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

Percentage Accurate: 89.1% → 96.8%

Time: 11.2s

Alternatives: 21

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: 89.1% 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: 96.8% accurate, 1.0× speedup

Math

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

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(Float64(x / 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[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in x around 0 89.3%

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

   1. associate-/l/ 98.5%

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

5. Simplified 98.5%

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

Alternative 2: 64.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot t}\\ t_2 := \frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+128}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{-1}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) t))) (t_2 (/ x (* z (- t z)))))
   (if (<= z -2.25e+128)
     t_2
     (if (<= z 2.8e-75)
       t_1
       (if (<= z 2.2e+15)
         (/ (/ x y) (- z))
         (if (<= z 5.2e+104)
           t_1
           (if (<= z 1.6e+130) (* (/ -1.0 y) (/ x z)) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * t);
	double t_2 = x / (z * (t - z));
	double tmp;
	if (z <= -2.25e+128) {
		tmp = t_2;
	} else if (z <= 2.8e-75) {
		tmp = t_1;
	} else if (z <= 2.2e+15) {
		tmp = (x / y) / -z;
	} else if (z <= 5.2e+104) {
		tmp = t_1;
	} else if (z <= 1.6e+130) {
		tmp = (-1.0 / y) * (x / z);
	} 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 - z) * t)
    t_2 = x / (z * (t - z))
    if (z <= (-2.25d+128)) then
        tmp = t_2
    else if (z <= 2.8d-75) then
        tmp = t_1
    else if (z <= 2.2d+15) then
        tmp = (x / y) / -z
    else if (z <= 5.2d+104) then
        tmp = t_1
    else if (z <= 1.6d+130) then
        tmp = ((-1.0d0) / y) * (x / z)
    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 - z) * t);
	double t_2 = x / (z * (t - z));
	double tmp;
	if (z <= -2.25e+128) {
		tmp = t_2;
	} else if (z <= 2.8e-75) {
		tmp = t_1;
	} else if (z <= 2.2e+15) {
		tmp = (x / y) / -z;
	} else if (z <= 5.2e+104) {
		tmp = t_1;
	} else if (z <= 1.6e+130) {
		tmp = (-1.0 / y) * (x / z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * t)
	t_2 = x / (z * (t - z))
	tmp = 0
	if z <= -2.25e+128:
		tmp = t_2
	elif z <= 2.8e-75:
		tmp = t_1
	elif z <= 2.2e+15:
		tmp = (x / y) / -z
	elif z <= 5.2e+104:
		tmp = t_1
	elif z <= 1.6e+130:
		tmp = (-1.0 / y) * (x / z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * t))
	t_2 = Float64(x / Float64(z * Float64(t - z)))
	tmp = 0.0
	if (z <= -2.25e+128)
		tmp = t_2;
	elseif (z <= 2.8e-75)
		tmp = t_1;
	elseif (z <= 2.2e+15)
		tmp = Float64(Float64(x / y) / Float64(-z));
	elseif (z <= 5.2e+104)
		tmp = t_1;
	elseif (z <= 1.6e+130)
		tmp = Float64(Float64(-1.0 / y) * Float64(x / z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * t);
	t_2 = x / (z * (t - z));
	tmp = 0.0;
	if (z <= -2.25e+128)
		tmp = t_2;
	elseif (z <= 2.8e-75)
		tmp = t_1;
	elseif (z <= 2.2e+15)
		tmp = (x / y) / -z;
	elseif (z <= 5.2e+104)
		tmp = t_1;
	elseif (z <= 1.6e+130)
		tmp = (-1.0 / y) * (x / z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+128], t$95$2, If[LessEqual[z, 2.8e-75], t$95$1, If[LessEqual[z, 2.2e+15], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 5.2e+104], t$95$1, If[LessEqual[z, 1.6e+130], N[(N[(-1.0 / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2500000000000001e128 or 1.6e130 < z

   1. Initial program 84.8%

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

   3. Taylor expanded in y around 0 83.6%

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

      1. associate-*r/ 83.6%

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

      2. neg-mul-1 83.6%

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

   5. Simplified 83.6%

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

      1. div-inv 83.6%

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

      2. add-sqr-sqrt 52.0%

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

      3. sqrt-unprod 70.9%

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

      4. sqr-neg 70.9%

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

      5. sqrt-unprod 30.3%

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

      6. add-sqr-sqrt 82.3%

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

   7. Applied egg-rr 82.3%

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

      1. associate-*r/ 82.3%

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

      2. *-rgt-identity 82.3%

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

   9. Simplified 82.3%

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

   if -2.2500000000000001e128 < z < 2.79999999999999998e-75 or 2.2e15 < z < 5.20000000000000001e104

   1. Initial program 91.2%

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

   3. Taylor expanded in t around inf 70.8%

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

   if 2.79999999999999998e-75 < z < 2.2e15

   1. Initial program 96.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 64.9%

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

      1. associate-*r/ 64.9%

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

      2. neg-mul-1 64.9%

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

   7. Simplified 64.9%

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

   8. Taylor expanded in z around 0 38.4%

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

      1. mul-1-neg 38.4%

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

      2. associate-/r* 38.5%

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

      3. distribute-neg-frac2 38.5%

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

   10. Simplified 38.5%

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

   if 5.20000000000000001e104 < z < 1.6e130

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf 19.2%

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

      1. *-commutative 19.2%

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

   5. Simplified 19.2%

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

   6. Taylor expanded in t around 0 19.4%

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

      1. associate-*r/ 19.4%

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

      2. mul-1-neg 19.4%

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

      3. *-commutative 19.4%

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

   8. Simplified 19.4%

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

      1. neg-mul-1 19.4%

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

      2. *-commutative 19.4%

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

      3. times-frac 34.7%

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

   10. Applied egg-rr 34.7%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+128}:\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{-1}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{-1}{y} \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+105}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.3e+106)
   (* (/ -1.0 y) (/ x z))
   (if (<= z 4.5e-75)
     (/ (/ x y) t)
     (if (<= z 6.2e+19)
       (/ (/ x y) (- z))
       (if (<= z 1.05e+105) (/ (- x) (* z t)) (/ (/ (- x) z) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e+106) {
		tmp = (-1.0 / y) * (x / z);
	} else if (z <= 4.5e-75) {
		tmp = (x / y) / t;
	} else if (z <= 6.2e+19) {
		tmp = (x / y) / -z;
	} else if (z <= 1.05e+105) {
		tmp = -x / (z * t);
	} 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 <= (-3.3d+106)) then
        tmp = ((-1.0d0) / y) * (x / z)
    else if (z <= 4.5d-75) then
        tmp = (x / y) / t
    else if (z <= 6.2d+19) then
        tmp = (x / y) / -z
    else if (z <= 1.05d+105) then
        tmp = -x / (z * t)
    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 <= -3.3e+106) {
		tmp = (-1.0 / y) * (x / z);
	} else if (z <= 4.5e-75) {
		tmp = (x / y) / t;
	} else if (z <= 6.2e+19) {
		tmp = (x / y) / -z;
	} else if (z <= 1.05e+105) {
		tmp = -x / (z * t);
	} else {
		tmp = (-x / z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.3e+106:
		tmp = (-1.0 / y) * (x / z)
	elif z <= 4.5e-75:
		tmp = (x / y) / t
	elif z <= 6.2e+19:
		tmp = (x / y) / -z
	elif z <= 1.05e+105:
		tmp = -x / (z * t)
	else:
		tmp = (-x / z) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.3e+106)
		tmp = Float64(Float64(-1.0 / y) * Float64(x / z));
	elseif (z <= 4.5e-75)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 6.2e+19)
		tmp = Float64(Float64(x / y) / Float64(-z));
	elseif (z <= 1.05e+105)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(Float64(Float64(-x) / z) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.3e+106)
		tmp = (-1.0 / y) * (x / z);
	elseif (z <= 4.5e-75)
		tmp = (x / y) / t;
	elseif (z <= 6.2e+19)
		tmp = (x / y) / -z;
	elseif (z <= 1.05e+105)
		tmp = -x / (z * t);
	else
		tmp = (-x / z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.3e+106], N[(N[(-1.0 / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-75], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 6.2e+19], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 1.05e+105], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.30000000000000008e106

   1. Initial program 85.2%

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

   3. Taylor expanded in y around inf 57.2%

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

      1. *-commutative 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in t around 0 52.8%

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

      1. associate-*r/ 52.8%

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

      2. mul-1-neg 52.8%

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

      3. *-commutative 52.8%

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

   8. Simplified 52.8%

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

      1. neg-mul-1 52.8%

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

      2. *-commutative 52.8%

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

      3. times-frac 62.3%

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

   10. Applied egg-rr 62.3%

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

   if -3.30000000000000008e106 < z < 4.5000000000000003e-75

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0 90.9%

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

      1. associate-/l/ 97.3%

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

   5. Simplified 97.3%

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

      1. clear-num 96.8%

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

      2. associate-/r/ 97.2%

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

   7. Applied egg-rr 97.2%

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

   8. Taylor expanded in z around 0 67.6%

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

      1. associate-/l/ 72.2%

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

   10. Simplified 72.2%

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

   if 4.5000000000000003e-75 < z < 6.2e19

   1. Initial program 96.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 64.9%

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

      1. associate-*r/ 64.9%

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

      2. neg-mul-1 64.9%

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

   7. Simplified 64.9%

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

   8. Taylor expanded in z around 0 38.4%

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

      1. mul-1-neg 38.4%

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

      2. associate-/r* 38.5%

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

      3. distribute-neg-frac2 38.5%

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

   10. Simplified 38.5%

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

   if 6.2e19 < z < 1.05000000000000005e105

   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 71.7%

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

      1. associate-*r/ 71.7%

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

      2. neg-mul-1 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in z around 0 26.6%

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

      1. associate-*r/ 26.6%

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

      2. mul-1-neg 26.6%

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

   8. Simplified 26.6%

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

   if 1.05000000000000005e105 < z

   1. Initial program 81.2%

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

   3. Taylor expanded in y around inf 52.0%

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

      1. *-commutative 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in t around 0 49.1%

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

      1. associate-*r/ 49.1%

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

      2. mul-1-neg 49.1%

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

      3. *-commutative 49.1%

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

   8. Simplified 49.1%

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

   9. Taylor expanded in x around 0 49.1%

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

       1. associate-*r/ 49.1%

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

       2. times-frac 60.2%

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

       3. associate-*l/ 60.2%

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

       4. mul-1-neg 60.2%

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

       5. distribute-neg-frac2 60.2%

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

   11. Simplified 60.2%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{-1}{y} \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+105}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{-x}{z}}{y}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+104}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ (- x) z) y)))
   (if (<= z -3.3e+106)
     t_1
     (if (<= z 4.1e-75)
       (/ (/ x y) t)
       (if (<= z 2.1e+18)
         (/ (/ x y) (- z))
         (if (<= z 5.2e+104) (/ (- x) (* z t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-x / z) / y;
	double tmp;
	if (z <= -3.3e+106) {
		tmp = t_1;
	} else if (z <= 4.1e-75) {
		tmp = (x / y) / t;
	} else if (z <= 2.1e+18) {
		tmp = (x / y) / -z;
	} else if (z <= 5.2e+104) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-x / z) / y
    if (z <= (-3.3d+106)) then
        tmp = t_1
    else if (z <= 4.1d-75) then
        tmp = (x / y) / t
    else if (z <= 2.1d+18) then
        tmp = (x / y) / -z
    else if (z <= 5.2d+104) then
        tmp = -x / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (-x / z) / y;
	double tmp;
	if (z <= -3.3e+106) {
		tmp = t_1;
	} else if (z <= 4.1e-75) {
		tmp = (x / y) / t;
	} else if (z <= 2.1e+18) {
		tmp = (x / y) / -z;
	} else if (z <= 5.2e+104) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-x / z) / y
	tmp = 0
	if z <= -3.3e+106:
		tmp = t_1
	elif z <= 4.1e-75:
		tmp = (x / y) / t
	elif z <= 2.1e+18:
		tmp = (x / y) / -z
	elif z <= 5.2e+104:
		tmp = -x / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-x) / z) / y)
	tmp = 0.0
	if (z <= -3.3e+106)
		tmp = t_1;
	elseif (z <= 4.1e-75)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 2.1e+18)
		tmp = Float64(Float64(x / y) / Float64(-z));
	elseif (z <= 5.2e+104)
		tmp = Float64(Float64(-x) / Float64(z * t));
	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 <= -3.3e+106)
		tmp = t_1;
	elseif (z <= 4.1e-75)
		tmp = (x / y) / t;
	elseif (z <= 2.1e+18)
		tmp = (x / y) / -z;
	elseif (z <= 5.2e+104)
		tmp = -x / (z * t);
	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, -3.3e+106], t$95$1, If[LessEqual[z, 4.1e-75], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.1e+18], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 5.2e+104], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.30000000000000008e106 or 5.20000000000000001e104 < z

   1. Initial program 83.0%

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

   3. Taylor expanded in y around inf 54.4%

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

      1. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in t around 0 50.8%

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

      1. associate-*r/ 50.8%

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

      2. mul-1-neg 50.8%

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

      3. *-commutative 50.8%

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

   8. Simplified 50.8%

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

   9. Taylor expanded in x around 0 50.8%

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

       1. associate-*r/ 50.8%

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

       2. times-frac 61.1%

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

       3. associate-*l/ 61.1%

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

       4. mul-1-neg 61.1%

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

       5. distribute-neg-frac2 61.1%

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

   11. Simplified 61.1%

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

   if -3.30000000000000008e106 < z < 4.10000000000000002e-75

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0 90.9%

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

      1. associate-/l/ 97.3%

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

   5. Simplified 97.3%

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

      1. clear-num 96.8%

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

      2. associate-/r/ 97.2%

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

   7. Applied egg-rr 97.2%

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

   8. Taylor expanded in z around 0 67.6%

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

      1. associate-/l/ 72.2%

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

   10. Simplified 72.2%

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

   if 4.10000000000000002e-75 < z < 2.1e18

   1. Initial program 96.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 64.9%

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

      1. associate-*r/ 64.9%

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

      2. neg-mul-1 64.9%

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

   7. Simplified 64.9%

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

   8. Taylor expanded in z around 0 38.4%

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

      1. mul-1-neg 38.4%

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

      2. associate-/r* 38.5%

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

      3. distribute-neg-frac2 38.5%

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

   10. Simplified 38.5%

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

   if 2.1e18 < z < 5.20000000000000001e104

   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 71.7%

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

      1. associate-*r/ 71.7%

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

      2. neg-mul-1 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in z around 0 26.6%

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

      1. associate-*r/ 26.6%

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

      2. mul-1-neg 26.6%

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

   8. Simplified 26.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+104}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-142}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 31000000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (- z t))))
   (if (<= z -5.6e-65)
     t_1
     (if (<= z 8.5e-142)
       (/ (/ x (- y z)) t)
       (if (<= z 31000000000000.0) (/ (/ x y) (- t z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - t);
	double tmp;
	if (z <= -5.6e-65) {
		tmp = t_1;
	} else if (z <= 8.5e-142) {
		tmp = (x / (y - z)) / t;
	} else if (z <= 31000000000000.0) {
		tmp = (x / y) / (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) / (z - t)
    if (z <= (-5.6d-65)) then
        tmp = t_1
    else if (z <= 8.5d-142) then
        tmp = (x / (y - z)) / t
    else if (z <= 31000000000000.0d0) then
        tmp = (x / y) / (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) / (z - t);
	double tmp;
	if (z <= -5.6e-65) {
		tmp = t_1;
	} else if (z <= 8.5e-142) {
		tmp = (x / (y - z)) / t;
	} else if (z <= 31000000000000.0) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) / (z - t)
	tmp = 0
	if z <= -5.6e-65:
		tmp = t_1
	elif z <= 8.5e-142:
		tmp = (x / (y - z)) / t
	elif z <= 31000000000000.0:
		tmp = (x / y) / (t - z)
	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 <= -5.6e-65)
		tmp = t_1;
	elseif (z <= 8.5e-142)
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	elseif (z <= 31000000000000.0)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	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 <= -5.6e-65)
		tmp = t_1;
	elseif (z <= 8.5e-142)
		tmp = (x / (y - z)) / t;
	elseif (z <= 31000000000000.0)
		tmp = (x / y) / (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] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e-65], t$95$1, If[LessEqual[z, 8.5e-142], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 31000000000000.0], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6000000000000001e-65 or 3.1e13 < z

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0 86.0%

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

      1. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 84.6%

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

      1. associate-*r/ 84.6%

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

      2. mul-1-neg 84.6%

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

   8. Simplified 84.6%

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

   if -5.6000000000000001e-65 < z < 8.4999999999999996e-142

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 91.9%

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

      1. associate-/l/ 96.4%

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

   5. Simplified 96.4%

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

      1. clear-num 95.8%

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

      2. associate-/r/ 96.3%

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

   7. Applied egg-rr 96.3%

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

   8. Taylor expanded in t around inf 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-/r* 86.3%

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

   10. Simplified 86.3%

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

   if 8.4999999999999996e-142 < z < 3.1e13

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 93.5%

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

      1. associate-/l/ 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in y around inf 62.7%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-142}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 31000000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+128}:\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.25e+128)
   (/ x (* z (- t z)))
   (if (<= z 1.1e-71)
     (/ x (* (- y z) t))
     (if (<= z 7e+38) (/ (/ x y) (- z)) (/ x (* z (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.25e+128) {
		tmp = x / (z * (t - z));
	} else if (z <= 1.1e-71) {
		tmp = x / ((y - z) * t);
	} else if (z <= 7e+38) {
		tmp = (x / y) / -z;
	} else {
		tmp = x / (z * (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 (z <= (-2.25d+128)) then
        tmp = x / (z * (t - z))
    else if (z <= 1.1d-71) then
        tmp = x / ((y - z) * t)
    else if (z <= 7d+38) then
        tmp = (x / y) / -z
    else
        tmp = x / (z * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.25e+128) {
		tmp = x / (z * (t - z));
	} else if (z <= 1.1e-71) {
		tmp = x / ((y - z) * t);
	} else if (z <= 7e+38) {
		tmp = (x / y) / -z;
	} else {
		tmp = x / (z * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.25e+128:
		tmp = x / (z * (t - z))
	elif z <= 1.1e-71:
		tmp = x / ((y - z) * t)
	elif z <= 7e+38:
		tmp = (x / y) / -z
	else:
		tmp = x / (z * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.25e+128)
		tmp = Float64(x / Float64(z * Float64(t - z)));
	elseif (z <= 1.1e-71)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (z <= 7e+38)
		tmp = Float64(Float64(x / y) / Float64(-z));
	else
		tmp = Float64(x / Float64(z * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.25e+128)
		tmp = x / (z * (t - z));
	elseif (z <= 1.1e-71)
		tmp = x / ((y - z) * t);
	elseif (z <= 7e+38)
		tmp = (x / y) / -z;
	else
		tmp = x / (z * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.25e+128], N[(x / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-71], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+38], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision], N[(x / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2500000000000001e128

   1. Initial program 86.7%

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

   3. Taylor expanded in y around 0 86.7%

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

      1. associate-*r/ 86.7%

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

      2. neg-mul-1 86.7%

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

   5. Simplified 86.7%

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

      1. div-inv 86.7%

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

      2. add-sqr-sqrt 48.9%

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

      3. sqrt-unprod 77.3%

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

      4. sqr-neg 77.3%

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

      5. sqrt-unprod 37.8%

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

      6. add-sqr-sqrt 86.7%

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

   7. Applied egg-rr 86.7%

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

      1. associate-*r/ 86.7%

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

      2. *-rgt-identity 86.7%

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

   9. Simplified 86.7%

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

   if -2.2500000000000001e128 < z < 1.09999999999999999e-71

   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 inf 74.3%

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

   if 1.09999999999999999e-71 < z < 7.00000000000000003e38

   1. Initial program 96.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 64.0%

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

      1. associate-*r/ 64.0%

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

      2. neg-mul-1 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in z around 0 38.2%

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

      1. mul-1-neg 38.2%

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

      2. associate-/r* 38.4%

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

      3. distribute-neg-frac2 38.4%

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

   10. Simplified 38.4%

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

   if 7.00000000000000003e38 < z

   1. Initial program 84.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 91.4%

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

      1. associate-*r/ 91.4%

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

      2. neg-mul-1 91.4%

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

   7. Simplified 91.4%

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

      1. *-un-lft-identity 91.4%

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

      2. add-sqr-sqrt 57.9%

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

      3. sqrt-unprod 67.5%

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

      4. sqr-neg 67.5%

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

      5. sqrt-unprod 22.0%

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

      6. add-sqr-sqrt 67.9%

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

   9. Applied egg-rr 67.9%

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

       1. *-lft-identity 67.9%

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

   11. Simplified 67.9%

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

   12. Taylor expanded in x around 0 68.1%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+128}:\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t \cdot \left(-z\right)}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-71}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* t (- z)))))
   (if (<= z -1.5e-77)
     t_1
     (if (<= z 1.1e-71)
       (/ (/ x y) t)
       (if (<= z 4.4e+19) (/ (/ x y) (- z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t * -z);
	double tmp;
	if (z <= -1.5e-77) {
		tmp = t_1;
	} else if (z <= 1.1e-71) {
		tmp = (x / y) / t;
	} else if (z <= 4.4e+19) {
		tmp = (x / y) / -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 / (t * -z)
    if (z <= (-1.5d-77)) then
        tmp = t_1
    else if (z <= 1.1d-71) then
        tmp = (x / y) / t
    else if (z <= 4.4d+19) then
        tmp = (x / y) / -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t * -z);
	double tmp;
	if (z <= -1.5e-77) {
		tmp = t_1;
	} else if (z <= 1.1e-71) {
		tmp = (x / y) / t;
	} else if (z <= 4.4e+19) {
		tmp = (x / y) / -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t * -z)
	tmp = 0
	if z <= -1.5e-77:
		tmp = t_1
	elif z <= 1.1e-71:
		tmp = (x / y) / t
	elif z <= 4.4e+19:
		tmp = (x / y) / -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t * Float64(-z)))
	tmp = 0.0
	if (z <= -1.5e-77)
		tmp = t_1;
	elseif (z <= 1.1e-71)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 4.4e+19)
		tmp = Float64(Float64(x / y) / Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t * -z);
	tmp = 0.0;
	if (z <= -1.5e-77)
		tmp = t_1;
	elseif (z <= 1.1e-71)
		tmp = (x / y) / t;
	elseif (z <= 4.4e+19)
		tmp = (x / y) / -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e-77], t$95$1, If[LessEqual[z, 1.1e-71], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.4e+19], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.50000000000000008e-77 or 4.4e19 < z

   1. Initial program 86.6%

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

   3. Taylor expanded in y around 0 75.5%

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

      1. associate-*r/ 75.5%

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

      2. neg-mul-1 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in z around 0 37.3%

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

      1. associate-*r/ 37.3%

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

      2. mul-1-neg 37.3%

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

   8. Simplified 37.3%

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

   if -1.50000000000000008e-77 < z < 1.09999999999999999e-71

   1. Initial program 91.0%

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

   3. Taylor expanded in x around 0 91.0%

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

      1. associate-/l/ 96.5%

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

   5. Simplified 96.5%

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

      1. clear-num 95.9%

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

      2. associate-/r/ 96.5%

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

   7. Applied egg-rr 96.5%

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

   8. Taylor expanded in z around 0 76.7%

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

      1. associate-/l/ 80.9%

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

   10. Simplified 80.9%

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

   if 1.09999999999999999e-71 < z < 4.4e19

   1. Initial program 96.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 64.9%

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

      1. associate-*r/ 64.9%

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

      2. neg-mul-1 64.9%

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

   7. Simplified 64.9%

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

   8. Taylor expanded in z around 0 38.4%

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

      1. mul-1-neg 38.4%

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

      2. associate-/r* 38.5%

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

      3. distribute-neg-frac2 38.5%

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

   10. Simplified 38.5%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-71}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot t}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z t))))
   (if (<= z -3.8e-77)
     t_1
     (if (<= z 1.75e-75)
       (/ (/ x y) t)
       (if (<= z 5e+19) (/ x (* z (- y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double tmp;
	if (z <= -3.8e-77) {
		tmp = t_1;
	} else if (z <= 1.75e-75) {
		tmp = (x / y) / t;
	} else if (z <= 5e+19) {
		tmp = x / (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 * t)
    if (z <= (-3.8d-77)) then
        tmp = t_1
    else if (z <= 1.75d-75) then
        tmp = (x / y) / t
    else if (z <= 5d+19) then
        tmp = x / (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 * t);
	double tmp;
	if (z <= -3.8e-77) {
		tmp = t_1;
	} else if (z <= 1.75e-75) {
		tmp = (x / y) / t;
	} else if (z <= 5e+19) {
		tmp = x / (z * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / (z * t)
	tmp = 0
	if z <= -3.8e-77:
		tmp = t_1
	elif z <= 1.75e-75:
		tmp = (x / y) / t
	elif z <= 5e+19:
		tmp = x / (z * -y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * t))
	tmp = 0.0
	if (z <= -3.8e-77)
		tmp = t_1;
	elseif (z <= 1.75e-75)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 5e+19)
		tmp = Float64(x / Float64(z * Float64(-y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * t);
	tmp = 0.0;
	if (z <= -3.8e-77)
		tmp = t_1;
	elseif (z <= 1.75e-75)
		tmp = (x / y) / t;
	elseif (z <= 5e+19)
		tmp = x / (z * -y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e-77], t$95$1, If[LessEqual[z, 1.75e-75], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 5e+19], N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7999999999999999e-77 or 5e19 < z

   1. Initial program 86.6%

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

   3. Taylor expanded in y around 0 75.5%

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

      1. associate-*r/ 75.5%

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

      2. neg-mul-1 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in z around 0 37.3%

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

      1. associate-*r/ 37.3%

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

      2. mul-1-neg 37.3%

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

   8. Simplified 37.3%

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

   if -3.7999999999999999e-77 < z < 1.74999999999999993e-75

   1. Initial program 91.0%

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

   3. Taylor expanded in x around 0 91.0%

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

      1. associate-/l/ 96.5%

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

   5. Simplified 96.5%

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

      1. clear-num 95.9%

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

      2. associate-/r/ 96.5%

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

   7. Applied egg-rr 96.5%

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

   8. Taylor expanded in z around 0 76.7%

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

      1. associate-/l/ 80.9%

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

   10. Simplified 80.9%

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

   if 1.74999999999999993e-75 < z < 5e19

   1. Initial program 96.2%

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

   3. Taylor expanded in y around inf 45.9%

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

      1. *-commutative 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in t around 0 38.4%

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

      1. associate-*r/ 38.4%

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

      2. mul-1-neg 38.4%

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

      3. *-commutative 38.4%

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

   8. Simplified 38.4%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-139} \lor \neg \left(t \leq 7.8 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.15e-139) (not (<= t 7.8e-88)))
   (/ x (* (- y z) t))
   (/ (/ (- x) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.15e-139) || !(t <= 7.8e-88)) {
		tmp = x / ((y - z) * t);
	} 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 ((t <= (-1.15d-139)) .or. (.not. (t <= 7.8d-88))) then
        tmp = x / ((y - z) * t)
    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 ((t <= -1.15e-139) || !(t <= 7.8e-88)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (-x / z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.15e-139) or not (t <= 7.8e-88):
		tmp = x / ((y - z) * t)
	else:
		tmp = (-x / z) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.15e-139) || !(t <= 7.8e-88))
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(Float64(-x) / z) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.15e-139) || ~((t <= 7.8e-88)))
		tmp = x / ((y - z) * t);
	else
		tmp = (-x / z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.15e-139], N[Not[LessEqual[t, 7.8e-88]], $MachinePrecision]], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15000000000000006e-139 or 7.79999999999999985e-88 < t

   1. Initial program 86.4%

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

   3. Taylor expanded in t around inf 75.5%

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

   if -1.15000000000000006e-139 < t < 7.79999999999999985e-88

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in t around 0 58.0%

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

      1. associate-*r/ 58.0%

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

      2. mul-1-neg 58.0%

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

      3. *-commutative 58.0%

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

   8. Simplified 58.0%

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

   9. Taylor expanded in x around 0 58.0%

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

       1. associate-*r/ 58.0%

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

       2. times-frac 59.6%

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

       3. associate-*l/ 59.6%

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

       4. mul-1-neg 59.6%

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

       5. distribute-neg-frac2 59.6%

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

   11. Simplified 59.6%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-139} \lor \neg \left(t \leq 7.8 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{-139}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.36e-139)
   (/ (/ x y) (- t z))
   (if (<= t 1.2e-49) (/ (/ x z) (- z y)) (/ (/ x (- y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.36e-139) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.2e-49) {
		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 <= (-1.36d-139)) then
        tmp = (x / y) / (t - z)
    else if (t <= 1.2d-49) 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 <= -1.36e-139) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.2e-49) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.36e-139:
		tmp = (x / y) / (t - z)
	elif t <= 1.2e-49:
		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 <= -1.36e-139)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1.2e-49)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	else
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.36e-139)
		tmp = (x / y) / (t - z);
	elseif (t <= 1.2e-49)
		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, -1.36e-139], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-49], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.36000000000000003e-139

   1. Initial program 87.9%

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

   3. Taylor expanded in x around 0 87.9%

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

      1. associate-/l/ 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in y around inf 69.1%

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

   if -1.36000000000000003e-139 < t < 1.19999999999999996e-49

   1. Initial program 94.8%

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

      1. associate-/l/ 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around 0 84.7%

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

      1. associate-*r/ 84.7%

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

      2. neg-mul-1 84.7%

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

   7. Simplified 84.7%

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

   if 1.19999999999999996e-49 < t

   1. Initial program 83.9%

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

   3. Taylor expanded in x around 0 83.9%

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

      1. associate-/l/ 98.7%

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

   5. Simplified 98.7%

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

      1. clear-num 98.6%

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

      2. associate-/r/ 98.7%

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

   7. Applied egg-rr 98.7%

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

   8. Taylor expanded in t around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-/r* 84.5%

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

   10. Simplified 84.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{-139}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.35e-118)
   (/ (/ x y) (- t z))
   (if (<= y 1.3e-161) (/ x (* z (- z t))) (/ (/ x (- y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-118) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.3e-161) {
		tmp = x / (z * (z - t));
	} 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 (y <= (-1.35d-118)) then
        tmp = (x / y) / (t - z)
    else if (y <= 1.3d-161) then
        tmp = x / (z * (z - t))
    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 (y <= -1.35e-118) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.3e-161) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.35e-118:
		tmp = (x / y) / (t - z)
	elif y <= 1.3e-161:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.35e-118)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 1.3e-161)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.35e-118)
		tmp = (x / y) / (t - z);
	elseif (y <= 1.3e-161)
		tmp = x / (z * (z - t));
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.35e-118], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-161], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.34999999999999997e-118

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0 87.5%

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

      1. associate-/l/ 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around inf 87.1%

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

   if -1.34999999999999997e-118 < y < 1.29999999999999998e-161

   1. Initial program 88.1%

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

   3. Taylor expanded in y around 0 71.1%

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

      1. associate-*r/ 71.1%

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

      2. neg-mul-1 71.1%

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

   5. Simplified 71.1%

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

   if 1.29999999999999998e-161 < y

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0 91.4%

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

      1. associate-/l/ 98.6%

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

   5. Simplified 98.6%

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

      1. clear-num 98.1%

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

      2. associate-/r/ 98.6%

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

   7. Applied egg-rr 98.6%

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

   8. Taylor expanded in t around inf 59.0%

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

      1. *-commutative 59.0%

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

      2. associate-/r* 71.2%

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

   10. Simplified 71.2%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-77} \lor \neg \left(z \leq 1.08 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.4e-77) (not (<= z 1.08e-32)))
   (/ x (* t (- z)))
   (/ (/ x y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e-77) || !(z <= 1.08e-32)) {
		tmp = x / (t * -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 <= (-3.4d-77)) .or. (.not. (z <= 1.08d-32))) then
        tmp = x / (t * -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 <= -3.4e-77) || !(z <= 1.08e-32)) {
		tmp = x / (t * -z);
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.4e-77) or not (z <= 1.08e-32):
		tmp = x / (t * -z)
	else:
		tmp = (x / y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.4e-77) || !(z <= 1.08e-32))
		tmp = Float64(x / Float64(t * Float64(-z)));
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.4e-77) || ~((z <= 1.08e-32)))
		tmp = x / (t * -z);
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.4e-77], N[Not[LessEqual[z, 1.08e-32]], $MachinePrecision]], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.39999999999999983e-77 or 1.08e-32 < z

   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 0 75.4%

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

      1. associate-*r/ 75.4%

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

      2. neg-mul-1 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in z around 0 37.0%

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

      1. associate-*r/ 37.0%

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

      2. mul-1-neg 37.0%

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

   8. Simplified 37.0%

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

   if -3.39999999999999983e-77 < z < 1.08e-32

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0 91.3%

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

      1. associate-/l/ 97.0%

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

   5. Simplified 97.0%

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

      1. clear-num 96.5%

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

      2. associate-/r/ 96.9%

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

   7. Applied egg-rr 96.9%

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

   8. Taylor expanded in z around 0 68.3%

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

      1. associate-/l/ 72.7%

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

   10. Simplified 72.7%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-77} \lor \neg \left(z \leq 1.08 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+107} \lor \neg \left(z \leq 3.35 \cdot 10^{+143}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.6e+107) (not (<= z 3.35e+143))) (/ x (* y z)) (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.6e+107) || !(z <= 3.35e+143)) {
		tmp = x / (y * 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 <= (-5.6d+107)) .or. (.not. (z <= 3.35d+143))) then
        tmp = x / (y * 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 <= -5.6e+107) || !(z <= 3.35e+143)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.6e+107) or not (z <= 3.35e+143):
		tmp = x / (y * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.6e+107) || !(z <= 3.35e+143))
		tmp = Float64(x / Float64(y * 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 <= -5.6e+107) || ~((z <= 3.35e+143)))
		tmp = x / (y * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.6e+107], N[Not[LessEqual[z, 3.35e+143]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.59999999999999969e107 or 3.3500000000000001e143 < z

   1. Initial program 83.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 93.5%

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

      1. associate-*r/ 93.5%

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

      2. neg-mul-1 93.5%

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

   7. Simplified 93.5%

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

      1. *-un-lft-identity 93.5%

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

      2. add-sqr-sqrt 52.9%

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

      3. sqrt-unprod 67.1%

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

      4. sqr-neg 67.1%

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

      5. sqrt-unprod 30.5%

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

      6. add-sqr-sqrt 76.7%

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

   9. Applied egg-rr 76.7%

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

       1. *-lft-identity 76.7%

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

   11. Simplified 76.7%

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

   12. Taylor expanded in z around 0 54.4%

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

       1. *-commutative 54.4%

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

   14. Simplified 54.4%

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

   if -5.59999999999999969e107 < z < 3.3500000000000001e143

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0 53.7%

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

      1. clear-num 54.3%

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

      2. associate-/r/ 53.7%

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

      3. *-commutative 53.7%

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

      4. associate-/r* 53.7%

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

   5. Applied egg-rr 53.7%

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

      1. *-commutative 53.7%

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

      2. associate-*r/ 59.5%

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

      3. div-inv 59.5%

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

      4. add-sqr-sqrt 30.3%

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

      5. sqrt-unprod 33.0%

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

      6. sqr-neg 33.0%

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

      7. sqrt-unprod 9.5%

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

      8. add-sqr-sqrt 22.8%

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

      9. associate-/l/ 20.9%

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

      10. associate-/r* 23.1%

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

      11. add-sqr-sqrt 8.1%

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

      12. sqrt-unprod 33.7%

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

      13. sqr-neg 33.7%

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

      14. sqrt-unprod 30.7%

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

      15. add-sqr-sqrt 57.5%

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

   7. Applied egg-rr 57.5%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+107} \lor \neg \left(z \leq 3.35 \cdot 10^{+143}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+25} \lor \neg \left(z \leq 4.7 \cdot 10^{+98}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.7e+25) (not (<= z 4.7e+98))) (/ x (* y z)) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.7e+25) || !(z <= 4.7e+98)) {
		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 <= (-5.7d+25)) .or. (.not. (z <= 4.7d+98))) 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 <= -5.7e+25) || !(z <= 4.7e+98)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.7e+25) or not (z <= 4.7e+98):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.7e+25) || !(z <= 4.7e+98))
		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 <= -5.7e+25) || ~((z <= 4.7e+98)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.7e+25], N[Not[LessEqual[z, 4.7e+98]], $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 < -5.6999999999999996e25 or 4.6999999999999997e98 < z

   1. Initial program 82.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 90.8%

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

      1. associate-*r/ 90.8%

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

      2. neg-mul-1 90.8%

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

   7. Simplified 90.8%

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

      1. *-un-lft-identity 90.8%

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

      2. add-sqr-sqrt 51.3%

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

      3. sqrt-unprod 65.9%

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

      4. sqr-neg 65.9%

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

      5. sqrt-unprod 28.4%

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

      6. add-sqr-sqrt 70.4%

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

   9. Applied egg-rr 70.4%

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

       1. *-lft-identity 70.4%

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

   11. Simplified 70.4%

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

   12. Taylor expanded in z around 0 47.9%

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

       1. *-commutative 47.9%

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

   14. Simplified 47.9%

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

   if -5.6999999999999996e25 < z < 4.6999999999999997e98

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 57.7%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+25} \lor \neg \left(z \leq 4.7 \cdot 10^{+98}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 90.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.35e+151) (/ x (* (- y z) (- t z))) (/ (/ x (- y z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.35e+151) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.35d+151) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (x / (y - z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.35e+151) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.35e+151:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.35e+151)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.35e+151)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.35e+151], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.3500000000000001e151

   1. Initial program 91.1%

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

   if 1.3500000000000001e151 < t

   1. Initial program 78.9%

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

   3. Taylor expanded in x around 0 78.9%

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

      1. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in t around inf 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-/r* 97.4%

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

   10. Simplified 97.4%

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

Alternative 16: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-103}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e-103) (/ (/ x y) (- t z)) (/ (/ x (- y z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-103) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.8d-103)) then
        tmp = (x / y) / (t - z)
    else
        tmp = (x / (y - z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-103) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e-103:
		tmp = (x / y) / (t - z)
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e-103)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.8e-103)
		tmp = (x / y) / (t - z);
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e-103], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7999999999999997e-103

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0 87.2%

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

      1. associate-/l/ 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around inf 87.9%

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

   if -5.7999999999999997e-103 < y

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0 90.3%

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

      1. associate-/l/ 97.9%

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

   5. Simplified 97.9%

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

      1. clear-num 97.6%

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

      2. associate-/r/ 97.9%

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

   7. Applied egg-rr 97.9%

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

   8. Taylor expanded in t around inf 59.2%

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

      1. *-commutative 59.2%

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

      2. associate-/r* 67.5%

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

   10. Simplified 67.5%

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

Alternative 17: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 8.8 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 8.8e-88) (/ (/ x y) (- t z)) (/ (/ x t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 8.8e-88) {
		tmp = (x / y) / (t - 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 (t <= 8.8d-88) then
        tmp = (x / y) / (t - 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 (t <= 8.8e-88) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 8.8e-88:
		tmp = (x / y) / (t - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 8.8e-88)
		tmp = Float64(Float64(x / y) / Float64(t - 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 (t <= 8.8e-88)
		tmp = (x / y) / (t - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 8.8e-88], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 8.8000000000000002e-88

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0 91.5%

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

      1. associate-/l/ 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in y around inf 67.8%

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

   if 8.8000000000000002e-88 < t

   1. Initial program 85.0%

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

      1. associate-/l/ 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around inf 81.7%

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

Alternative 18: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 8.8 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 8.8e-88) (/ x (* y (- t z))) (/ (/ x t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 8.8e-88) {
		tmp = x / (y * (t - 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 (t <= 8.8d-88) then
        tmp = x / (y * (t - 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 (t <= 8.8e-88) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 8.8e-88:
		tmp = x / (y * (t - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 8.8e-88)
		tmp = Float64(x / Float64(y * Float64(t - 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 (t <= 8.8e-88)
		tmp = x / (y * (t - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 8.8e-88], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 8.8000000000000002e-88

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 66.7%

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

      1. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   if 8.8000000000000002e-88 < t

   1. Initial program 85.0%

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

      1. associate-/l/ 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in t around inf 81.7%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8.8 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e-109) (/ x (* y (- t z))) (/ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e-109) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.8d-109)) then
        tmp = x / (y * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e-109) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e-109:
		tmp = x / (y * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e-109)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.8e-109)
		tmp = x / (y * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e-109], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e-109

   1. Initial program 87.3%

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

   3. Taylor expanded in y around inf 80.1%

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

      1. *-commutative 80.1%

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

   5. Simplified 80.1%

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

   if -1.8e-109 < y

   1. Initial program 90.3%

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

   3. Taylor expanded in t around inf 59.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 96.9% 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 89.3%

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

   1. associate-/l/ 96.7%

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

3. Simplified 96.7%

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

Alternative 21: 40.0% 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 89.3%

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

3. Taylor expanded in z around 0 43.2%

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

4. Final simplification 43.2%

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

Developer target: 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 2024085 
(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))))