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

Percentage Accurate: 89.2% → 96.7%

Time: 11.5s

Alternatives: 16

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: 89.2% 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, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{1}{y - z}}{\frac{t - z}{x}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.6%

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

   1. associate-/l/ 98.7%

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

   2. div-inv 98.6%

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

4. Applied egg-rr 98.6%

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

   1. *-commutative 98.6%

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

   2. clear-num 98.3%

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

   3. un-div-inv 98.5%

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

6. Applied egg-rr 98.5%

   \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]
7. Add Preprocessing

Alternative 2: 71.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t - z}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x y) (- t z))))
   (if (<= t -5.8e-147)
     t_1
     (if (<= t 4.5e-158)
       (/ x (* z (- z y)))
       (if (<= t 2.1e-82)
         t_1
         (if (<= t 2e-37) (/ x (* z (- z t))) (/ (/ x t) (- y z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / (t - z);
	double tmp;
	if (t <= -5.8e-147) {
		tmp = t_1;
	} else if (t <= 4.5e-158) {
		tmp = x / (z * (z - y));
	} else if (t <= 2.1e-82) {
		tmp = t_1;
	} else if (t <= 2e-37) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) / (t - z)
    if (t <= (-5.8d-147)) then
        tmp = t_1
    else if (t <= 4.5d-158) then
        tmp = x / (z * (z - y))
    else if (t <= 2.1d-82) then
        tmp = t_1
    else if (t <= 2d-37) 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 t_1 = (x / y) / (t - z);
	double tmp;
	if (t <= -5.8e-147) {
		tmp = t_1;
	} else if (t <= 4.5e-158) {
		tmp = x / (z * (z - y));
	} else if (t <= 2.1e-82) {
		tmp = t_1;
	} else if (t <= 2e-37) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) / (t - z)
	tmp = 0
	if t <= -5.8e-147:
		tmp = t_1
	elif t <= 4.5e-158:
		tmp = x / (z * (z - y))
	elif t <= 2.1e-82:
		tmp = t_1
	elif t <= 2e-37:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) / Float64(t - z))
	tmp = 0.0
	if (t <= -5.8e-147)
		tmp = t_1;
	elseif (t <= 4.5e-158)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	elseif (t <= 2.1e-82)
		tmp = t_1;
	elseif (t <= 2e-37)
		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)
	t_1 = (x / y) / (t - z);
	tmp = 0.0;
	if (t <= -5.8e-147)
		tmp = t_1;
	elseif (t <= 4.5e-158)
		tmp = x / (z * (z - y));
	elseif (t <= 2.1e-82)
		tmp = t_1;
	elseif (t <= 2e-37)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e-147], t$95$1, If[LessEqual[t, 4.5e-158], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-82], t$95$1, If[LessEqual[t, 2e-37], 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 t < -5.8000000000000002e-147 or 4.5e-158 < t < 2.1e-82

   1. Initial program 91.1%

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

   3. Taylor expanded in y around inf 58.6%

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

      1. associate-/r* 61.5%

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

   5. Simplified 61.5%

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

   if -5.8000000000000002e-147 < t < 4.5e-158

   1. Initial program 87.6%

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

   3. Taylor expanded in t around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. distribute-rgt-neg-in 80.4%

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

      3. neg-sub0 80.4%

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

      4. sub-neg 80.4%

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

      5. +-commutative 80.4%

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

      6. associate--r+ 80.4%

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

      7. neg-sub0 80.4%

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

      8. remove-double-neg 80.4%

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

   5. Simplified 80.4%

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

   if 2.1e-82 < t < 2.00000000000000013e-37

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. distribute-rgt-neg-in 90.3%

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

      3. sub-neg 90.3%

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

      4. +-commutative 90.3%

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

      5. distribute-neg-in 90.3%

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

      6. remove-double-neg 90.3%

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

      7. unsub-neg 90.3%

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

   5. Simplified 90.3%

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

   if 2.00000000000000013e-37 < t

   1. Initial program 84.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 88.0%

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

Alternative 3: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.5e+123)
   (/ (/ x y) t)
   (if (<= y -2.3e-112)
     (/ x (* z (- z y)))
     (if (<= y 1.6e-154) (/ x (* z (- z t))) (/ (/ x t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+123) {
		tmp = (x / y) / t;
	} else if (y <= -2.3e-112) {
		tmp = x / (z * (z - y));
	} else if (y <= 1.6e-154) {
		tmp = x / (z * (z - t));
	} 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 (y <= (-1.5d+123)) then
        tmp = (x / y) / t
    else if (y <= (-2.3d-112)) then
        tmp = x / (z * (z - y))
    else if (y <= 1.6d-154) then
        tmp = x / (z * (z - t))
    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 (y <= -1.5e+123) {
		tmp = (x / y) / t;
	} else if (y <= -2.3e-112) {
		tmp = x / (z * (z - y));
	} else if (y <= 1.6e-154) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.5e+123:
		tmp = (x / y) / t
	elif y <= -2.3e-112:
		tmp = x / (z * (z - y))
	elif y <= 1.6e-154:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.5e+123)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= -2.3e-112)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	elseif (y <= 1.6e-154)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.5e+123)
		tmp = (x / y) / t;
	elseif (y <= -2.3e-112)
		tmp = x / (z * (z - y));
	elseif (y <= 1.6e-154)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.5e+123], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, -2.3e-112], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-154], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.50000000000000004e123

   1. Initial program 87.6%

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

   3. Taylor expanded in y around inf 84.9%

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

      1. associate-/r* 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in t around inf 75.7%

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

   if -1.50000000000000004e123 < y < -2.29999999999999991e-112

   1. Initial program 90.5%

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

   3. Taylor expanded in t around 0 53.8%

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

      1. mul-1-neg 53.8%

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

      2. distribute-rgt-neg-in 53.8%

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

      3. neg-sub0 53.8%

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

      4. sub-neg 53.8%

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

      5. +-commutative 53.8%

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

      6. associate--r+ 53.8%

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

      7. neg-sub0 53.8%

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

      8. remove-double-neg 53.8%

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

   5. Simplified 53.8%

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

   if -2.29999999999999991e-112 < y < 1.60000000000000002e-154

   1. Initial program 90.3%

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

   3. Taylor expanded in y around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. distribute-rgt-neg-in 78.5%

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

      3. sub-neg 78.5%

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

      4. +-commutative 78.5%

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

      5. distribute-neg-in 78.5%

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

      6. remove-double-neg 78.5%

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

      7. unsub-neg 78.5%

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

   5. Simplified 78.5%

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

   if 1.60000000000000002e-154 < y

   1. Initial program 86.3%

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

      1. associate-/l/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in t around inf 53.3%

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

   6. Taylor expanded in y around inf 49.6%

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

Alternative 4: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{+99}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.04e+99)
   (/ (/ x y) t)
   (if (<= y -5.2e+23)
     (/ x (* y (- z)))
     (if (<= y 1.6e-154) (/ x (* z (- z t))) (/ (/ x t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.04e+99) {
		tmp = (x / y) / t;
	} else if (y <= -5.2e+23) {
		tmp = x / (y * -z);
	} else if (y <= 1.6e-154) {
		tmp = x / (z * (z - t));
	} 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 (y <= (-1.04d+99)) then
        tmp = (x / y) / t
    else if (y <= (-5.2d+23)) then
        tmp = x / (y * -z)
    else if (y <= 1.6d-154) then
        tmp = x / (z * (z - t))
    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 (y <= -1.04e+99) {
		tmp = (x / y) / t;
	} else if (y <= -5.2e+23) {
		tmp = x / (y * -z);
	} else if (y <= 1.6e-154) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.04e+99:
		tmp = (x / y) / t
	elif y <= -5.2e+23:
		tmp = x / (y * -z)
	elif y <= 1.6e-154:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.04e+99)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= -5.2e+23)
		tmp = Float64(x / Float64(y * Float64(-z)));
	elseif (y <= 1.6e-154)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.04e+99)
		tmp = (x / y) / t;
	elseif (y <= -5.2e+23)
		tmp = x / (y * -z);
	elseif (y <= 1.6e-154)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.04e+99], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, -5.2e+23], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-154], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.04e99

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf 83.6%

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

      1. associate-/r* 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in t around inf 72.9%

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

   if -1.04e99 < y < -5.19999999999999983e23

   1. Initial program 90.4%

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

   3. Taylor expanded in t around 0 65.0%

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

      1. mul-1-neg 65.0%

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

      2. distribute-rgt-neg-in 65.0%

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

      3. neg-sub0 65.0%

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

      4. sub-neg 65.0%

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

      5. +-commutative 65.0%

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

      6. associate--r+ 65.0%

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

      7. neg-sub0 65.0%

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

      8. remove-double-neg 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in z around 0 53.3%

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

      1. associate-*r/ 53.3%

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

      2. neg-mul-1 53.3%

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

      3. *-commutative 53.3%

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

   8. Simplified 53.3%

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

   if -5.19999999999999983e23 < y < 1.60000000000000002e-154

   1. Initial program 90.0%

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

   3. Taylor expanded in y around 0 67.0%

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

      1. mul-1-neg 67.0%

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

      2. distribute-rgt-neg-in 67.0%

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

      3. sub-neg 67.0%

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

      4. +-commutative 67.0%

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

      5. distribute-neg-in 67.0%

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

      6. remove-double-neg 67.0%

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

      7. unsub-neg 67.0%

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

   5. Simplified 67.0%

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

   if 1.60000000000000002e-154 < y

   1. Initial program 86.3%

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

      1. associate-/l/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in t around inf 53.3%

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

   6. Taylor expanded in y around inf 49.6%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{+99}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 2e+301) (/ x t_1) (* (/ x (- t z)) (/ -1.0 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 2e+301) {
		tmp = x / t_1;
	} else {
		tmp = (x / (t - z)) * (-1.0 / 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 = (y - z) * (t - z)
    if (t_1 <= 2d+301) then
        tmp = x / t_1
    else
        tmp = (x / (t - z)) * ((-1.0d0) / z)
    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 (t_1 <= 2e+301) {
		tmp = x / t_1;
	} else {
		tmp = (x / (t - z)) * (-1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= 2e+301:
		tmp = x / t_1
	else:
		tmp = (x / (t - z)) * (-1.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= 2e+301)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(-1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= 2e+301)
		tmp = x / t_1;
	else
		tmp = (x / (t - z)) * (-1.0 / z);
	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[LessEqual[t$95$1, 2e+301], N[(x / t$95$1), $MachinePrecision], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 2.00000000000000011e301

   1. Initial program 94.6%

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

   if 2.00000000000000011e301 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 72.9%

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

      1. associate-/l/ 100.0%

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

      2. div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 84.3%

      \[\leadsto \frac{x}{t - z} \cdot \color{blue}{\frac{-1}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.9e-75)
   (/ (/ x y) (- t z))
   (if (<= y 1.35e-67) (* (/ x (- t z)) (/ -1.0 z)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e-75) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.35e-67) {
		tmp = (x / (t - z)) * (-1.0 / z);
	} 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 <= (-1.9d-75)) then
        tmp = (x / y) / (t - z)
    else if (y <= 1.35d-67) then
        tmp = (x / (t - z)) * ((-1.0d0) / z)
    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 <= -1.9e-75) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.35e-67) {
		tmp = (x / (t - z)) * (-1.0 / z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.9e-75:
		tmp = (x / y) / (t - z)
	elif y <= 1.35e-67:
		tmp = (x / (t - z)) * (-1.0 / z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.9e-75)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 1.35e-67)
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(-1.0 / z));
	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 <= -1.9e-75)
		tmp = (x / y) / (t - z);
	elseif (y <= 1.35e-67)
		tmp = (x / (t - z)) * (-1.0 / z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.9e-75], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-67], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.89999999999999997e-75

   1. Initial program 89.1%

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

   3. Taylor expanded in y around inf 77.4%

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

      1. associate-/r* 83.4%

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

   5. Simplified 83.4%

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

   if -1.89999999999999997e-75 < y < 1.35000000000000008e-67

   1. Initial program 88.8%

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

      1. associate-/l/ 98.7%

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

      2. div-inv 98.6%

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

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in y around 0 84.1%

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

   if 1.35000000000000008e-67 < y

   1. Initial program 87.8%

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

      1. associate-/l/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 56.1%

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

Alternative 7: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-147}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-37}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.3e-147)
   (/ (/ x y) (- t z))
   (if (<= t 2e-37) (/ (/ x z) (- z y)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.3e-147) {
		tmp = (x / y) / (t - z);
	} else if (t <= 2e-37) {
		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 <= (-1.3d-147)) then
        tmp = (x / y) / (t - z)
    else if (t <= 2d-37) 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 <= -1.3e-147) {
		tmp = (x / y) / (t - z);
	} else if (t <= 2e-37) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.3e-147:
		tmp = (x / y) / (t - z)
	elif t <= 2e-37:
		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 <= -1.3e-147)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 2e-37)
		tmp = Float64(Float64(x / 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 <= -1.3e-147)
		tmp = (x / y) / (t - z);
	elseif (t <= 2e-37)
		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, -1.3e-147], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-37], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2999999999999999e-147

   1. Initial program 90.0%

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

   3. Taylor expanded in y around inf 53.3%

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

      1. associate-/r* 56.6%

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

   5. Simplified 56.6%

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

   if -1.2999999999999999e-147 < t < 2.00000000000000013e-37

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. associate-/r* 81.8%

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

      3. distribute-neg-frac2 81.8%

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

      4. neg-sub0 81.8%

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

      5. sub-neg 81.8%

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

      6. +-commutative 81.8%

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

      7. associate--r+ 81.8%

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

      8. neg-sub0 81.8%

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

      9. remove-double-neg 81.8%

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

   5. Simplified 81.8%

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

   if 2.00000000000000013e-37 < t

   1. Initial program 84.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 88.0%

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

Alternative 8: 70.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-295}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.32e-74)
   (/ (/ x y) (- t z))
   (if (<= y 1.25e-295) (/ (/ x z) (- z t)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.32e-74) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.25e-295) {
		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 <= (-1.32d-74)) then
        tmp = (x / y) / (t - z)
    else if (y <= 1.25d-295) 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 <= -1.32e-74) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.25e-295) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.32e-74:
		tmp = (x / y) / (t - z)
	elif y <= 1.25e-295:
		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 <= -1.32e-74)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 1.25e-295)
		tmp = Float64(Float64(x / 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 <= -1.32e-74)
		tmp = (x / y) / (t - z);
	elseif (y <= 1.25e-295)
		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, -1.32e-74], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-295], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.32e-74

   1. Initial program 89.1%

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

   3. Taylor expanded in y around inf 77.4%

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

      1. associate-/r* 83.4%

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

   5. Simplified 83.4%

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

   if -1.32e-74 < y < 1.25000000000000002e-295

   1. Initial program 90.1%

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

   3. Taylor expanded in y around 0 79.6%

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

      1. mul-1-neg 79.6%

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

      2. associate-/r* 87.2%

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

      3. distribute-neg-frac2 87.2%

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

      4. sub-neg 87.2%

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

      5. +-commutative 87.2%

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

      6. distribute-neg-in 87.2%

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

      7. remove-double-neg 87.2%

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

      8. unsub-neg 87.2%

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

   5. Simplified 87.2%

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

   if 1.25000000000000002e-295 < y

   1. Initial program 87.6%

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

      1. associate-/l/ 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t around inf 60.6%

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

Alternative 9: 71.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.5e-21)
   (/ (/ x t) y)
   (if (<= t 4.8e-100) (/ x (* z (- z y))) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e-21) {
		tmp = (x / t) / y;
	} else if (t <= 4.8e-100) {
		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 <= (-6.5d-21)) then
        tmp = (x / t) / y
    else if (t <= 4.8d-100) 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 <= -6.5e-21) {
		tmp = (x / t) / y;
	} else if (t <= 4.8e-100) {
		tmp = x / (z * (z - y));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.5e-21:
		tmp = (x / t) / y
	elif t <= 4.8e-100:
		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 <= -6.5e-21)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 4.8e-100)
		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 <= -6.5e-21)
		tmp = (x / t) / y;
	elseif (t <= 4.8e-100)
		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, -6.5e-21], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4.8e-100], 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 < -6.49999999999999987e-21

   1. Initial program 89.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 83.6%

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

   6. Taylor expanded in y around inf 61.2%

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

   if -6.49999999999999987e-21 < t < 4.8000000000000005e-100

   1. Initial program 89.7%

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

   3. Taylor expanded in t around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. distribute-rgt-neg-in 71.9%

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

      3. neg-sub0 71.9%

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

      4. sub-neg 71.9%

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

      5. +-commutative 71.9%

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

      6. associate--r+ 71.9%

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

      7. neg-sub0 71.9%

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

      8. remove-double-neg 71.9%

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

   5. Simplified 71.9%

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

   if 4.8000000000000005e-100 < t

   1. Initial program 86.9%

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

      1. associate-/l/ 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around inf 84.0%

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

Alternative 10: 70.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-103}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.7e-18)
   (/ (/ x t) y)
   (if (<= t 6.2e-103) (/ x (* z (- z y))) (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e-18) {
		tmp = (x / t) / y;
	} else if (t <= 6.2e-103) {
		tmp = x / (z * (z - y));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.7d-18)) then
        tmp = (x / t) / y
    else if (t <= 6.2d-103) then
        tmp = x / (z * (z - y))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e-18) {
		tmp = (x / t) / y;
	} else if (t <= 6.2e-103) {
		tmp = x / (z * (z - y));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.7e-18:
		tmp = (x / t) / y
	elif t <= 6.2e-103:
		tmp = x / (z * (z - y))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.7e-18)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 6.2e-103)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.7e-18)
		tmp = (x / t) / y;
	elseif (t <= 6.2e-103)
		tmp = x / (z * (z - y));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.7e-18], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 6.2e-103], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.70000000000000001e-18

   1. Initial program 89.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 83.6%

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

   6. Taylor expanded in y around inf 61.2%

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

   if -1.70000000000000001e-18 < t < 6.2000000000000003e-103

   1. Initial program 89.7%

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

   3. Taylor expanded in t around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. distribute-rgt-neg-in 71.9%

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

      3. neg-sub0 71.9%

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

      4. sub-neg 71.9%

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

      5. +-commutative 71.9%

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

      6. associate--r+ 71.9%

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

      7. neg-sub0 71.9%

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

      8. remove-double-neg 71.9%

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

   5. Simplified 71.9%

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

   if 6.2000000000000003e-103 < t

   1. Initial program 86.9%

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

   3. Taylor expanded in t around inf 75.8%

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

Alternative 11: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+45} \lor \neg \left(z \leq 3.1 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.8e+45) (not (<= z 3.1e+71))) (/ (/ x z) z) (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e+45) || !(z <= 3.1e+71)) {
		tmp = (x / z) / 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 <= (-4.8d+45)) .or. (.not. (z <= 3.1d+71))) then
        tmp = (x / z) / 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 <= -4.8e+45) || !(z <= 3.1e+71)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.8e+45) or not (z <= 3.1e+71):
		tmp = (x / z) / z
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.8e+45) || !(z <= 3.1e+71))
		tmp = Float64(Float64(x / z) / z);
	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 <= -4.8e+45) || ~((z <= 3.1e+71)))
		tmp = (x / z) / z;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.8e+45], N[Not[LessEqual[z, 3.1e+71]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999979e45 or 3.10000000000000018e71 < z

   1. Initial program 81.8%

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

   3. Taylor expanded in t around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. distribute-rgt-neg-in 77.6%

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

      3. neg-sub0 77.6%

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

      4. sub-neg 77.6%

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

      5. +-commutative 77.6%

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

      6. associate--r+ 77.6%

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

      7. neg-sub0 77.6%

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

      8. remove-double-neg 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in z around inf 74.6%

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

      1. associate-/r* 84.2%

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

      2. div-inv 84.2%

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

   8. Applied egg-rr 84.2%

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

      1. associate-*r/ 84.2%

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

      2. *-rgt-identity 84.2%

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

   10. Simplified 84.2%

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

   if -4.79999999999999979e45 < z < 3.10000000000000018e71

   1. Initial program 92.0%

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

      1. associate-/l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around inf 74.7%

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

   6. Taylor expanded in y around inf 56.8%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+45} \lor \neg \left(z \leq 3.1 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+47} \lor \neg \left(z \leq 2.8 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.1e+47) (not (<= z 2.8e+71))) (/ x (* z z)) (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1e+47) || !(z <= 2.8e+71)) {
		tmp = x / (z * 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 <= (-1.1d+47)) .or. (.not. (z <= 2.8d+71))) then
        tmp = x / (z * 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 <= -1.1e+47) || !(z <= 2.8e+71)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.1e+47) or not (z <= 2.8e+71):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.1e+47) || !(z <= 2.8e+71))
		tmp = Float64(x / Float64(z * z));
	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 <= -1.1e+47) || ~((z <= 2.8e+71)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.1e+47], N[Not[LessEqual[z, 2.8e+71]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e47 or 2.80000000000000002e71 < z

   1. Initial program 81.8%

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

   3. Taylor expanded in t around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. distribute-rgt-neg-in 77.6%

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

      3. neg-sub0 77.6%

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

      4. sub-neg 77.6%

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

      5. +-commutative 77.6%

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

      6. associate--r+ 77.6%

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

      7. neg-sub0 77.6%

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

      8. remove-double-neg 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in z around inf 74.6%

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

   if -1.1e47 < z < 2.80000000000000002e71

   1. Initial program 92.0%

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

      1. associate-/l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around inf 74.7%

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

   6. Taylor expanded in y around inf 56.8%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+47} \lor \neg \left(z \leq 2.8 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+25} \lor \neg \left(z \leq 2.8 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e+25) (not (<= z 2.8e+71))) (/ x (* z z)) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+25) || !(z <= 2.8e+71)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * 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 <= (-1.8d+25)) .or. (.not. (z <= 2.8d+71))) then
        tmp = x / (z * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+25) || !(z <= 2.8e+71)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e+25) or not (z <= 2.8e+71):
		tmp = x / (z * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e+25) || !(z <= 2.8e+71))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.8e+25) || ~((z <= 2.8e+71)))
		tmp = x / (z * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e+25], N[Not[LessEqual[z, 2.8e+71]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000008e25 or 2.80000000000000002e71 < z

   1. Initial program 82.2%

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

   3. Taylor expanded in t around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. distribute-rgt-neg-in 77.0%

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

      3. neg-sub0 77.0%

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

      4. sub-neg 77.0%

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

      5. +-commutative 77.0%

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

      6. associate--r+ 77.0%

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

      7. neg-sub0 77.0%

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

      8. remove-double-neg 77.0%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in z around inf 74.1%

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

   if -1.80000000000000008e25 < z < 2.80000000000000002e71

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 51.0%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+25} \lor \neg \left(z \leq 2.8 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+47} \lor \neg \left(z \leq 5400\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e+47) (not (<= z 5400.0))) (/ x (* y z)) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+47) || !(z <= 5400.0)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * 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 <= (-1d+47)) .or. (.not. (z <= 5400.0d0))) then
        tmp = x / (y * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+47) || !(z <= 5400.0)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1e+47) or not (z <= 5400.0):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1e+47) || !(z <= 5400.0))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1e+47) || ~((z <= 5400.0)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1e+47], N[Not[LessEqual[z, 5400.0]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e47 or 5400 < z

   1. Initial program 84.0%

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

   3. Taylor expanded in t around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. distribute-rgt-neg-in 75.5%

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

      3. neg-sub0 75.5%

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

      4. sub-neg 75.5%

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

      5. +-commutative 75.5%

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

      6. associate--r+ 75.5%

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

      7. neg-sub0 75.5%

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

      8. remove-double-neg 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in z around 0 42.2%

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

      1. associate-*r/ 42.2%

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

      2. neg-mul-1 42.2%

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

      3. *-commutative 42.2%

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

   8. Simplified 42.2%

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

      1. add-sqr-sqrt 18.0%

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

      2. sqrt-unprod 46.0%

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

      3. sqr-neg 46.0%

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

      4. sqrt-unprod 23.2%

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

      5. add-sqr-sqrt 39.5%

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

      6. *-un-lft-identity 39.5%

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

      7. *-commutative 39.5%

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

   10. Applied egg-rr 39.5%

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

       1. *-lft-identity 39.5%

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

       2. *-commutative 39.5%

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

   12. Simplified 39.5%

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

   if -1e47 < z < 5400

   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 51.6%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+47} \lor \neg \left(z \leq 5400\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 96.8% 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 88.6%

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

   1. associate-/l/ 98.7%

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

3. Simplified 98.7%

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

Alternative 16: 40.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 * t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.6%

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

3. Taylor expanded in z around 0 39.6%

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

4. Final simplification 39.6%

   \[\leadsto \frac{x}{y \cdot t} \]
5. Add Preprocessing

Developer Target 1: 88.0% 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 2024146 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ x (* (- y z) (- t z))) 0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z))))))

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