses 90.0%

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

      6. *-rgt-identity 90.0%

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

   5. Simplified 90.0%

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

4. Final simplification 93.3%

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

Alternative 9: 43.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-10} \lor \neg \left(z \leq 9.5 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e-10) (not (<= z 9.5e-37))) (* x (/ t z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e-10) || !(z <= 9.5e-37)) {
		tmp = x * (t / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.2d-10)) .or. (.not. (z <= 9.5d-37))) then
        tmp = x * (t / z)
    else
        tmp = t * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e-10) || !(z <= 9.5e-37)) {
		tmp = x * (t / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e-10) or not (z <= 9.5e-37):
		tmp = x * (t / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e-10) || !(z <= 9.5e-37))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2e-10) || ~((z <= 9.5e-37)))
		tmp = x * (t / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e-10], N[Not[LessEqual[z, 9.5e-37]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000003e-10 or 9.49999999999999927e-37 < z

   1. Initial program 97.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 87.1%

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

      1. *-commutative 87.1%

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

      2. remove-double-neg 87.1%

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

      3. cancel-sign-sub-inv 87.1%

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

      4. metadata-eval 87.1%

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

      5. *-lft-identity 87.1%

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

      6. distribute-neg-out 87.1%

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

      7. neg-mul-1 87.1%

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

      8. sub-neg 87.1%

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

      9. distribute-lft-neg-in 87.1%

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

      10. *-commutative 87.1%

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

      11. distribute-neg-frac 87.1%

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

      12. associate-/l* 95.8%

          \[\leadsto -\color{blue}{x \cdot \frac{-1 \cdot y - t}{z}} \]

      13. distribute-rgt-neg-in 95.8%

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

      14. distribute-neg-frac 95.8%

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

   5. Simplified 95.8%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   6. Taylor expanded in y around inf 78.9%

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

      1. times-frac 77.5%

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

      2. distribute-rgt1-in 77.5%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in y around 0 46.5%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   10. Step-by-step derivation

       1. *-commutative 46.5%

          \[\leadsto \frac{\color{blue}{x \cdot t}}{z} \]

       2. associate-/l* 52.2%

          \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]

   11. Simplified 52.2%

       \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]

   if -6.2000000000000003e-10 < z < 9.49999999999999927e-37

   1. Initial program 90.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 90.0%

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

      2. distribute-rgt-in 87.6%

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

      3. distribute-neg-frac 87.6%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\frac{-t}{1 - z}} \cdot x \]

   4. Applied egg-rr 87.6%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x + \frac{-t}{1 - z} \cdot x} \]

   5. Taylor expanded in z around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. associate-*r* 93.8%

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

      3. *-commutative 93.8%

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

      4. neg-mul-1 93.8%

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

      5. distribute-lft-neg-in 93.8%

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

      6. cancel-sign-sub-inv 93.8%

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

      7. *-commutative 93.8%

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

      8. associate-*r* 95.2%

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

      9. distribute-rgt-out-- 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in y around 0 30.1%

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

      1. associate-*r* 30.1%

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

      2. neg-mul-1 30.1%

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

   10. Simplified 30.1%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-10} \lor \neg \left(z \leq 9.5 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-10} \lor \neg \left(z \leq 9.5 \cdot 10^{-37}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e-10) (not (<= z 9.5e-37))) (* t (/ x z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e-10) || !(z <= 9.5e-37)) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.2d-10)) .or. (.not. (z <= 9.5d-37))) then
        tmp = t * (x / z)
    else
        tmp = t * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e-10) || !(z <= 9.5e-37)) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e-10) or not (z <= 9.5e-37):
		tmp = t * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e-10) || !(z <= 9.5e-37))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2e-10) || ~((z <= 9.5e-37)))
		tmp = t * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e-10], N[Not[LessEqual[z, 9.5e-37]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000003e-10 or 9.49999999999999927e-37 < z

   1. Initial program 97.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 87.1%

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

      1. *-commutative 87.1%

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

      2. remove-double-neg 87.1%

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

      3. cancel-sign-sub-inv 87.1%

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

      4. metadata-eval 87.1%

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

      5. *-lft-identity 87.1%

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

      6. distribute-neg-out 87.1%

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

      7. neg-mul-1 87.1%

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

      8. sub-neg 87.1%

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

      9. distribute-lft-neg-in 87.1%

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

      10. *-commutative 87.1%

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

      11. distribute-neg-frac 87.1%

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

      12. associate-/l* 95.8%

          \[\leadsto -\color{blue}{x \cdot \frac{-1 \cdot y - t}{z}} \]

      13. distribute-rgt-neg-in 95.8%

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

      14. distribute-neg-frac 95.8%

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

   5. Simplified 95.8%

      \[\leadsto \color{blue}{x \cdot \frac{t + y}{z}} \]

   6. Taylor expanded in t around 0 85.6%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z} + \frac{x \cdot y}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 84.8%

         \[\leadsto \color{blue}{t \cdot \frac{x}{z}} + \frac{x \cdot y}{z} \]

      2. *-commutative 84.8%

         \[\leadsto t \cdot \frac{x}{z} + \frac{\color{blue}{y \cdot x}}{z} \]

      3. associate-/l* 82.0%

         \[\leadsto t \cdot \frac{x}{z} + \color{blue}{y \cdot \frac{x}{z}} \]

      4. distribute-rgt-out 83.5%

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

      5. +-commutative 83.5%

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

   8. Simplified 83.5%

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

   9. Taylor expanded in y around 0 46.5%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   10. Step-by-step derivation

       1. associate-/l* 47.2%

          \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   11. Simplified 47.2%

       \[\leadsto \color{blue}{t \cdot \frac{x}{z}} \]

   if -6.2000000000000003e-10 < z < 9.49999999999999927e-37

   1. Initial program 90.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 90.0%

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

      2. distribute-rgt-in 87.6%

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

      3. distribute-neg-frac 87.6%

         \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\frac{-t}{1 - z}} \cdot x \]

   4. Applied egg-rr 87.6%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x + \frac{-t}{1 - z} \cdot x} \]

   5. Taylor expanded in z around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. associate-*r* 93.8%

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

      3. *-commutative 93.8%

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

      4. neg-mul-1 93.8%

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

      5. distribute-lft-neg-in 93.8%

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

      6. cancel-sign-sub-inv 93.8%

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

      7. *-commutative 93.8%

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

      8. associate-*r* 95.2%

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

      9. distribute-rgt-out-- 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in y around 0 30.1%

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

      1. associate-*r* 30.1%

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

      2. neg-mul-1 30.1%

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

   10. Simplified 30.1%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-10} \lor \neg \left(z \leq 9.5 \cdot 10^{-37}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 22.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(-x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t (- x)))

C

double code(double x, double y, double z, double t) {
	return t * -x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t * -x
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * -x;
}

Python

def code(x, y, z, t):
	return t * -x

Julia

function code(x, y, z, t)
	return Float64(t * Float64(-x))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * -x;
end

Wolfram

code[x_, y_, z_, t_] := N[(t * (-x)), $MachinePrecision]

Derivation

1. Initial program 93.6%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg 93.6%

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

   2. distribute-rgt-in 91.3%

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

   3. distribute-neg-frac 91.3%

      \[\leadsto \frac{y}{z} \cdot x + \color{blue}{\frac{-t}{1 - z}} \cdot x \]

4. Applied egg-rr 91.3%

   \[\leadsto \color{blue}{\frac{y}{z} \cdot x + \frac{-t}{1 - z} \cdot x} \]

5. Taylor expanded in z around 0 67.1%

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

   1. +-commutative 67.1%

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

   2. associate-*r* 68.3%

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

   3. *-commutative 68.3%

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

   4. neg-mul-1 68.3%

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

   5. distribute-lft-neg-in 68.3%

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

   6. cancel-sign-sub-inv 68.3%

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

   7. *-commutative 68.3%

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

   8. associate-*r* 69.0%

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

   9. distribute-rgt-out-- 70.6%

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

7. Simplified 70.6%

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

8. Taylor expanded in y around 0 23.6%

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

   1. associate-*r* 23.6%

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

   2. neg-mul-1 23.6%

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

10. Simplified 23.6%

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

11. Final simplification 23.6%

    \[\leadsto t \cdot \left(-x\right) \]
12. Add Preprocessing

Alternative 12: 9.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ t \cdot x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t x))

C

double code(double x, double y, double z, double t) {
	return t * x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t * x
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * x;
}

Python

def code(x, y, z, t):
	return t * x

Julia

function code(x, y, z, t)
	return Float64(t * x)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * x;
end

Wolfram

code[x_, y_, z_, t_] := N[(t * x), $MachinePrecision]

Derivation

1. Initial program 93.6%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0 67.1%

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

   1. +-commutative 67.1%

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

   2. mul-1-neg 67.1%

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

   3. unsub-neg 67.1%

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

5. Simplified 67.1%

   \[\leadsto \color{blue}{\frac{x \cdot y - t \cdot \left(x \cdot z\right)}{z}} \]
6. Step-by-step derivation

   1. clear-num 67.1%

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

   2. inv-pow 67.1%

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

   3. cancel-sign-sub-inv 67.1%

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

   4. *-commutative 67.1%

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

   5. fma-define 67.8%

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

   6. add-sqr-sqrt 37.6%

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

   7. sqrt-unprod 54.1%

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

   8. sqr-neg 54.1%

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

   9. sqrt-unprod 23.8%

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

   10. add-sqr-sqrt 54.6%

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

   11. *-commutative 54.6%

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

7. Applied egg-rr 54.6%

   \[\leadsto \color{blue}{{\left(\frac{z}{\mathsf{fma}\left(y, x, t \cdot \left(z \cdot x\right)\right)}\right)}^{-1}} \]
8. Step-by-step derivation

   1. unpow-1 54.6%

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

   2. fma-define 54.6%

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

   3. associate-*r* 55.4%

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

   4. *-commutative 55.4%

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

   5. distribute-rgt-out 56.2%

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

9. Simplified 56.2%

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

10. Taylor expanded in z around inf 9.8%

    \[\leadsto \color{blue}{t \cdot x} \]
11. Add Preprocessing

Developer target: 94.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t\_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - 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 t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024086 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))