Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B

Percentage Accurate: 88.5% → 96.7%

Time: 12.1s

Alternatives: 23

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - 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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - 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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{t - z}}{y - z} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x / (t - z)) / (y - 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 / (t - z)) / (y - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.9%

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

   1. associate-/l/ 98.2%

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

3. Simplified 98.2%

   \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
4. Add Preprocessing

5. Final simplification 98.2%

   \[\leadsto \frac{\frac{x}{t - z}}{y - z} \]
6. Add Preprocessing

Alternative 2: 51.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ t_2 := \frac{\frac{x}{-z}}{y}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-142}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-255}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 44000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) y)) (t_2 (/ (/ x (- z)) y)))
   (if (<= z -1.15e+71)
     t_2
     (if (<= z -2e-61)
       t_1
       (if (<= z -7e-142)
         (/ (/ x t) (- z))
         (if (<= z 1.85e-255)
           (/ x (* t y))
           (if (<= z 44000000000.0)
             t_1
             (if (<= z 1.3e+185) (* (/ x z) (/ -1.0 t)) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = (x / -z) / y;
	double tmp;
	if (z <= -1.15e+71) {
		tmp = t_2;
	} else if (z <= -2e-61) {
		tmp = t_1;
	} else if (z <= -7e-142) {
		tmp = (x / t) / -z;
	} else if (z <= 1.85e-255) {
		tmp = x / (t * y);
	} else if (z <= 44000000000.0) {
		tmp = t_1;
	} else if (z <= 1.3e+185) {
		tmp = (x / z) * (-1.0 / t);
	} 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 = (x / t) / y
    t_2 = (x / -z) / y
    if (z <= (-1.15d+71)) then
        tmp = t_2
    else if (z <= (-2d-61)) then
        tmp = t_1
    else if (z <= (-7d-142)) then
        tmp = (x / t) / -z
    else if (z <= 1.85d-255) then
        tmp = x / (t * y)
    else if (z <= 44000000000.0d0) then
        tmp = t_1
    else if (z <= 1.3d+185) then
        tmp = (x / z) * ((-1.0d0) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = (x / -z) / y;
	double tmp;
	if (z <= -1.15e+71) {
		tmp = t_2;
	} else if (z <= -2e-61) {
		tmp = t_1;
	} else if (z <= -7e-142) {
		tmp = (x / t) / -z;
	} else if (z <= 1.85e-255) {
		tmp = x / (t * y);
	} else if (z <= 44000000000.0) {
		tmp = t_1;
	} else if (z <= 1.3e+185) {
		tmp = (x / z) * (-1.0 / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / t) / y
	t_2 = (x / -z) / y
	tmp = 0
	if z <= -1.15e+71:
		tmp = t_2
	elif z <= -2e-61:
		tmp = t_1
	elif z <= -7e-142:
		tmp = (x / t) / -z
	elif z <= 1.85e-255:
		tmp = x / (t * y)
	elif z <= 44000000000.0:
		tmp = t_1
	elif z <= 1.3e+185:
		tmp = (x / z) * (-1.0 / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	t_2 = Float64(Float64(x / Float64(-z)) / y)
	tmp = 0.0
	if (z <= -1.15e+71)
		tmp = t_2;
	elseif (z <= -2e-61)
		tmp = t_1;
	elseif (z <= -7e-142)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (z <= 1.85e-255)
		tmp = Float64(x / Float64(t * y));
	elseif (z <= 44000000000.0)
		tmp = t_1;
	elseif (z <= 1.3e+185)
		tmp = Float64(Float64(x / z) * Float64(-1.0 / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	t_2 = (x / -z) / y;
	tmp = 0.0;
	if (z <= -1.15e+71)
		tmp = t_2;
	elseif (z <= -2e-61)
		tmp = t_1;
	elseif (z <= -7e-142)
		tmp = (x / t) / -z;
	elseif (z <= 1.85e-255)
		tmp = x / (t * y);
	elseif (z <= 44000000000.0)
		tmp = t_1;
	elseif (z <= 1.3e+185)
		tmp = (x / z) * (-1.0 / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / (-z)), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -1.15e+71], t$95$2, If[LessEqual[z, -2e-61], t$95$1, If[LessEqual[z, -7e-142], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 1.85e-255], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 44000000000.0], t$95$1, If[LessEqual[z, 1.3e+185], N[(N[(x / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.1500000000000001e71 or 1.3e185 < z

   1. Initial program 79.7%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 58.5%

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

   6. Taylor expanded in t around 0 55.4%

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

      1. associate-*r/ 55.4%

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

      2. neg-mul-1 55.4%

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

   8. Simplified 55.4%

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

      1. un-div-inv 55.4%

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

      2. frac-2neg 55.4%

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

      3. add-sqr-sqrt 31.0%

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

      4. sqrt-unprod 51.7%

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

      5. sqr-neg 51.7%

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

      6. sqrt-unprod 24.4%

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

      7. add-sqr-sqrt 51.2%

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

      8. distribute-frac-neg2 51.2%

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

      9. add-sqr-sqrt 34.6%

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

      10. sqrt-unprod 70.1%

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

      11. sqr-neg 70.1%

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

      12. sqrt-unprod 16.6%

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

      13. add-sqr-sqrt 55.4%

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

   10. Applied egg-rr 55.4%

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

   if -1.1500000000000001e71 < z < -2.0000000000000001e-61 or 1.8500000000000001e-255 < z < 4.4e10

   1. Initial program 90.0%

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

   3. Taylor expanded in z around 0 45.5%

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

      1. clear-num 45.5%

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

      2. associate-/r/ 45.5%

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

      3. associate-/r* 45.4%

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

   5. Applied egg-rr 45.4%

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

      1. associate-*l/ 51.5%

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

      2. associate-*l/ 51.6%

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

      3. *-un-lft-identity 51.6%

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

   7. Applied egg-rr 51.6%

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

   if -2.0000000000000001e-61 < z < -7.00000000000000029e-142

   1. Initial program 92.9%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 64.5%

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

   6. Taylor expanded in y around 0 40.2%

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

      1. associate-*r/ 40.2%

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

      2. mul-1-neg 40.2%

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

   8. Simplified 40.2%

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

   9. Taylor expanded in x around 0 40.2%

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

       1. mul-1-neg 40.2%

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

       2. associate-/r* 46.8%

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

       3. distribute-neg-frac2 46.8%

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

   11. Simplified 46.8%

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

   if -7.00000000000000029e-142 < z < 1.8500000000000001e-255

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 80.9%

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

   if 4.4e10 < z < 1.3e185

   1. Initial program 74.0%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 32.6%

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

   6. Taylor expanded in y around 0 23.1%

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

      1. associate-*r/ 23.1%

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

      2. mul-1-neg 23.1%

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

   8. Simplified 23.1%

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

      1. neg-mul-1 23.1%

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

      2. times-frac 30.4%

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

   10. Applied egg-rr 30.4%

       \[\leadsto \color{blue}{\frac{-1}{t} \cdot \frac{x}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+71}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-61}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-142}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-255}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 44000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \frac{1}{t}\\ t_2 := \frac{\frac{x}{-z}}{y}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 92000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (/ 1.0 t))) (t_2 (/ (/ x (- z)) y)))
   (if (<= z -1.7e+71)
     t_2
     (if (<= z -5e-62)
       t_1
       (if (<= z -8.8e-138)
         (/ (/ x t) (- z))
         (if (<= z 2e-117)
           (/ x (* t y))
           (if (<= z 92000000000.0)
             t_1
             (if (<= z 3.5e+185) (* (/ x z) (/ -1.0 t)) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * (1.0 / t);
	double t_2 = (x / -z) / y;
	double tmp;
	if (z <= -1.7e+71) {
		tmp = t_2;
	} else if (z <= -5e-62) {
		tmp = t_1;
	} else if (z <= -8.8e-138) {
		tmp = (x / t) / -z;
	} else if (z <= 2e-117) {
		tmp = x / (t * y);
	} else if (z <= 92000000000.0) {
		tmp = t_1;
	} else if (z <= 3.5e+185) {
		tmp = (x / z) * (-1.0 / t);
	} 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 = (x / y) * (1.0d0 / t)
    t_2 = (x / -z) / y
    if (z <= (-1.7d+71)) then
        tmp = t_2
    else if (z <= (-5d-62)) then
        tmp = t_1
    else if (z <= (-8.8d-138)) then
        tmp = (x / t) / -z
    else if (z <= 2d-117) then
        tmp = x / (t * y)
    else if (z <= 92000000000.0d0) then
        tmp = t_1
    else if (z <= 3.5d+185) then
        tmp = (x / z) * ((-1.0d0) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * (1.0 / t);
	double t_2 = (x / -z) / y;
	double tmp;
	if (z <= -1.7e+71) {
		tmp = t_2;
	} else if (z <= -5e-62) {
		tmp = t_1;
	} else if (z <= -8.8e-138) {
		tmp = (x / t) / -z;
	} else if (z <= 2e-117) {
		tmp = x / (t * y);
	} else if (z <= 92000000000.0) {
		tmp = t_1;
	} else if (z <= 3.5e+185) {
		tmp = (x / z) * (-1.0 / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * (1.0 / t)
	t_2 = (x / -z) / y
	tmp = 0
	if z <= -1.7e+71:
		tmp = t_2
	elif z <= -5e-62:
		tmp = t_1
	elif z <= -8.8e-138:
		tmp = (x / t) / -z
	elif z <= 2e-117:
		tmp = x / (t * y)
	elif z <= 92000000000.0:
		tmp = t_1
	elif z <= 3.5e+185:
		tmp = (x / z) * (-1.0 / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(1.0 / t))
	t_2 = Float64(Float64(x / Float64(-z)) / y)
	tmp = 0.0
	if (z <= -1.7e+71)
		tmp = t_2;
	elseif (z <= -5e-62)
		tmp = t_1;
	elseif (z <= -8.8e-138)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (z <= 2e-117)
		tmp = Float64(x / Float64(t * y));
	elseif (z <= 92000000000.0)
		tmp = t_1;
	elseif (z <= 3.5e+185)
		tmp = Float64(Float64(x / z) * Float64(-1.0 / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * (1.0 / t);
	t_2 = (x / -z) / y;
	tmp = 0.0;
	if (z <= -1.7e+71)
		tmp = t_2;
	elseif (z <= -5e-62)
		tmp = t_1;
	elseif (z <= -8.8e-138)
		tmp = (x / t) / -z;
	elseif (z <= 2e-117)
		tmp = x / (t * y);
	elseif (z <= 92000000000.0)
		tmp = t_1;
	elseif (z <= 3.5e+185)
		tmp = (x / z) * (-1.0 / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / (-z)), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -1.7e+71], t$95$2, If[LessEqual[z, -5e-62], t$95$1, If[LessEqual[z, -8.8e-138], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 2e-117], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 92000000000.0], t$95$1, If[LessEqual[z, 3.5e+185], N[(N[(x / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.6999999999999999e71 or 3.50000000000000023e185 < z

   1. Initial program 79.7%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 58.5%

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

   6. Taylor expanded in t around 0 55.4%

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

      1. associate-*r/ 55.4%

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

      2. neg-mul-1 55.4%

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

   8. Simplified 55.4%

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

      1. un-div-inv 55.4%

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

      2. frac-2neg 55.4%

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

      3. add-sqr-sqrt 31.0%

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

      4. sqrt-unprod 51.7%

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

      5. sqr-neg 51.7%

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

      6. sqrt-unprod 24.4%

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

      7. add-sqr-sqrt 51.2%

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

      8. distribute-frac-neg2 51.2%

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

      9. add-sqr-sqrt 34.6%

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

      10. sqrt-unprod 70.1%

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

      11. sqr-neg 70.1%

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

      12. sqrt-unprod 16.6%

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

      13. add-sqr-sqrt 55.4%

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

   10. Applied egg-rr 55.4%

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

   if -1.6999999999999999e71 < z < -5.0000000000000002e-62 or 2.00000000000000006e-117 < z < 9.2e10

   1. Initial program 88.9%

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

   3. Taylor expanded in z around 0 31.7%

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

      1. *-un-lft-identity 31.7%

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

      2. times-frac 49.2%

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

   5. Applied egg-rr 49.2%

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

   if -5.0000000000000002e-62 < z < -8.7999999999999995e-138

   1. Initial program 92.9%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 64.5%

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

   6. Taylor expanded in y around 0 40.2%

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

      1. associate-*r/ 40.2%

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

      2. mul-1-neg 40.2%

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

   8. Simplified 40.2%

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

   9. Taylor expanded in x around 0 40.2%

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

       1. mul-1-neg 40.2%

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

       2. associate-/r* 46.8%

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

       3. distribute-neg-frac2 46.8%

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

   11. Simplified 46.8%

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

   if -8.7999999999999995e-138 < z < 2.00000000000000006e-117

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0 79.3%

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

   if 9.2e10 < z < 3.50000000000000023e185

   1. Initial program 74.0%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 32.6%

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

   6. Taylor expanded in y around 0 23.1%

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

      1. associate-*r/ 23.1%

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

      2. mul-1-neg 23.1%

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

   8. Simplified 23.1%

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

      1. neg-mul-1 23.1%

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

      2. times-frac 30.4%

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

   10. Applied egg-rr 30.4%

       \[\leadsto \color{blue}{\frac{-1}{t} \cdot \frac{x}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+71}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 92000000000:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ t_2 := \frac{\frac{x}{-z}}{t}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-255}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 17000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+185}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) y)) (t_2 (/ (/ x (- z)) t)))
   (if (<= z -1.3e+97)
     t_2
     (if (<= z -4.8e-60)
       t_1
       (if (<= z -2.6e-138)
         (/ (/ x t) (- z))
         (if (<= z 6.8e-255)
           (/ x (* t y))
           (if (<= z 17000000000.0)
             t_1
             (if (<= z 3.2e+185) t_2 (/ (/ x z) y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = (x / -z) / t;
	double tmp;
	if (z <= -1.3e+97) {
		tmp = t_2;
	} else if (z <= -4.8e-60) {
		tmp = t_1;
	} else if (z <= -2.6e-138) {
		tmp = (x / t) / -z;
	} else if (z <= 6.8e-255) {
		tmp = x / (t * y);
	} else if (z <= 17000000000.0) {
		tmp = t_1;
	} else if (z <= 3.2e+185) {
		tmp = t_2;
	} else {
		tmp = (x / z) / y;
	}
	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 / t) / y
    t_2 = (x / -z) / t
    if (z <= (-1.3d+97)) then
        tmp = t_2
    else if (z <= (-4.8d-60)) then
        tmp = t_1
    else if (z <= (-2.6d-138)) then
        tmp = (x / t) / -z
    else if (z <= 6.8d-255) then
        tmp = x / (t * y)
    else if (z <= 17000000000.0d0) then
        tmp = t_1
    else if (z <= 3.2d+185) then
        tmp = t_2
    else
        tmp = (x / z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = (x / -z) / t;
	double tmp;
	if (z <= -1.3e+97) {
		tmp = t_2;
	} else if (z <= -4.8e-60) {
		tmp = t_1;
	} else if (z <= -2.6e-138) {
		tmp = (x / t) / -z;
	} else if (z <= 6.8e-255) {
		tmp = x / (t * y);
	} else if (z <= 17000000000.0) {
		tmp = t_1;
	} else if (z <= 3.2e+185) {
		tmp = t_2;
	} else {
		tmp = (x / z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / t) / y
	t_2 = (x / -z) / t
	tmp = 0
	if z <= -1.3e+97:
		tmp = t_2
	elif z <= -4.8e-60:
		tmp = t_1
	elif z <= -2.6e-138:
		tmp = (x / t) / -z
	elif z <= 6.8e-255:
		tmp = x / (t * y)
	elif z <= 17000000000.0:
		tmp = t_1
	elif z <= 3.2e+185:
		tmp = t_2
	else:
		tmp = (x / z) / y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	t_2 = Float64(Float64(x / Float64(-z)) / t)
	tmp = 0.0
	if (z <= -1.3e+97)
		tmp = t_2;
	elseif (z <= -4.8e-60)
		tmp = t_1;
	elseif (z <= -2.6e-138)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (z <= 6.8e-255)
		tmp = Float64(x / Float64(t * y));
	elseif (z <= 17000000000.0)
		tmp = t_1;
	elseif (z <= 3.2e+185)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / z) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	t_2 = (x / -z) / t;
	tmp = 0.0;
	if (z <= -1.3e+97)
		tmp = t_2;
	elseif (z <= -4.8e-60)
		tmp = t_1;
	elseif (z <= -2.6e-138)
		tmp = (x / t) / -z;
	elseif (z <= 6.8e-255)
		tmp = x / (t * y);
	elseif (z <= 17000000000.0)
		tmp = t_1;
	elseif (z <= 3.2e+185)
		tmp = t_2;
	else
		tmp = (x / z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -1.3e+97], t$95$2, If[LessEqual[z, -4.8e-60], t$95$1, If[LessEqual[z, -2.6e-138], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 6.8e-255], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 17000000000.0], t$95$1, If[LessEqual[z, 3.2e+185], t$95$2, N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.3e97 or 1.7e10 < z < 3.20000000000000006e185

   1. Initial program 76.2%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 35.7%

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

   6. Taylor expanded in y around 0 32.7%

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

      1. associate-*r/ 32.7%

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

      2. mul-1-neg 32.7%

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

   8. Simplified 32.7%

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

      1. clear-num 33.6%

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

      2. associate-/r/ 32.7%

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

      3. associate-/r* 32.7%

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

      4. add-sqr-sqrt 14.2%

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

      5. sqrt-unprod 38.1%

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

      6. sqr-neg 38.1%

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

      7. sqrt-unprod 15.4%

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

      8. add-sqr-sqrt 29.4%

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

   10. Applied egg-rr 29.4%

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

       1. associate-/l/ 29.5%

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

       2. associate-/r/ 30.3%

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

       3. clear-num 29.5%

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

       4. associate-/r* 35.3%

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

       5. frac-2neg 35.3%

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

       6. distribute-frac-neg 35.3%

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

       7. add-sqr-sqrt 15.1%

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

       8. sqrt-unprod 42.1%

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

       9. sqr-neg 42.1%

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

       10. sqrt-unprod 25.4%

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

       11. add-sqr-sqrt 41.6%

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

   12. Applied egg-rr 41.6%

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

   if -1.3e97 < z < -4.80000000000000019e-60 or 6.79999999999999967e-255 < z < 1.7e10

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0 41.9%

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

      1. clear-num 41.8%

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

      2. associate-/r/ 41.8%

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

      3. associate-/r* 41.8%

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

   5. Applied egg-rr 41.8%

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

      1. associate-*l/ 48.7%

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

      2. associate-*l/ 48.8%

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

      3. *-un-lft-identity 48.8%

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

   7. Applied egg-rr 48.8%

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

   if -4.80000000000000019e-60 < z < -2.6e-138

   1. Initial program 92.9%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 64.5%

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

   6. Taylor expanded in y around 0 40.2%

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

      1. associate-*r/ 40.2%

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

      2. mul-1-neg 40.2%

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

   8. Simplified 40.2%

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

   9. Taylor expanded in x around 0 40.2%

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

       1. mul-1-neg 40.2%

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

       2. associate-/r* 46.8%

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

       3. distribute-neg-frac2 46.8%

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

   11. Simplified 46.8%

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

   if -2.6e-138 < z < 6.79999999999999967e-255

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 80.9%

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

   if 3.20000000000000006e185 < z

   1. Initial program 85.2%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf 52.8%

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

   6. Taylor expanded in t around 0 49.8%

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

      1. associate-*r/ 49.8%

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

      2. neg-mul-1 49.8%

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

   8. Simplified 49.8%

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

      1. un-div-inv 49.8%

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

      2. clear-num 49.8%

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

      3. clear-num 49.8%

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

      4. add-sqr-sqrt 31.7%

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

      5. sqrt-unprod 49.0%

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

      6. sqr-neg 49.0%

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

      7. sqrt-unprod 18.1%

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

      8. add-sqr-sqrt 49.8%

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

   10. Applied egg-rr 49.8%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-255}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 17000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ t_2 := \frac{x}{-z}\\ t_3 := \frac{t\_2}{y}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+75}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-257}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 12000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+185}:\\ \;\;\;\;\frac{t\_2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) y)) (t_2 (/ x (- z))) (t_3 (/ t_2 y)))
   (if (<= z -3.1e+75)
     t_3
     (if (<= z -5e-62)
       t_1
       (if (<= z -8.2e-138)
         (/ (/ x t) (- z))
         (if (<= z 7e-257)
           (/ x (* t y))
           (if (<= z 12000000.0) t_1 (if (<= z 2.5e+185) (/ t_2 t) t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = x / -z;
	double t_3 = t_2 / y;
	double tmp;
	if (z <= -3.1e+75) {
		tmp = t_3;
	} else if (z <= -5e-62) {
		tmp = t_1;
	} else if (z <= -8.2e-138) {
		tmp = (x / t) / -z;
	} else if (z <= 7e-257) {
		tmp = x / (t * y);
	} else if (z <= 12000000.0) {
		tmp = t_1;
	} else if (z <= 2.5e+185) {
		tmp = t_2 / t;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (x / t) / y
    t_2 = x / -z
    t_3 = t_2 / y
    if (z <= (-3.1d+75)) then
        tmp = t_3
    else if (z <= (-5d-62)) then
        tmp = t_1
    else if (z <= (-8.2d-138)) then
        tmp = (x / t) / -z
    else if (z <= 7d-257) then
        tmp = x / (t * y)
    else if (z <= 12000000.0d0) then
        tmp = t_1
    else if (z <= 2.5d+185) then
        tmp = t_2 / t
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = x / -z;
	double t_3 = t_2 / y;
	double tmp;
	if (z <= -3.1e+75) {
		tmp = t_3;
	} else if (z <= -5e-62) {
		tmp = t_1;
	} else if (z <= -8.2e-138) {
		tmp = (x / t) / -z;
	} else if (z <= 7e-257) {
		tmp = x / (t * y);
	} else if (z <= 12000000.0) {
		tmp = t_1;
	} else if (z <= 2.5e+185) {
		tmp = t_2 / t;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / t) / y
	t_2 = x / -z
	t_3 = t_2 / y
	tmp = 0
	if z <= -3.1e+75:
		tmp = t_3
	elif z <= -5e-62:
		tmp = t_1
	elif z <= -8.2e-138:
		tmp = (x / t) / -z
	elif z <= 7e-257:
		tmp = x / (t * y)
	elif z <= 12000000.0:
		tmp = t_1
	elif z <= 2.5e+185:
		tmp = t_2 / t
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	t_2 = Float64(x / Float64(-z))
	t_3 = Float64(t_2 / y)
	tmp = 0.0
	if (z <= -3.1e+75)
		tmp = t_3;
	elseif (z <= -5e-62)
		tmp = t_1;
	elseif (z <= -8.2e-138)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (z <= 7e-257)
		tmp = Float64(x / Float64(t * y));
	elseif (z <= 12000000.0)
		tmp = t_1;
	elseif (z <= 2.5e+185)
		tmp = Float64(t_2 / t);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	t_2 = x / -z;
	t_3 = t_2 / y;
	tmp = 0.0;
	if (z <= -3.1e+75)
		tmp = t_3;
	elseif (z <= -5e-62)
		tmp = t_1;
	elseif (z <= -8.2e-138)
		tmp = (x / t) / -z;
	elseif (z <= 7e-257)
		tmp = x / (t * y);
	elseif (z <= 12000000.0)
		tmp = t_1;
	elseif (z <= 2.5e+185)
		tmp = t_2 / t;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / (-z)), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / y), $MachinePrecision]}, If[LessEqual[z, -3.1e+75], t$95$3, If[LessEqual[z, -5e-62], t$95$1, If[LessEqual[z, -8.2e-138], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 7e-257], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 12000000.0], t$95$1, If[LessEqual[z, 2.5e+185], N[(t$95$2 / t), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.1000000000000001e75 or 2.49999999999999995e185 < z

   1. Initial program 79.7%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 58.5%

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

   6. Taylor expanded in t around 0 55.4%

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

      1. associate-*r/ 55.4%

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

      2. neg-mul-1 55.4%

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

   8. Simplified 55.4%

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

      1. un-div-inv 55.4%

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

      2. frac-2neg 55.4%

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

      3. add-sqr-sqrt 31.0%

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

      4. sqrt-unprod 51.7%

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

      5. sqr-neg 51.7%

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

      6. sqrt-unprod 24.4%

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

      7. add-sqr-sqrt 51.2%

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

      8. distribute-frac-neg2 51.2%

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

      9. add-sqr-sqrt 34.6%

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

      10. sqrt-unprod 70.1%

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

      11. sqr-neg 70.1%

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

      12. sqrt-unprod 16.6%

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

      13. add-sqr-sqrt 55.4%

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

   10. Applied egg-rr 55.4%

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

   if -3.1000000000000001e75 < z < -5.0000000000000002e-62 or 7.00000000000000058e-257 < z < 1.2e7

   1. Initial program 90.0%

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

   3. Taylor expanded in z around 0 45.5%

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

      1. clear-num 45.5%

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

      2. associate-/r/ 45.5%

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

      3. associate-/r* 45.4%

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

   5. Applied egg-rr 45.4%

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

      1. associate-*l/ 51.5%

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

      2. associate-*l/ 51.6%

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

      3. *-un-lft-identity 51.6%

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

   7. Applied egg-rr 51.6%

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

   if -5.0000000000000002e-62 < z < -8.19999999999999998e-138

   1. Initial program 92.9%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 64.5%

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

   6. Taylor expanded in y around 0 40.2%

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

      1. associate-*r/ 40.2%

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

      2. mul-1-neg 40.2%

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

   8. Simplified 40.2%

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

   9. Taylor expanded in x around 0 40.2%

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

       1. mul-1-neg 40.2%

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

       2. associate-/r* 46.8%

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

       3. distribute-neg-frac2 46.8%

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

   11. Simplified 46.8%

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

   if -8.19999999999999998e-138 < z < 7.00000000000000058e-257

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 80.9%

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

   if 1.2e7 < z < 2.49999999999999995e185

   1. Initial program 74.0%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 32.6%

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

   6. Taylor expanded in y around 0 23.1%

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

      1. associate-*r/ 23.1%

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

      2. mul-1-neg 23.1%

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

   8. Simplified 23.1%

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

      1. clear-num 23.1%

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

      2. associate-/r/ 23.1%

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

      3. associate-/r* 23.1%

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

      4. add-sqr-sqrt 14.2%

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

      5. sqrt-unprod 31.8%

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

      6. sqr-neg 31.8%

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

      7. sqrt-unprod 3.9%

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

      8. add-sqr-sqrt 17.8%

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

   10. Applied egg-rr 17.8%

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

       1. associate-/l/ 17.8%

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

       2. associate-/r/ 17.8%

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

       3. clear-num 17.8%

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

       4. associate-/r* 20.3%

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

       5. frac-2neg 20.3%

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

       6. distribute-frac-neg 20.3%

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

       7. add-sqr-sqrt 11.6%

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

       8. sqrt-unprod 34.4%

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

       9. sqr-neg 34.4%

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

       10. sqrt-unprod 16.1%

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

       11. add-sqr-sqrt 30.4%

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

   12. Applied egg-rr 30.4%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{-t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+75}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-257}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 12000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{-z}\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-160}:\\ \;\;\;\;\frac{t\_1}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-135}:\\ \;\;\;\;\frac{t\_1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- z))))
   (if (<= t -4.7e-63)
     (/ (/ x t) y)
     (if (<= t 4.2e-244)
       (/ x (* z (- y)))
       (if (<= t 7.5e-160)
         (/ t_1 t)
         (if (<= t 3e-135) (/ t_1 y) (/ x (* t (- y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / -z;
	double tmp;
	if (t <= -4.7e-63) {
		tmp = (x / t) / y;
	} else if (t <= 4.2e-244) {
		tmp = x / (z * -y);
	} else if (t <= 7.5e-160) {
		tmp = t_1 / t;
	} else if (t <= 3e-135) {
		tmp = t_1 / y;
	} else {
		tmp = x / (t * (y - 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 / -z
    if (t <= (-4.7d-63)) then
        tmp = (x / t) / y
    else if (t <= 4.2d-244) then
        tmp = x / (z * -y)
    else if (t <= 7.5d-160) then
        tmp = t_1 / t
    else if (t <= 3d-135) then
        tmp = t_1 / y
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / -z;
	double tmp;
	if (t <= -4.7e-63) {
		tmp = (x / t) / y;
	} else if (t <= 4.2e-244) {
		tmp = x / (z * -y);
	} else if (t <= 7.5e-160) {
		tmp = t_1 / t;
	} else if (t <= 3e-135) {
		tmp = t_1 / y;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / -z
	tmp = 0
	if t <= -4.7e-63:
		tmp = (x / t) / y
	elif t <= 4.2e-244:
		tmp = x / (z * -y)
	elif t <= 7.5e-160:
		tmp = t_1 / t
	elif t <= 3e-135:
		tmp = t_1 / y
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(-z))
	tmp = 0.0
	if (t <= -4.7e-63)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 4.2e-244)
		tmp = Float64(x / Float64(z * Float64(-y)));
	elseif (t <= 7.5e-160)
		tmp = Float64(t_1 / t);
	elseif (t <= 3e-135)
		tmp = Float64(t_1 / y);
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / -z;
	tmp = 0.0;
	if (t <= -4.7e-63)
		tmp = (x / t) / y;
	elseif (t <= 4.2e-244)
		tmp = x / (z * -y);
	elseif (t <= 7.5e-160)
		tmp = t_1 / t;
	elseif (t <= 3e-135)
		tmp = t_1 / y;
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / (-z)), $MachinePrecision]}, If[LessEqual[t, -4.7e-63], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4.2e-244], N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e-160], N[(t$95$1 / t), $MachinePrecision], If[LessEqual[t, 3e-135], N[(t$95$1 / y), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.7000000000000001e-63

   1. Initial program 81.6%

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

   3. Taylor expanded in z around 0 51.2%

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

      1. clear-num 51.2%

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

      2. associate-/r/ 51.2%

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

      3. associate-/r* 49.6%

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

   5. Applied egg-rr 49.6%

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

      1. associate-*l/ 55.1%

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

      2. associate-*l/ 55.1%

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

      3. *-un-lft-identity 55.1%

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

   7. Applied egg-rr 55.1%

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

   if -4.7000000000000001e-63 < t < 4.20000000000000003e-244

   1. Initial program 87.5%

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

      1. associate-/l/ 96.1%

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

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 86.2%

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

      1. associate-*r/ 52.1%

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

      2. neg-mul-1 52.1%

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

   7. Simplified 86.2%

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

   8. Taylor expanded in z around 0 47.7%

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

      1. associate-*r/ 47.7%

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

      2. mul-1-neg 47.7%

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

      3. *-commutative 47.7%

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

   10. Simplified 47.7%

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

   if 4.20000000000000003e-244 < t < 7.50000000000000023e-160

   1. Initial program 86.7%

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

      1. associate-/l/ 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 46.5%

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

   6. Taylor expanded in y around 0 29.7%

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

      1. associate-*r/ 29.7%

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

      2. mul-1-neg 29.7%

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

   8. Simplified 29.7%

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

      1. clear-num 29.7%

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

      2. associate-/r/ 29.7%

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

      3. associate-/r* 29.7%

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

      4. add-sqr-sqrt 10.1%

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

      5. sqrt-unprod 37.3%

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

      6. sqr-neg 37.3%

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

      7. sqrt-unprod 10.5%

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

      8. add-sqr-sqrt 11.1%

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

   10. Applied egg-rr 11.1%

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

       1. associate-/l/ 11.1%

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

       2. associate-/r/ 11.1%

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

       3. clear-num 11.1%

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

       4. associate-/r* 19.8%

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

       5. frac-2neg 19.8%

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

       6. distribute-frac-neg 19.8%

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

       7. add-sqr-sqrt 0.6%

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

       8. sqrt-unprod 38.1%

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

       9. sqr-neg 38.1%

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

       10. sqrt-unprod 28.3%

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

       11. add-sqr-sqrt 45.7%

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

   12. Applied egg-rr 45.7%

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

   if 7.50000000000000023e-160 < t < 3.00000000000000012e-135

   1. Initial program 63.9%

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

      1. associate-/l/ 99.7%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 80.4%

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

   6. Taylor expanded in t around 0 60.7%

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

      1. associate-*r/ 60.7%

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

      2. neg-mul-1 60.7%

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

   8. Simplified 60.7%

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

      1. un-div-inv 60.7%

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

      2. frac-2neg 60.7%

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

      3. add-sqr-sqrt 60.7%

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

      4. sqrt-unprod 21.7%

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

      5. sqr-neg 21.7%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 42.6%

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

      8. distribute-frac-neg2 42.6%

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

      9. add-sqr-sqrt 41.5%

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

      10. sqrt-unprod 44.1%

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

      11. sqr-neg 44.1%

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

      12. sqrt-unprod 0.2%

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

      13. add-sqr-sqrt 60.7%

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

   10. Applied egg-rr 60.7%

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

   if 3.00000000000000012e-135 < t

   1. Initial program 85.9%

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

   3. Taylor expanded in t around inf 68.6%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-160}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-260}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (- z t))))
   (if (<= z -4.6e-40)
     t_1
     (if (<= z -3.8e-186)
       (/ x (* t (- y z)))
       (if (<= z -1.5e-260)
         (/ (/ x y) (- t z))
         (if (<= z 7.5e+32) (/ (/ x (- t z)) y) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - t);
	double tmp;
	if (z <= -4.6e-40) {
		tmp = t_1;
	} else if (z <= -3.8e-186) {
		tmp = x / (t * (y - z));
	} else if (z <= -1.5e-260) {
		tmp = (x / y) / (t - z);
	} else if (z <= 7.5e+32) {
		tmp = (x / (t - z)) / y;
	} 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 / z) / (z - t)
    if (z <= (-4.6d-40)) then
        tmp = t_1
    else if (z <= (-3.8d-186)) then
        tmp = x / (t * (y - z))
    else if (z <= (-1.5d-260)) then
        tmp = (x / y) / (t - z)
    else if (z <= 7.5d+32) then
        tmp = (x / (t - z)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - t);
	double tmp;
	if (z <= -4.6e-40) {
		tmp = t_1;
	} else if (z <= -3.8e-186) {
		tmp = x / (t * (y - z));
	} else if (z <= -1.5e-260) {
		tmp = (x / y) / (t - z);
	} else if (z <= 7.5e+32) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) / (z - t)
	tmp = 0
	if z <= -4.6e-40:
		tmp = t_1
	elif z <= -3.8e-186:
		tmp = x / (t * (y - z))
	elif z <= -1.5e-260:
		tmp = (x / y) / (t - z)
	elif z <= 7.5e+32:
		tmp = (x / (t - z)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / Float64(z - t))
	tmp = 0.0
	if (z <= -4.6e-40)
		tmp = t_1;
	elseif (z <= -3.8e-186)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (z <= -1.5e-260)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (z <= 7.5e+32)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / (z - t);
	tmp = 0.0;
	if (z <= -4.6e-40)
		tmp = t_1;
	elseif (z <= -3.8e-186)
		tmp = x / (t * (y - z));
	elseif (z <= -1.5e-260)
		tmp = (x / y) / (t - z);
	elseif (z <= 7.5e+32)
		tmp = (x / (t - z)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e-40], t$95$1, If[LessEqual[z, -3.8e-186], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-260], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+32], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.6e-40 or 7.49999999999999959e32 < z

   1. Initial program 78.6%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. clear-num 99.7%

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

      2. frac-times 98.8%

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

      3. metadata-eval 98.8%

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

   6. Applied egg-rr 98.8%

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

   7. Taylor expanded in y around 0 71.2%

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

      1. neg-mul-1 71.2%

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

      2. associate-/r* 84.0%

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

      3. distribute-frac-neg 84.0%

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

      4. distribute-neg-frac2 84.0%

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

   9. Simplified 84.0%

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

   if -4.6e-40 < z < -3.79999999999999974e-186

   1. Initial program 96.1%

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

   3. Taylor expanded in t around inf 73.4%

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

   if -3.79999999999999974e-186 < z < -1.5e-260

   1. Initial program 95.3%

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

      1. associate-/l/ 93.2%

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

      2. div-inv 93.2%

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

   4. Applied egg-rr 93.2%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. clear-num 93.0%

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

      2. frac-times 88.9%

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

      3. metadata-eval 88.9%

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

   6. Applied egg-rr 88.9%

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

   7. Taylor expanded in y around inf 88.7%

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

      1. associate-/r* 86.2%

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

   9. Simplified 86.2%

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

   if -1.5e-260 < z < 7.49999999999999959e32

   1. Initial program 91.3%

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

      1. associate-/l/ 95.8%

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

      2. div-inv 95.7%

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

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in y around inf 80.3%

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

      1. un-div-inv 80.3%

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

   7. Applied egg-rr 80.3%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-40}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-260}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot y}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+196}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{elif}\;z \leq -300 \lor \neg \left(z \leq 1.55 \cdot 10^{+34}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z y))))
   (if (<= z -1.5e+274)
     t_1
     (if (<= z -4.2e+196)
       (/ x (* t z))
       (if (or (<= z -300.0) (not (<= z 1.55e+34))) t_1 (/ x (* t y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * y);
	double tmp;
	if (z <= -1.5e+274) {
		tmp = t_1;
	} else if (z <= -4.2e+196) {
		tmp = x / (t * z);
	} else if ((z <= -300.0) || !(z <= 1.55e+34)) {
		tmp = t_1;
	} else {
		tmp = x / (t * y);
	}
	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 / (z * y)
    if (z <= (-1.5d+274)) then
        tmp = t_1
    else if (z <= (-4.2d+196)) then
        tmp = x / (t * z)
    else if ((z <= (-300.0d0)) .or. (.not. (z <= 1.55d+34))) then
        tmp = t_1
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * y);
	double tmp;
	if (z <= -1.5e+274) {
		tmp = t_1;
	} else if (z <= -4.2e+196) {
		tmp = x / (t * z);
	} else if ((z <= -300.0) || !(z <= 1.55e+34)) {
		tmp = t_1;
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * y)
	tmp = 0
	if z <= -1.5e+274:
		tmp = t_1
	elif z <= -4.2e+196:
		tmp = x / (t * z)
	elif (z <= -300.0) or not (z <= 1.55e+34):
		tmp = t_1
	else:
		tmp = x / (t * y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * y))
	tmp = 0.0
	if (z <= -1.5e+274)
		tmp = t_1;
	elseif (z <= -4.2e+196)
		tmp = Float64(x / Float64(t * z));
	elseif ((z <= -300.0) || !(z <= 1.55e+34))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * y);
	tmp = 0.0;
	if (z <= -1.5e+274)
		tmp = t_1;
	elseif (z <= -4.2e+196)
		tmp = x / (t * z);
	elseif ((z <= -300.0) || ~((z <= 1.55e+34)))
		tmp = t_1;
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+274], t$95$1, If[LessEqual[z, -4.2e+196], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -300.0], N[Not[LessEqual[z, 1.55e+34]], $MachinePrecision]], t$95$1, N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.49999999999999998e274 or -4.20000000000000029e196 < z < -300 or 1.54999999999999989e34 < z

   1. Initial program 80.5%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 53.1%

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

   6. Taylor expanded in t around 0 47.2%

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

      1. associate-*r/ 47.2%

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

      2. neg-mul-1 47.2%

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

   8. Simplified 47.2%

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

      1. un-div-inv 47.2%

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

      2. associate-/l/ 39.1%

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

      3. add-sqr-sqrt 21.2%

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

      4. sqrt-unprod 44.9%

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

      5. sqr-neg 44.9%

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

      6. sqrt-unprod 18.0%

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

      7. add-sqr-sqrt 37.4%

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

   10. Applied egg-rr 37.4%

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

       1. *-commutative 37.4%

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

   12. Simplified 37.4%

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

   if -1.49999999999999998e274 < z < -4.20000000000000029e196

   1. Initial program 65.6%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 35.1%

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

   6. Taylor expanded in y around 0 35.2%

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

      1. associate-*r/ 35.2%

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

      2. mul-1-neg 35.2%

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

   8. Simplified 35.2%

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

      1. add-sqr-sqrt 11.6%

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

      2. sqrt-unprod 34.5%

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

      3. sqr-neg 34.5%

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

      4. sqrt-unprod 23.9%

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

      5. add-sqr-sqrt 35.4%

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

      6. *-un-lft-identity 35.4%

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

      7. associate-/r* 35.0%

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

   10. Applied egg-rr 35.0%

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

       1. *-lft-identity 35.0%

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

       2. associate-/l/ 35.4%

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

   12. Simplified 35.4%

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

   if -300 < z < 1.54999999999999989e34

   1. Initial program 92.0%

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

   3. Taylor expanded in z around 0 59.0%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+274}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+196}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{elif}\;z \leq -300 \lor \neg \left(z \leq 1.55 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot y}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+198}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+115} \lor \neg \left(z \leq 1.7 \cdot 10^{+42}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z y))))
   (if (<= z -6.5e+272)
     t_1
     (if (<= z -1e+198)
       (/ x (* t z))
       (if (or (<= z -2.5e+115) (not (<= z 1.7e+42))) t_1 (/ (/ x t) y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * y);
	double tmp;
	if (z <= -6.5e+272) {
		tmp = t_1;
	} else if (z <= -1e+198) {
		tmp = x / (t * z);
	} else if ((z <= -2.5e+115) || !(z <= 1.7e+42)) {
		tmp = t_1;
	} else {
		tmp = (x / t) / y;
	}
	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 / (z * y)
    if (z <= (-6.5d+272)) then
        tmp = t_1
    else if (z <= (-1d+198)) then
        tmp = x / (t * z)
    else if ((z <= (-2.5d+115)) .or. (.not. (z <= 1.7d+42))) then
        tmp = t_1
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * y);
	double tmp;
	if (z <= -6.5e+272) {
		tmp = t_1;
	} else if (z <= -1e+198) {
		tmp = x / (t * z);
	} else if ((z <= -2.5e+115) || !(z <= 1.7e+42)) {
		tmp = t_1;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * y)
	tmp = 0
	if z <= -6.5e+272:
		tmp = t_1
	elif z <= -1e+198:
		tmp = x / (t * z)
	elif (z <= -2.5e+115) or not (z <= 1.7e+42):
		tmp = t_1
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * y))
	tmp = 0.0
	if (z <= -6.5e+272)
		tmp = t_1;
	elseif (z <= -1e+198)
		tmp = Float64(x / Float64(t * z));
	elseif ((z <= -2.5e+115) || !(z <= 1.7e+42))
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * y);
	tmp = 0.0;
	if (z <= -6.5e+272)
		tmp = t_1;
	elseif (z <= -1e+198)
		tmp = x / (t * z);
	elseif ((z <= -2.5e+115) || ~((z <= 1.7e+42)))
		tmp = t_1;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+272], t$95$1, If[LessEqual[z, -1e+198], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.5e+115], N[Not[LessEqual[z, 1.7e+42]], $MachinePrecision]], t$95$1, N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.49999999999999983e272 or -1.00000000000000002e198 < z < -2.50000000000000004e115 or 1.69999999999999988e42 < z

   1. Initial program 80.0%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 53.4%

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

   6. Taylor expanded in t around 0 50.4%

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

      1. associate-*r/ 50.4%

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

      2. neg-mul-1 50.4%

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

   8. Simplified 50.4%

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

      1. un-div-inv 50.4%

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

      2. associate-/l/ 41.3%

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

      3. add-sqr-sqrt 22.7%

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

      4. sqrt-unprod 47.4%

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

      5. sqr-neg 47.4%

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

      6. sqrt-unprod 18.7%

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

      7. add-sqr-sqrt 40.2%

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

   10. Applied egg-rr 40.2%

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

       1. *-commutative 40.2%

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

   12. Simplified 40.2%

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

   if -6.49999999999999983e272 < z < -1.00000000000000002e198

   1. Initial program 65.6%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 35.1%

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

   6. Taylor expanded in y around 0 35.2%

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

      1. associate-*r/ 35.2%

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

      2. mul-1-neg 35.2%

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

   8. Simplified 35.2%

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

      1. add-sqr-sqrt 11.6%

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

      2. sqrt-unprod 34.5%

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

      3. sqr-neg 34.5%

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

      4. sqrt-unprod 23.9%

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

      5. add-sqr-sqrt 35.4%

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

      6. *-un-lft-identity 35.4%

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

      7. associate-/r* 35.0%

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

   10. Applied egg-rr 35.0%

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

       1. *-lft-identity 35.0%

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

       2. associate-/l/ 35.4%

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

   12. Simplified 35.4%

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

   if -2.50000000000000004e115 < z < 1.69999999999999988e42

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0 52.0%

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

      1. clear-num 51.9%

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

      2. associate-/r/ 51.9%

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

      3. associate-/r* 52.5%

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

   5. Applied egg-rr 52.5%

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

      1. associate-*l/ 57.6%

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

      2. associate-*l/ 57.6%

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

      3. *-un-lft-identity 57.6%

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

   7. Applied egg-rr 57.6%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+272}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+198}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+115} \lor \neg \left(z \leq 1.7 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -0.00145:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.06e+154)
   (/ (/ x (- t z)) y)
   (if (<= y -0.00145)
     (/ x (* (- t z) y))
     (if (<= y 9e-163) (/ x (* z (- z t))) (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.06e+154) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -0.00145) {
		tmp = x / ((t - z) * y);
	} else if (y <= 9e-163) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - 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 (y <= (-1.06d+154)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-0.00145d0)) then
        tmp = x / ((t - z) * y)
    else if (y <= 9d-163) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.06e+154) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -0.00145) {
		tmp = x / ((t - z) * y);
	} else if (y <= 9e-163) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.06e+154:
		tmp = (x / (t - z)) / y
	elif y <= -0.00145:
		tmp = x / ((t - z) * y)
	elif y <= 9e-163:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.06e+154)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -0.00145)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 9e-163)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.06e+154)
		tmp = (x / (t - z)) / y;
	elseif (y <= -0.00145)
		tmp = x / ((t - z) * y);
	elseif (y <= 9e-163)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.06e+154], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -0.00145], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-163], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.06e154

   1. Initial program 82.3%

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

      1. associate-/l/ 97.3%

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

      2. div-inv 97.3%

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

   4. Applied egg-rr 97.3%

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

   5. Taylor expanded in y around inf 97.3%

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

      1. un-div-inv 97.3%

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

   7. Applied egg-rr 97.3%

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

   if -1.06e154 < y < -0.00145

   1. Initial program 87.0%

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

   3. Taylor expanded in y around inf 76.2%

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

      1. *-commutative 76.2%

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

   5. Simplified 76.2%

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

   if -0.00145 < y < 8.9999999999999995e-163

   1. Initial program 87.7%

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

   3. Taylor expanded in y around 0 71.8%

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

      1. associate-*r/ 71.8%

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

      2. neg-mul-1 71.8%

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

   5. Simplified 71.8%

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

   if 8.9999999999999995e-163 < y

   1. Initial program 82.4%

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

      1. associate-/l/ 98.8%

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

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 58.2%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+154}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -0.00145:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-37}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-187}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.55e-37)
   (/ (/ x z) (- z y))
   (if (<= z -6e-187)
     (/ x (* t (- y z)))
     (if (<= z 5.4e+32) (/ (/ x (- t z)) y) (/ (/ x z) (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e-37) {
		tmp = (x / z) / (z - y);
	} else if (z <= -6e-187) {
		tmp = x / (t * (y - z));
	} else if (z <= 5.4e+32) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / z) / (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 <= (-1.55d-37)) then
        tmp = (x / z) / (z - y)
    else if (z <= (-6d-187)) then
        tmp = x / (t * (y - z))
    else if (z <= 5.4d+32) then
        tmp = (x / (t - z)) / y
    else
        tmp = (x / z) / (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 <= -1.55e-37) {
		tmp = (x / z) / (z - y);
	} else if (z <= -6e-187) {
		tmp = x / (t * (y - z));
	} else if (z <= 5.4e+32) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.55e-37:
		tmp = (x / z) / (z - y)
	elif z <= -6e-187:
		tmp = x / (t * (y - z))
	elif z <= 5.4e+32:
		tmp = (x / (t - z)) / y
	else:
		tmp = (x / z) / (z - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.55e-37)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= -6e-187)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (z <= 5.4e+32)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(Float64(x / z) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.55e-37)
		tmp = (x / z) / (z - y);
	elseif (z <= -6e-187)
		tmp = x / (t * (y - z));
	elseif (z <= 5.4e+32)
		tmp = (x / (t - z)) / y;
	else
		tmp = (x / z) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.55e-37], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e-187], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+32], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.54999999999999997e-37

   1. Initial program 79.8%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 89.7%

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

      1. associate-*r/ 51.8%

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

      2. neg-mul-1 51.8%

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

   7. Simplified 89.7%

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

   if -1.54999999999999997e-37 < z < -6.00000000000000008e-187

   1. Initial program 96.3%

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

   3. Taylor expanded in t around inf 74.4%

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

   if -6.00000000000000008e-187 < z < 5.40000000000000025e32

   1. Initial program 91.8%

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

      1. associate-/l/ 95.3%

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

      2. div-inv 95.3%

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in y around inf 81.1%

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

      1. un-div-inv 81.1%

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

   7. Applied egg-rr 81.1%

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

   if 5.40000000000000025e32 < z

   1. Initial program 77.2%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. clear-num 99.7%

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

      2. frac-times 98.7%

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

      3. metadata-eval 98.7%

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

   6. Applied egg-rr 98.7%

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

   7. Taylor expanded in y around 0 71.6%

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

      1. neg-mul-1 71.6%

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

      2. associate-/r* 85.7%

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

      3. distribute-frac-neg 85.7%

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

      4. distribute-neg-frac2 85.7%

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

   9. Simplified 85.7%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-37}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-187}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{y}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 26000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) y)))
   (if (<= z -8.5e+114)
     t_1
     (if (<= z 26000000000.0)
       (/ (/ x t) y)
       (if (<= z 2.55e+185) (/ (/ x t) (- z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / y;
	double tmp;
	if (z <= -8.5e+114) {
		tmp = t_1;
	} else if (z <= 26000000000.0) {
		tmp = (x / t) / y;
	} else if (z <= 2.55e+185) {
		tmp = (x / t) / -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) :: tmp
    t_1 = (x / z) / y
    if (z <= (-8.5d+114)) then
        tmp = t_1
    else if (z <= 26000000000.0d0) then
        tmp = (x / t) / y
    else if (z <= 2.55d+185) then
        tmp = (x / t) / -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 / z) / y;
	double tmp;
	if (z <= -8.5e+114) {
		tmp = t_1;
	} else if (z <= 26000000000.0) {
		tmp = (x / t) / y;
	} else if (z <= 2.55e+185) {
		tmp = (x / t) / -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) / y
	tmp = 0
	if z <= -8.5e+114:
		tmp = t_1
	elif z <= 26000000000.0:
		tmp = (x / t) / y
	elif z <= 2.55e+185:
		tmp = (x / t) / -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / y)
	tmp = 0.0
	if (z <= -8.5e+114)
		tmp = t_1;
	elseif (z <= 26000000000.0)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 2.55e+185)
		tmp = Float64(Float64(x / t) / Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / y;
	tmp = 0.0;
	if (z <= -8.5e+114)
		tmp = t_1;
	elseif (z <= 26000000000.0)
		tmp = (x / t) / y;
	elseif (z <= 2.55e+185)
		tmp = (x / t) / -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -8.5e+114], t$95$1, If[LessEqual[z, 26000000000.0], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 2.55e+185], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000001e114 or 2.54999999999999998e185 < z

   1. Initial program 79.3%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 58.9%

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

   6. Taylor expanded in t around 0 57.7%

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

      1. associate-*r/ 57.7%

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

      2. neg-mul-1 57.7%

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

   8. Simplified 57.7%

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

      1. un-div-inv 57.7%

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

      2. clear-num 57.7%

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

      3. clear-num 57.7%

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

      4. add-sqr-sqrt 30.2%

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

      5. sqrt-unprod 53.5%

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

      6. sqr-neg 53.5%

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

      7. sqrt-unprod 27.6%

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

      8. add-sqr-sqrt 55.3%

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

   10. Applied egg-rr 55.3%

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

   if -8.5000000000000001e114 < z < 2.6e10

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 54.1%

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

      1. clear-num 54.0%

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

      2. associate-/r/ 54.1%

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

      3. associate-/r* 54.6%

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

   5. Applied egg-rr 54.6%

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

      1. associate-*l/ 59.3%

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

      2. associate-*l/ 59.4%

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

      3. *-un-lft-identity 59.4%

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

   7. Applied egg-rr 59.4%

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

   if 2.6e10 < z < 2.54999999999999998e185

   1. Initial program 74.0%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 32.6%

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

   6. Taylor expanded in y around 0 23.1%

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

      1. associate-*r/ 23.1%

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

      2. mul-1-neg 23.1%

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

   8. Simplified 23.1%

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

   9. Taylor expanded in x around 0 23.1%

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

       1. mul-1-neg 23.1%

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

       2. associate-/r* 25.5%

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

       3. distribute-neg-frac2 25.5%

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

   11. Simplified 25.5%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;z \leq 26000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{t}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+58}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) t)))
   (if (<= z -3e+131)
     t_1
     (if (<= z 1.95e+58)
       (/ (/ x t) y)
       (if (<= z 4.6e+187) t_1 (/ x (* z y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / t;
	double tmp;
	if (z <= -3e+131) {
		tmp = t_1;
	} else if (z <= 1.95e+58) {
		tmp = (x / t) / y;
	} else if (z <= 4.6e+187) {
		tmp = t_1;
	} else {
		tmp = x / (z * y);
	}
	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 / z) / t
    if (z <= (-3d+131)) then
        tmp = t_1
    else if (z <= 1.95d+58) then
        tmp = (x / t) / y
    else if (z <= 4.6d+187) then
        tmp = t_1
    else
        tmp = x / (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / t;
	double tmp;
	if (z <= -3e+131) {
		tmp = t_1;
	} else if (z <= 1.95e+58) {
		tmp = (x / t) / y;
	} else if (z <= 4.6e+187) {
		tmp = t_1;
	} else {
		tmp = x / (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) / t
	tmp = 0
	if z <= -3e+131:
		tmp = t_1
	elif z <= 1.95e+58:
		tmp = (x / t) / y
	elif z <= 4.6e+187:
		tmp = t_1
	else:
		tmp = x / (z * y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / t)
	tmp = 0.0
	if (z <= -3e+131)
		tmp = t_1;
	elseif (z <= 1.95e+58)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 4.6e+187)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / t;
	tmp = 0.0;
	if (z <= -3e+131)
		tmp = t_1;
	elseif (z <= 1.95e+58)
		tmp = (x / t) / y;
	elseif (z <= 4.6e+187)
		tmp = t_1;
	else
		tmp = x / (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -3e+131], t$95$1, If[LessEqual[z, 1.95e+58], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 4.6e+187], t$95$1, N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0000000000000001e131 or 1.95000000000000005e58 < z < 4.60000000000000008e187

   1. Initial program 72.7%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 33.6%

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

   6. Taylor expanded in y around 0 32.5%

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

      1. associate-*r/ 32.5%

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

      2. mul-1-neg 32.5%

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

   8. Simplified 32.5%

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

      1. div-inv 32.5%

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

      2. add-sqr-sqrt 14.8%

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

      3. sqrt-unprod 40.6%

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

      4. sqr-neg 40.6%

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

      5. sqrt-unprod 17.6%

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

      6. add-sqr-sqrt 32.4%

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

      7. associate-/r* 32.4%

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

   10. Applied egg-rr 32.4%

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

       1. *-commutative 32.4%

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

       2. associate-*l/ 29.7%

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

       3. associate-*r/ 42.1%

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

       4. associate-*l/ 42.1%

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

       5. *-lft-identity 42.1%

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

   12. Simplified 42.1%

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

   if -3.0000000000000001e131 < z < 1.95000000000000005e58

   1. Initial program 91.0%

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

   3. Taylor expanded in z around 0 51.0%

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

      1. clear-num 50.9%

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

      2. associate-/r/ 51.0%

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

      3. associate-/r* 51.5%

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

   5. Applied egg-rr 51.5%

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

      1. associate-*l/ 56.3%

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

      2. associate-*l/ 56.4%

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

      3. *-un-lft-identity 56.4%

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

   7. Applied egg-rr 56.4%

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

   if 4.60000000000000008e187 < z

   1. Initial program 84.7%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf 51.1%

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

   6. Taylor expanded in t around 0 48.0%

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

      1. associate-*r/ 48.0%

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

      2. neg-mul-1 48.0%

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

   8. Simplified 48.0%

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

      1. un-div-inv 48.0%

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

      2. associate-/l/ 45.4%

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

      3. add-sqr-sqrt 26.9%

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

      4. sqrt-unprod 46.6%

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

      5. sqr-neg 46.6%

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

      6. sqrt-unprod 18.5%

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

      7. add-sqr-sqrt 45.4%

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

   10. Applied egg-rr 45.4%

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

       1. *-commutative 45.4%

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

   12. Simplified 45.4%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+58}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+187}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 92.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+157}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+124}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.4e+157)
   (/ (/ x z) (- z y))
   (if (<= z 1.2e+124) (/ x (* (- t z) (- y z))) (/ (/ x z) (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e+157) {
		tmp = (x / z) / (z - y);
	} else if (z <= 1.2e+124) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / z) / (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 <= (-1.4d+157)) then
        tmp = (x / z) / (z - y)
    else if (z <= 1.2d+124) then
        tmp = x / ((t - z) * (y - z))
    else
        tmp = (x / z) / (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 <= -1.4e+157) {
		tmp = (x / z) / (z - y);
	} else if (z <= 1.2e+124) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.4e+157:
		tmp = (x / z) / (z - y)
	elif z <= 1.2e+124:
		tmp = x / ((t - z) * (y - z))
	else:
		tmp = (x / z) / (z - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.4e+157)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 1.2e+124)
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.4e+157)
		tmp = (x / z) / (z - y);
	elseif (z <= 1.2e+124)
		tmp = x / ((t - z) * (y - z));
	else
		tmp = (x / z) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.4e+157], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+124], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4000000000000001e157

   1. Initial program 71.7%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 97.6%

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

      1. associate-*r/ 60.9%

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

      2. neg-mul-1 60.9%

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

   7. Simplified 97.6%

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

   if -1.4000000000000001e157 < z < 1.20000000000000003e124

   1. Initial program 91.4%

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

   if 1.20000000000000003e124 < z

   1. Initial program 72.7%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. clear-num 99.8%

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

      2. frac-times 98.2%

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

      3. metadata-eval 98.2%

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

   6. Applied egg-rr 98.2%

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

   7. Taylor expanded in y around 0 70.5%

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

      1. neg-mul-1 70.5%

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

      2. associate-/r* 93.4%

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

      3. distribute-frac-neg 93.4%

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

      4. distribute-neg-frac2 93.4%

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

   9. Simplified 93.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+157}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+124}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+154}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.8e+154)
   (/ (/ x y) (- t z))
   (if (<= y -5.8e-40) (/ x (* (- t z) y)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e+154) {
		tmp = (x / y) / (t - z);
	} else if (y <= -5.8e-40) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = (x / t) / (y - 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 (y <= (-3.8d+154)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-5.8d-40)) then
        tmp = x / ((t - z) * y)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e+154) {
		tmp = (x / y) / (t - z);
	} else if (y <= -5.8e-40) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.8e+154:
		tmp = (x / y) / (t - z)
	elif y <= -5.8e-40:
		tmp = x / ((t - z) * y)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.8e+154)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -5.8e-40)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.8e+154)
		tmp = (x / y) / (t - z);
	elseif (y <= -5.8e-40)
		tmp = x / ((t - z) * y);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.8e+154], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e-40], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999998e154

   1. Initial program 82.3%

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

      1. associate-/l/ 97.3%

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

      2. div-inv 97.3%

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

   4. Applied egg-rr 97.3%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. clear-num 97.3%

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

      2. frac-times 97.1%

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

      3. metadata-eval 97.1%

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

   6. Applied egg-rr 97.1%

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

   7. Taylor expanded in y around inf 82.3%

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

      1. associate-/r* 92.9%

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

   9. Simplified 92.9%

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

   if -3.7999999999999998e154 < y < -5.7999999999999998e-40

   1. Initial program 85.8%

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

   3. Taylor expanded in y around inf 66.2%

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

      1. *-commutative 66.2%

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

   5. Simplified 66.2%

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

   if -5.7999999999999998e-40 < y

   1. Initial program 85.2%

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

      1. associate-/l/ 98.4%

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

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 57.1%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+154}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.05e-65)
   (/ (/ x (- t z)) y)
   (if (<= t 2.15e-35) (/ x (* z (- z y))) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e-65) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 2.15e-35) {
		tmp = x / (z * (z - y));
	} else {
		tmp = (x / t) / (y - 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 (t <= (-1.05d-65)) then
        tmp = (x / (t - z)) / y
    else if (t <= 2.15d-35) then
        tmp = x / (z * (z - y))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e-65) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 2.15e-35) {
		tmp = x / (z * (z - y));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.05e-65:
		tmp = (x / (t - z)) / y
	elif t <= 2.15e-35:
		tmp = x / (z * (z - y))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.05e-65)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 2.15e-35)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.05e-65)
		tmp = (x / (t - z)) / y;
	elseif (t <= 2.15e-35)
		tmp = x / (z * (z - y));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.05e-65], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 2.15e-35], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05000000000000001e-65

   1. Initial program 82.2%

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

      1. associate-/l/ 98.5%

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

      2. div-inv 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in y around inf 61.1%

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

      1. un-div-inv 61.1%

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

   7. Applied egg-rr 61.1%

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

   if -1.05000000000000001e-65 < t < 2.1500000000000001e-35

   1. Initial program 87.9%

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

   3. Taylor expanded in t around 0 72.6%

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

      1. associate-*r/ 72.6%

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

      2. neg-mul-1 72.6%

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

   5. Simplified 72.6%

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

   if 2.1500000000000001e-35 < t

   1. Initial program 82.2%

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

      1. associate-/l/ 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 86.9%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;z \leq 46000000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.6e+114)
   (/ (/ x z) y)
   (if (<= z 46000000000000.0) (/ (/ x t) y) (/ x (* z (- y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.6e+114) {
		tmp = (x / z) / y;
	} else if (z <= 46000000000000.0) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (z * -y);
	}
	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 <= (-9.6d+114)) then
        tmp = (x / z) / y
    else if (z <= 46000000000000.0d0) then
        tmp = (x / t) / y
    else
        tmp = x / (z * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.6e+114) {
		tmp = (x / z) / y;
	} else if (z <= 46000000000000.0) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (z * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.6e+114:
		tmp = (x / z) / y
	elif z <= 46000000000000.0:
		tmp = (x / t) / y
	else:
		tmp = x / (z * -y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.6e+114)
		tmp = Float64(Float64(x / z) / y);
	elseif (z <= 46000000000000.0)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x / Float64(z * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.6e+114)
		tmp = (x / z) / y;
	elseif (z <= 46000000000000.0)
		tmp = (x / t) / y;
	else
		tmp = x / (z * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.6e+114], N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 46000000000000.0], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.6e114

   1. Initial program 75.7%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 62.6%

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

   6. Taylor expanded in t around 0 62.6%

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

      1. associate-*r/ 62.6%

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

      2. neg-mul-1 62.6%

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

   8. Simplified 62.6%

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

      1. un-div-inv 62.6%

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

      2. clear-num 62.6%

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

      3. clear-num 62.6%

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

      4. add-sqr-sqrt 29.2%

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

      5. sqrt-unprod 56.3%

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

      6. sqr-neg 56.3%

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

      7. sqrt-unprod 33.3%

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

      8. add-sqr-sqrt 58.7%

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

   10. Applied egg-rr 58.7%

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

   if -9.6e114 < z < 4.6e13

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 54.1%

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

      1. clear-num 54.0%

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

      2. associate-/r/ 54.0%

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

      3. associate-/r* 54.6%

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

   5. Applied egg-rr 54.6%

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

      1. associate-*l/ 59.2%

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

      2. associate-*l/ 59.3%

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

      3. *-un-lft-identity 59.3%

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

   7. Applied egg-rr 59.3%

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

   if 4.6e13 < z

   1. Initial program 78.2%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 88.0%

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

      1. associate-*r/ 41.3%

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

      2. neg-mul-1 41.3%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in z around 0 34.7%

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

      1. associate-*r/ 34.7%

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

      2. mul-1-neg 34.7%

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

      3. *-commutative 34.7%

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

   10. Simplified 34.7%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;z \leq 46000000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 46.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+21} \lor \neg \left(z \leq 2.25 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.6e+21) (not (<= z 2.25e+63))) (/ x (* t z)) (/ x (* t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.6e+21) || !(z <= 2.25e+63)) {
		tmp = x / (t * z);
	} else {
		tmp = x / (t * y);
	}
	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 <= (-8.6d+21)) .or. (.not. (z <= 2.25d+63))) then
        tmp = x / (t * z)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.6e+21) || !(z <= 2.25e+63)) {
		tmp = x / (t * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.6e+21) or not (z <= 2.25e+63):
		tmp = x / (t * z)
	else:
		tmp = x / (t * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.6e+21) || !(z <= 2.25e+63))
		tmp = Float64(x / Float64(t * z));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.6e+21) || ~((z <= 2.25e+63)))
		tmp = x / (t * z);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.6e+21], N[Not[LessEqual[z, 2.25e+63]], $MachinePrecision]], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.6e21 or 2.25000000000000008e63 < z

   1. Initial program 78.6%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 38.0%

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

   6. Taylor expanded in y around 0 36.8%

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

      1. associate-*r/ 36.8%

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

      2. mul-1-neg 36.8%

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

   8. Simplified 36.8%

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

      1. add-sqr-sqrt 18.9%

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

      2. sqrt-unprod 41.9%

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

      3. sqr-neg 41.9%

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

      4. sqrt-unprod 16.8%

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

      5. add-sqr-sqrt 35.8%

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

      6. *-un-lft-identity 35.8%

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

      7. associate-/r* 31.0%

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

   10. Applied egg-rr 31.0%

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

       1. *-lft-identity 31.0%

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

       2. associate-/l/ 35.8%

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

   12. Simplified 35.8%

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

   if -8.6e21 < z < 2.25000000000000008e63

   1. Initial program 91.0%

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

   3. Taylor expanded in z around 0 56.4%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+21} \lor \neg \left(z \leq 2.25 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+115} \lor \neg \left(z \leq 5.6 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e+115) (not (<= z 5.6e+42))) (/ (/ x z) y) (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e+115) || !(z <= 5.6e+42)) {
		tmp = (x / z) / y;
	} else {
		tmp = (x / t) / y;
	}
	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 <= (-1.7d+115)) .or. (.not. (z <= 5.6d+42))) then
        tmp = (x / z) / y
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e+115) || !(z <= 5.6e+42)) {
		tmp = (x / z) / y;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e+115) or not (z <= 5.6e+42):
		tmp = (x / z) / y
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e+115) || !(z <= 5.6e+42))
		tmp = Float64(Float64(x / z) / y);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e+115) || ~((z <= 5.6e+42)))
		tmp = (x / z) / y;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e+115], N[Not[LessEqual[z, 5.6e+42]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e115 or 5.5999999999999999e42 < z

   1. Initial program 77.6%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 53.6%

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

   6. Taylor expanded in t around 0 51.0%

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

      1. associate-*r/ 51.0%

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

      2. neg-mul-1 51.0%

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

   8. Simplified 51.0%

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

      1. un-div-inv 51.0%

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

      2. clear-num 51.8%

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

      3. clear-num 51.0%

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

      4. add-sqr-sqrt 24.8%

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

      5. sqrt-unprod 49.5%

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

      6. sqr-neg 49.5%

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

      7. sqrt-unprod 24.6%

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

      8. add-sqr-sqrt 46.7%

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

   10. Applied egg-rr 46.7%

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

   if -1.7e115 < z < 5.5999999999999999e42

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0 52.0%

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

      1. clear-num 51.9%

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

      2. associate-/r/ 51.9%

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

      3. associate-/r* 52.5%

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

   5. Applied egg-rr 52.5%

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

      1. associate-*l/ 57.6%

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

      2. associate-*l/ 57.6%

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

      3. *-un-lft-identity 57.6%

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

   7. Applied egg-rr 57.6%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+115} \lor \neg \left(z \leq 5.6 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.35e-39) (/ x (* (- t z) y)) (/ x (* t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-39) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = x / (t * (y - 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 (y <= (-1.35d-39)) then
        tmp = x / ((t - z) * y)
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-39) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.35e-39:
		tmp = x / ((t - z) * y)
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.35e-39)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.35e-39)
		tmp = x / ((t - z) * y);
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.35e-39], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e-39

   1. Initial program 84.5%

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

   3. Taylor expanded in y around inf 72.4%

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

      1. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   if -1.35e-39 < y

   1. Initial program 85.2%

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

   3. Taylor expanded in t around inf 55.4%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 64.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.35e-39) (/ x (* (- t z) y)) (/ (/ x t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-39) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = (x / t) / (y - 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 (y <= (-1.35d-39)) then
        tmp = x / ((t - z) * y)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-39) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.35e-39:
		tmp = x / ((t - z) * y)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.35e-39)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.35e-39)
		tmp = x / ((t - z) * y);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.35e-39], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e-39

   1. Initial program 84.5%

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

   3. Taylor expanded in y around inf 72.4%

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

      1. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   if -1.35e-39 < y

   1. Initial program 85.2%

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

      1. associate-/l/ 98.4%

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

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 57.1%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 68.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.4e+17) (/ (/ x (- t z)) y) (/ (/ x t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.4e+17) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / t) / (y - 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 (t <= 1.4d+17) then
        tmp = (x / (t - z)) / y
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.4e+17) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.4e+17:
		tmp = (x / (t - z)) / y
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.4e+17)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.4e+17)
		tmp = (x / (t - z)) / y;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.4e+17], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.4e17

   1. Initial program 86.1%

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

      1. associate-/l/ 97.9%

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

      2. div-inv 97.8%

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in y around inf 63.2%

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

      1. un-div-inv 63.3%

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

   7. Applied egg-rr 63.3%

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

   if 1.4e17 < t

   1. Initial program 81.1%

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

      1. associate-/l/ 99.0%

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

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 88.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 39.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 / (t * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.9%

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

3. Taylor expanded in z around 0 37.6%

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

4. Final simplification 37.6%

   \[\leadsto \frac{x}{t \cdot y} \]
5. Add Preprocessing

Developer target: 87.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / 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 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    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);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024130 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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