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

Percentage Accurate: 89.3% → 97.9%

Time: 14.8s

Alternatives: 20

Speedup: 0.8×

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: 89.3% 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: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{-289}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 5e-289) (/ (/ x (- y z)) (- t z)) t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= 5e-289) {
		tmp = (x / (y - z)) / (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 / ((y - z) * (t - z))
    if (t_1 <= 5d-289) then
        tmp = (x / (y - z)) / (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 / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= 5e-289) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= 5e-289:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= 5e-289)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= 5e-289)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-289], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < 5.00000000000000029e-289

   1. Initial program 89.1%

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

      1. associate-/r* 97.8%

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

   3. Simplified 97.8%

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

   if 5.00000000000000029e-289 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 99.8%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq 5 \cdot 10^{-289}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 2: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t - z}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 140000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x y) (- t z))))
   (if (<= z -1.5e+55)
     (/ 1.0 (/ z (/ x z)))
     (if (<= z 1e-305)
       t_1
       (if (<= z 5e-119)
         (/ x (* (- y z) t))
         (if (<= z 2.25e-5)
           t_1
           (if (<= z 140000000000.0)
             (/ (/ x t) (- y z))
             (* (/ x z) (/ 1.0 z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / (t - z);
	double tmp;
	if (z <= -1.5e+55) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= 1e-305) {
		tmp = t_1;
	} else if (z <= 5e-119) {
		tmp = x / ((y - z) * t);
	} else if (z <= 2.25e-5) {
		tmp = t_1;
	} else if (z <= 140000000000.0) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) / (t - z)
    if (z <= (-1.5d+55)) then
        tmp = 1.0d0 / (z / (x / z))
    else if (z <= 1d-305) then
        tmp = t_1
    else if (z <= 5d-119) then
        tmp = x / ((y - z) * t)
    else if (z <= 2.25d-5) then
        tmp = t_1
    else if (z <= 140000000000.0d0) then
        tmp = (x / t) / (y - z)
    else
        tmp = (x / z) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / (t - z);
	double tmp;
	if (z <= -1.5e+55) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= 1e-305) {
		tmp = t_1;
	} else if (z <= 5e-119) {
		tmp = x / ((y - z) * t);
	} else if (z <= 2.25e-5) {
		tmp = t_1;
	} else if (z <= 140000000000.0) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) / (t - z)
	tmp = 0
	if z <= -1.5e+55:
		tmp = 1.0 / (z / (x / z))
	elif z <= 1e-305:
		tmp = t_1
	elif z <= 5e-119:
		tmp = x / ((y - z) * t)
	elif z <= 2.25e-5:
		tmp = t_1
	elif z <= 140000000000.0:
		tmp = (x / t) / (y - z)
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) / Float64(t - z))
	tmp = 0.0
	if (z <= -1.5e+55)
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	elseif (z <= 1e-305)
		tmp = t_1;
	elseif (z <= 5e-119)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (z <= 2.25e-5)
		tmp = t_1;
	elseif (z <= 140000000000.0)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) / (t - z);
	tmp = 0.0;
	if (z <= -1.5e+55)
		tmp = 1.0 / (z / (x / z));
	elseif (z <= 1e-305)
		tmp = t_1;
	elseif (z <= 5e-119)
		tmp = x / ((y - z) * t);
	elseif (z <= 2.25e-5)
		tmp = t_1;
	elseif (z <= 140000000000.0)
		tmp = (x / t) / (y - z);
	else
		tmp = (x / z) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+55], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-305], t$95$1, If[LessEqual[z, 5e-119], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e-5], t$95$1, If[LessEqual[z, 140000000000.0], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.50000000000000008e55

   1. Initial program 86.3%

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

   2. Taylor expanded in z around inf 80.9%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 80.9%

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

   4. Simplified 80.9%

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

      1. clear-num 80.9%

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

      2. inv-pow 80.9%

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

      3. associate-/l* 82.9%

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

   6. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   8. Simplified 82.9%

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

   if -1.50000000000000008e55 < z < 9.99999999999999996e-306 or 4.99999999999999993e-119 < z < 2.25000000000000014e-5

   1. Initial program 92.0%

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

      1. *-un-lft-identity 92.0%

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

      2. times-frac 94.2%

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

   3. Applied egg-rr 94.2%

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

      1. *-commutative 94.2%

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

      2. clear-num 93.9%

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

      3. frac-times 93.4%

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

      4. metadata-eval 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in y around inf 73.6%

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

      1. associate-/r* 77.2%

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

   8. Simplified 77.2%

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

   if 9.99999999999999996e-306 < z < 4.99999999999999993e-119

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 86.6%

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

   if 2.25000000000000014e-5 < z < 1.4e11

   1. Initial program 81.0%

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

   2. Taylor expanded in t around inf 42.9%

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

      1. associate-/r* 61.6%

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

   4. Simplified 61.6%

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

   if 1.4e11 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in z around inf 82.9%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 82.9%

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

   4. Simplified 82.9%

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

      1. associate-/r* 89.8%

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

      2. div-inv 89.8%

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

   6. Applied egg-rr 89.8%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 10^{-305}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 140000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 3: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ t_2 := \frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 30000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) y)) (t_2 (* (/ x z) (/ 1.0 z))))
   (if (<= z -7.2e+54)
     t_2
     (if (<= z 8.2e-110)
       t_1
       (if (<= z 4.5e-13) (/ (/ (- x) y) z) (if (<= z 30000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = (x / z) * (1.0 / z);
	double tmp;
	if (z <= -7.2e+54) {
		tmp = t_2;
	} else if (z <= 8.2e-110) {
		tmp = t_1;
	} else if (z <= 4.5e-13) {
		tmp = (-x / y) / z;
	} else if (z <= 30000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / t) / y
    t_2 = (x / z) * (1.0d0 / z)
    if (z <= (-7.2d+54)) then
        tmp = t_2
    else if (z <= 8.2d-110) then
        tmp = t_1
    else if (z <= 4.5d-13) then
        tmp = (-x / y) / z
    else if (z <= 30000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double t_2 = (x / z) * (1.0 / z);
	double tmp;
	if (z <= -7.2e+54) {
		tmp = t_2;
	} else if (z <= 8.2e-110) {
		tmp = t_1;
	} else if (z <= 4.5e-13) {
		tmp = (-x / y) / z;
	} else if (z <= 30000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / t) / y
	t_2 = (x / z) * (1.0 / z)
	tmp = 0
	if z <= -7.2e+54:
		tmp = t_2
	elif z <= 8.2e-110:
		tmp = t_1
	elif z <= 4.5e-13:
		tmp = (-x / y) / z
	elif z <= 30000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	t_2 = Float64(Float64(x / z) * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -7.2e+54)
		tmp = t_2;
	elseif (z <= 8.2e-110)
		tmp = t_1;
	elseif (z <= 4.5e-13)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (z <= 30000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	t_2 = (x / z) * (1.0 / z);
	tmp = 0.0;
	if (z <= -7.2e+54)
		tmp = t_2;
	elseif (z <= 8.2e-110)
		tmp = t_1;
	elseif (z <= 4.5e-13)
		tmp = (-x / y) / z;
	elseif (z <= 30000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+54], t$95$2, If[LessEqual[z, 8.2e-110], t$95$1, If[LessEqual[z, 4.5e-13], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 30000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000003e54 or 3e7 < z

   1. Initial program 88.7%

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

   2. Taylor expanded in z around inf 82.1%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 82.1%

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

   4. Simplified 82.1%

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

      1. associate-/r* 87.2%

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

      2. div-inv 87.2%

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

   6. Applied egg-rr 87.2%

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

   if -7.2000000000000003e54 < z < 8.19999999999999965e-110 or 4.5e-13 < z < 3e7

   1. Initial program 93.2%

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

      1. *-un-lft-identity 93.2%

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

      2. times-frac 94.7%

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

   3. Applied egg-rr 94.7%

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

      1. *-commutative 94.7%

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

      2. clear-num 93.8%

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

      3. frac-times 93.7%

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

      4. metadata-eval 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in z around 0 63.4%

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

      1. associate-/r* 67.8%

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

   8. Simplified 67.8%

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

   if 8.19999999999999965e-110 < z < 4.5e-13

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 51.8%

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

      1. *-commutative 51.8%

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

   4. Simplified 51.8%

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

   5. Taylor expanded in t around 0 45.0%

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

      1. associate-*r/ 45.0%

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

      2. neg-mul-1 45.0%

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

      3. *-commutative 45.0%

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

   7. Simplified 45.0%

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

   8. Taylor expanded in x around 0 45.0%

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

      1. associate-/l/ 38.3%

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

      2. associate-*r/ 38.3%

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

      3. neg-mul-1 38.3%

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

      4. distribute-neg-frac 38.3%

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

   10. Simplified 38.3%

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

   11. Taylor expanded in x around 0 45.0%

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

       1. mul-1-neg 45.0%

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

       2. associate-/r* 45.1%

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

       3. distribute-neg-frac 45.1%

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

   13. Simplified 45.1%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-110}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 30000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 4: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-110}:\\ \;\;\;\;\frac{1}{\frac{t}{\frac{x}{y}}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 11000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 1.0 z))))
   (if (<= z -1.65e+54)
     t_1
     (if (<= z 9.2e-110)
       (/ 1.0 (/ t (/ x y)))
       (if (<= z 3.8e-13)
         (/ (/ (- x) y) z)
         (if (<= z 11000000000.0) (/ (/ x t) y) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (z <= -1.65e+54) {
		tmp = t_1;
	} else if (z <= 9.2e-110) {
		tmp = 1.0 / (t / (x / y));
	} else if (z <= 3.8e-13) {
		tmp = (-x / y) / z;
	} else if (z <= 11000000000.0) {
		tmp = (x / t) / 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) * (1.0d0 / z)
    if (z <= (-1.65d+54)) then
        tmp = t_1
    else if (z <= 9.2d-110) then
        tmp = 1.0d0 / (t / (x / y))
    else if (z <= 3.8d-13) then
        tmp = (-x / y) / z
    else if (z <= 11000000000.0d0) then
        tmp = (x / t) / 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) * (1.0 / z);
	double tmp;
	if (z <= -1.65e+54) {
		tmp = t_1;
	} else if (z <= 9.2e-110) {
		tmp = 1.0 / (t / (x / y));
	} else if (z <= 3.8e-13) {
		tmp = (-x / y) / z;
	} else if (z <= 11000000000.0) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * (1.0 / z)
	tmp = 0
	if z <= -1.65e+54:
		tmp = t_1
	elif z <= 9.2e-110:
		tmp = 1.0 / (t / (x / y))
	elif z <= 3.8e-13:
		tmp = (-x / y) / z
	elif z <= 11000000000.0:
		tmp = (x / t) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -1.65e+54)
		tmp = t_1;
	elseif (z <= 9.2e-110)
		tmp = Float64(1.0 / Float64(t / Float64(x / y)));
	elseif (z <= 3.8e-13)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (z <= 11000000000.0)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (1.0 / z);
	tmp = 0.0;
	if (z <= -1.65e+54)
		tmp = t_1;
	elseif (z <= 9.2e-110)
		tmp = 1.0 / (t / (x / y));
	elseif (z <= 3.8e-13)
		tmp = (-x / y) / z;
	elseif (z <= 11000000000.0)
		tmp = (x / t) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+54], t$95$1, If[LessEqual[z, 9.2e-110], N[(1.0 / N[(t / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-13], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 11000000000.0], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.65e54 or 1.1e10 < z

   1. Initial program 88.7%

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

   2. Taylor expanded in z around inf 82.1%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 82.1%

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

   4. Simplified 82.1%

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

      1. associate-/r* 87.2%

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

      2. div-inv 87.2%

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

   6. Applied egg-rr 87.2%

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

   if -1.65e54 < z < 9.2000000000000006e-110

   1. Initial program 93.6%

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

      1. *-un-lft-identity 93.6%

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

      2. times-frac 94.4%

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

   3. Applied egg-rr 94.4%

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

      1. *-commutative 94.4%

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

      2. clear-num 93.6%

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

      3. frac-times 93.5%

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

      4. metadata-eval 93.5%

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

   5. Applied egg-rr 93.5%

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

   6. Taylor expanded in z around 0 65.9%

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

      1. associate-/l* 70.1%

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

   8. Simplified 70.1%

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

   if 9.2000000000000006e-110 < z < 3.8e-13

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 51.8%

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

      1. *-commutative 51.8%

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

   4. Simplified 51.8%

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

   5. Taylor expanded in t around 0 45.0%

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

      1. associate-*r/ 45.0%

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

      2. neg-mul-1 45.0%

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

      3. *-commutative 45.0%

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

   7. Simplified 45.0%

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

   8. Taylor expanded in x around 0 45.0%

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

      1. associate-/l/ 38.3%

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

      2. associate-*r/ 38.3%

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

      3. neg-mul-1 38.3%

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

      4. distribute-neg-frac 38.3%

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

   10. Simplified 38.3%

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

   11. Taylor expanded in x around 0 45.0%

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

       1. mul-1-neg 45.0%

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

       2. associate-/r* 45.1%

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

       3. distribute-neg-frac 45.1%

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

   13. Simplified 45.1%

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

   if 3.8e-13 < z < 1.1e10

   1. Initial program 84.2%

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

      1. *-un-lft-identity 84.2%

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

      2. times-frac 100.0%

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

   3. Applied egg-rr 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 99.3%

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

      3. frac-times 99.2%

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

      4. metadata-eval 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in z around 0 19.4%

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

      1. associate-/r* 50.8%

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

   8. Simplified 50.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-110}:\\ \;\;\;\;\frac{1}{\frac{t}{\frac{x}{y}}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 11000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 5: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-110}:\\ \;\;\;\;\frac{1}{\frac{t}{\frac{x}{y}}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 15000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.9e+54)
   (/ 1.0 (/ z (/ x z)))
   (if (<= z 9.2e-110)
     (/ 1.0 (/ t (/ x y)))
     (if (<= z 4.1e-13)
       (/ (/ (- x) y) z)
       (if (<= z 15000000000.0) (/ (/ x t) y) (* (/ x z) (/ 1.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+54) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= 9.2e-110) {
		tmp = 1.0 / (t / (x / y));
	} else if (z <= 4.1e-13) {
		tmp = (-x / y) / z;
	} else if (z <= 15000000000.0) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.9d+54)) then
        tmp = 1.0d0 / (z / (x / z))
    else if (z <= 9.2d-110) then
        tmp = 1.0d0 / (t / (x / y))
    else if (z <= 4.1d-13) then
        tmp = (-x / y) / z
    else if (z <= 15000000000.0d0) then
        tmp = (x / t) / y
    else
        tmp = (x / z) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+54) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= 9.2e-110) {
		tmp = 1.0 / (t / (x / y));
	} else if (z <= 4.1e-13) {
		tmp = (-x / y) / z;
	} else if (z <= 15000000000.0) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.9e+54:
		tmp = 1.0 / (z / (x / z))
	elif z <= 9.2e-110:
		tmp = 1.0 / (t / (x / y))
	elif z <= 4.1e-13:
		tmp = (-x / y) / z
	elif z <= 15000000000.0:
		tmp = (x / t) / y
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.9e+54)
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	elseif (z <= 9.2e-110)
		tmp = Float64(1.0 / Float64(t / Float64(x / y)));
	elseif (z <= 4.1e-13)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (z <= 15000000000.0)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.9e+54)
		tmp = 1.0 / (z / (x / z));
	elseif (z <= 9.2e-110)
		tmp = 1.0 / (t / (x / y));
	elseif (z <= 4.1e-13)
		tmp = (-x / y) / z;
	elseif (z <= 15000000000.0)
		tmp = (x / t) / y;
	else
		tmp = (x / z) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.9e+54], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-110], N[(1.0 / N[(t / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e-13], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 15000000000.0], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.8999999999999999e54

   1. Initial program 86.3%

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

   2. Taylor expanded in z around inf 80.9%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 80.9%

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

   4. Simplified 80.9%

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

      1. clear-num 80.9%

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

      2. inv-pow 80.9%

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

      3. associate-/l* 82.9%

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

   6. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   8. Simplified 82.9%

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

   if -2.8999999999999999e54 < z < 9.2000000000000006e-110

   1. Initial program 93.6%

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

      1. *-un-lft-identity 93.6%

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

      2. times-frac 94.4%

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

   3. Applied egg-rr 94.4%

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

      1. *-commutative 94.4%

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

      2. clear-num 93.6%

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

      3. frac-times 93.5%

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

      4. metadata-eval 93.5%

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

   5. Applied egg-rr 93.5%

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

   6. Taylor expanded in z around 0 65.9%

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

      1. associate-/l* 70.1%

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

   8. Simplified 70.1%

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

   if 9.2000000000000006e-110 < z < 4.1000000000000002e-13

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 51.8%

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

      1. *-commutative 51.8%

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

   4. Simplified 51.8%

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

   5. Taylor expanded in t around 0 45.0%

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

      1. associate-*r/ 45.0%

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

      2. neg-mul-1 45.0%

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

      3. *-commutative 45.0%

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

   7. Simplified 45.0%

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

   8. Taylor expanded in x around 0 45.0%

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

      1. associate-/l/ 38.3%

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

      2. associate-*r/ 38.3%

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

      3. neg-mul-1 38.3%

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

      4. distribute-neg-frac 38.3%

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

   10. Simplified 38.3%

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

   11. Taylor expanded in x around 0 45.0%

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

       1. mul-1-neg 45.0%

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

       2. associate-/r* 45.1%

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

       3. distribute-neg-frac 45.1%

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

   13. Simplified 45.1%

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

   if 4.1000000000000002e-13 < z < 1.5e10

   1. Initial program 84.2%

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

      1. *-un-lft-identity 84.2%

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

      2. times-frac 100.0%

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

   3. Applied egg-rr 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 99.3%

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

      3. frac-times 99.2%

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

      4. metadata-eval 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in z around 0 19.4%

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

      1. associate-/r* 50.8%

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

   8. Simplified 50.8%

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

   if 1.5e10 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in z around inf 82.9%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 82.9%

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

   4. Simplified 82.9%

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

      1. associate-/r* 89.8%

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

      2. div-inv 89.8%

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

   6. Applied egg-rr 89.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-110}:\\ \;\;\;\;\frac{1}{\frac{t}{\frac{x}{y}}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 15000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 6: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 15200000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) t))))
   (if (<= z -9e+54)
     (/ 1.0 (/ z (/ x z)))
     (if (<= z 5.5e-119)
       t_1
       (if (<= z 2.15e-10)
         (/ x (* y (- t z)))
         (if (<= z 15200000.0) t_1 (* (/ x z) (/ 1.0 z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * t);
	double tmp;
	if (z <= -9e+54) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= 5.5e-119) {
		tmp = t_1;
	} else if (z <= 2.15e-10) {
		tmp = x / (y * (t - z));
	} else if (z <= 15200000.0) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * t)
    if (z <= (-9d+54)) then
        tmp = 1.0d0 / (z / (x / z))
    else if (z <= 5.5d-119) then
        tmp = t_1
    else if (z <= 2.15d-10) then
        tmp = x / (y * (t - z))
    else if (z <= 15200000.0d0) then
        tmp = t_1
    else
        tmp = (x / z) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * t);
	double tmp;
	if (z <= -9e+54) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= 5.5e-119) {
		tmp = t_1;
	} else if (z <= 2.15e-10) {
		tmp = x / (y * (t - z));
	} else if (z <= 15200000.0) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * t)
	tmp = 0
	if z <= -9e+54:
		tmp = 1.0 / (z / (x / z))
	elif z <= 5.5e-119:
		tmp = t_1
	elif z <= 2.15e-10:
		tmp = x / (y * (t - z))
	elif z <= 15200000.0:
		tmp = t_1
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * t))
	tmp = 0.0
	if (z <= -9e+54)
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	elseif (z <= 5.5e-119)
		tmp = t_1;
	elseif (z <= 2.15e-10)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (z <= 15200000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * t);
	tmp = 0.0;
	if (z <= -9e+54)
		tmp = 1.0 / (z / (x / z));
	elseif (z <= 5.5e-119)
		tmp = t_1;
	elseif (z <= 2.15e-10)
		tmp = x / (y * (t - z));
	elseif (z <= 15200000.0)
		tmp = t_1;
	else
		tmp = (x / z) * (1.0 / z);
	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]}, If[LessEqual[z, -9e+54], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-119], t$95$1, If[LessEqual[z, 2.15e-10], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 15200000.0], t$95$1, N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.99999999999999968e54

   1. Initial program 86.3%

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

   2. Taylor expanded in z around inf 80.9%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 80.9%

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

   4. Simplified 80.9%

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

      1. clear-num 80.9%

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

      2. inv-pow 80.9%

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

      3. associate-/l* 82.9%

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

   6. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   8. Simplified 82.9%

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

   if -8.99999999999999968e54 < z < 5.49999999999999959e-119 or 2.15000000000000007e-10 < z < 1.52e7

   1. Initial program 92.9%

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

   2. Taylor expanded in t around inf 73.0%

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

   if 5.49999999999999959e-119 < z < 2.15000000000000007e-10

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 66.0%

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

      1. *-commutative 66.0%

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

   4. Simplified 66.0%

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

   if 1.52e7 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in z around inf 82.9%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 82.9%

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

   4. Simplified 82.9%

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

      1. associate-/r* 89.8%

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

      2. div-inv 89.8%

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

   6. Applied egg-rr 89.8%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 15200000:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 7: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{1}{z}\\ t_2 := \frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{if}\;t \leq 2.3 \cdot 10^{-270}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3500000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 1.0 z))) (t_2 (/ x (* y (- t z)))))
   (if (<= t 2.3e-270)
     t_2
     (if (<= t 6.4e-217)
       t_1
       (if (<= t 7.6e-106)
         t_2
         (if (<= t 3500000000.0) t_1 (/ (/ x t) (- y z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double t_2 = x / (y * (t - z));
	double tmp;
	if (t <= 2.3e-270) {
		tmp = t_2;
	} else if (t <= 6.4e-217) {
		tmp = t_1;
	} else if (t <= 7.6e-106) {
		tmp = t_2;
	} else if (t <= 3500000000.0) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) * (1.0d0 / z)
    t_2 = x / (y * (t - z))
    if (t <= 2.3d-270) then
        tmp = t_2
    else if (t <= 6.4d-217) then
        tmp = t_1
    else if (t <= 7.6d-106) then
        tmp = t_2
    else if (t <= 3500000000.0d0) then
        tmp = t_1
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double t_2 = x / (y * (t - z));
	double tmp;
	if (t <= 2.3e-270) {
		tmp = t_2;
	} else if (t <= 6.4e-217) {
		tmp = t_1;
	} else if (t <= 7.6e-106) {
		tmp = t_2;
	} else if (t <= 3500000000.0) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * (1.0 / z)
	t_2 = x / (y * (t - z))
	tmp = 0
	if t <= 2.3e-270:
		tmp = t_2
	elif t <= 6.4e-217:
		tmp = t_1
	elif t <= 7.6e-106:
		tmp = t_2
	elif t <= 3500000000.0:
		tmp = t_1
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(1.0 / z))
	t_2 = Float64(x / Float64(y * Float64(t - z)))
	tmp = 0.0
	if (t <= 2.3e-270)
		tmp = t_2;
	elseif (t <= 6.4e-217)
		tmp = t_1;
	elseif (t <= 7.6e-106)
		tmp = t_2;
	elseif (t <= 3500000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (1.0 / z);
	t_2 = x / (y * (t - z));
	tmp = 0.0;
	if (t <= 2.3e-270)
		tmp = t_2;
	elseif (t <= 6.4e-217)
		tmp = t_1;
	elseif (t <= 7.6e-106)
		tmp = t_2;
	elseif (t <= 3500000000.0)
		tmp = t_1;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 2.3e-270], t$95$2, If[LessEqual[t, 6.4e-217], t$95$1, If[LessEqual[t, 7.6e-106], t$95$2, If[LessEqual[t, 3500000000.0], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 2.3000000000000001e-270 or 6.4000000000000002e-217 < t < 7.5999999999999999e-106

   1. Initial program 93.9%

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

   2. Taylor expanded in y around inf 67.2%

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

      1. *-commutative 67.2%

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

   4. Simplified 67.2%

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

   if 2.3000000000000001e-270 < t < 6.4000000000000002e-217 or 7.5999999999999999e-106 < t < 3.5e9

   1. Initial program 87.1%

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

   2. Taylor expanded in z around inf 60.6%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 60.6%

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

   4. Simplified 60.6%

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

      1. associate-/r* 68.9%

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

      2. div-inv 68.9%

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

   6. Applied egg-rr 68.9%

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

   if 3.5e9 < t

   1. Initial program 89.3%

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

   2. Taylor expanded in t around inf 84.7%

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

      1. associate-/r* 87.7%

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

   4. Simplified 87.7%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.3 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-217}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 3500000000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 8: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+58}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e+58)
   (/ 1.0 (/ z (/ x z)))
   (if (<= z 9.2e-119)
     (/ (/ x (- y z)) t)
     (if (<= z 7.2e-6)
       (/ (/ x y) (- t z))
       (if (<= z 3.7e+67) (/ (/ x t) (- y z)) (* (/ x z) (/ 1.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e+58) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= 9.2e-119) {
		tmp = (x / (y - z)) / t;
	} else if (z <= 7.2e-6) {
		tmp = (x / y) / (t - z);
	} else if (z <= 3.7e+67) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.1d+58)) then
        tmp = 1.0d0 / (z / (x / z))
    else if (z <= 9.2d-119) then
        tmp = (x / (y - z)) / t
    else if (z <= 7.2d-6) then
        tmp = (x / y) / (t - z)
    else if (z <= 3.7d+67) then
        tmp = (x / t) / (y - z)
    else
        tmp = (x / z) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e+58) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= 9.2e-119) {
		tmp = (x / (y - z)) / t;
	} else if (z <= 7.2e-6) {
		tmp = (x / y) / (t - z);
	} else if (z <= 3.7e+67) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e+58:
		tmp = 1.0 / (z / (x / z))
	elif z <= 9.2e-119:
		tmp = (x / (y - z)) / t
	elif z <= 7.2e-6:
		tmp = (x / y) / (t - z)
	elif z <= 3.7e+67:
		tmp = (x / t) / (y - z)
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e+58)
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	elseif (z <= 9.2e-119)
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	elseif (z <= 7.2e-6)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (z <= 3.7e+67)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.1e+58)
		tmp = 1.0 / (z / (x / z));
	elseif (z <= 9.2e-119)
		tmp = (x / (y - z)) / t;
	elseif (z <= 7.2e-6)
		tmp = (x / y) / (t - z);
	elseif (z <= 3.7e+67)
		tmp = (x / t) / (y - z);
	else
		tmp = (x / z) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.1e+58], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-119], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 7.2e-6], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+67], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.1e58

   1. Initial program 86.3%

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

   2. Taylor expanded in z around inf 80.9%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 80.9%

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

   4. Simplified 80.9%

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

      1. clear-num 80.9%

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

      2. inv-pow 80.9%

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

      3. associate-/l* 82.9%

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

   6. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   8. Simplified 82.9%

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

   if -1.1e58 < z < 9.19999999999999973e-119

   1. Initial program 93.3%

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

   2. Taylor expanded in t around inf 74.0%

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

      1. *-commutative 74.0%

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

      2. associate-/r* 77.5%

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

   4. Simplified 77.5%

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

   if 9.19999999999999973e-119 < z < 7.19999999999999967e-6

   1. Initial program 99.7%

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

      1. *-un-lft-identity 99.7%

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

      2. times-frac 90.5%

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

   3. Applied egg-rr 90.5%

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

      1. *-commutative 90.5%

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

      2. clear-num 90.6%

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

      3. frac-times 90.6%

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

      4. metadata-eval 90.6%

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

   5. Applied egg-rr 90.6%

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

   6. Taylor expanded in y around inf 67.6%

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

      1. associate-/r* 67.6%

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

   8. Simplified 67.6%

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

   if 7.19999999999999967e-6 < z < 3.6999999999999997e67

   1. Initial program 84.2%

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

   2. Taylor expanded in t around inf 36.1%

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

      1. associate-/r* 43.9%

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

   4. Simplified 43.9%

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

   if 3.6999999999999997e67 < z

   1. Initial program 90.7%

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

   2. Taylor expanded in z around inf 87.2%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 87.2%

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

   4. Simplified 87.2%

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

      1. associate-/r* 94.9%

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

      2. div-inv 94.8%

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

   6. Applied egg-rr 94.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+58}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 9: 62.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 14000000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z z))) (t_2 (/ (/ x t) y)))
   (if (<= z -1.65e+54)
     t_1
     (if (<= z 5.1e-110)
       t_2
       (if (<= z 3.05e-12)
         (/ (/ (- x) y) z)
         (if (<= z 14000000000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double t_2 = (x / t) / y;
	double tmp;
	if (z <= -1.65e+54) {
		tmp = t_1;
	} else if (z <= 5.1e-110) {
		tmp = t_2;
	} else if (z <= 3.05e-12) {
		tmp = (-x / y) / z;
	} else if (z <= 14000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (z * z)
    t_2 = (x / t) / y
    if (z <= (-1.65d+54)) then
        tmp = t_1
    else if (z <= 5.1d-110) then
        tmp = t_2
    else if (z <= 3.05d-12) then
        tmp = (-x / y) / z
    else if (z <= 14000000000.0d0) then
        tmp = t_2
    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);
	double t_2 = (x / t) / y;
	double tmp;
	if (z <= -1.65e+54) {
		tmp = t_1;
	} else if (z <= 5.1e-110) {
		tmp = t_2;
	} else if (z <= 3.05e-12) {
		tmp = (-x / y) / z;
	} else if (z <= 14000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * z)
	t_2 = (x / t) / y
	tmp = 0
	if z <= -1.65e+54:
		tmp = t_1
	elif z <= 5.1e-110:
		tmp = t_2
	elif z <= 3.05e-12:
		tmp = (-x / y) / z
	elif z <= 14000000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	t_2 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (z <= -1.65e+54)
		tmp = t_1;
	elseif (z <= 5.1e-110)
		tmp = t_2;
	elseif (z <= 3.05e-12)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (z <= 14000000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	t_2 = (x / t) / y;
	tmp = 0.0;
	if (z <= -1.65e+54)
		tmp = t_1;
	elseif (z <= 5.1e-110)
		tmp = t_2;
	elseif (z <= 3.05e-12)
		tmp = (-x / y) / z;
	elseif (z <= 14000000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -1.65e+54], t$95$1, If[LessEqual[z, 5.1e-110], t$95$2, If[LessEqual[z, 3.05e-12], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 14000000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e54 or 1.4e10 < z

   1. Initial program 88.7%

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

   2. Taylor expanded in z around inf 82.1%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 82.1%

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

   4. Simplified 82.1%

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

   if -1.65e54 < z < 5.1000000000000002e-110 or 3.0500000000000001e-12 < z < 1.4e10

   1. Initial program 93.2%

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

      1. *-un-lft-identity 93.2%

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

      2. times-frac 94.7%

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

   3. Applied egg-rr 94.7%

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

      1. *-commutative 94.7%

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

      2. clear-num 93.8%

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

      3. frac-times 93.7%

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

      4. metadata-eval 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in z around 0 63.4%

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

      1. associate-/r* 67.8%

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

   8. Simplified 67.8%

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

   if 5.1000000000000002e-110 < z < 3.0500000000000001e-12

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 51.8%

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

      1. *-commutative 51.8%

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

   4. Simplified 51.8%

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

   5. Taylor expanded in t around 0 45.0%

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

      1. associate-*r/ 45.0%

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

      2. neg-mul-1 45.0%

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

      3. *-commutative 45.0%

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

   7. Simplified 45.0%

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

   8. Taylor expanded in x around 0 45.0%

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

      1. associate-/l/ 38.3%

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

      2. associate-*r/ 38.3%

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

      3. neg-mul-1 38.3%

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

      4. distribute-neg-frac 38.3%

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

   10. Simplified 38.3%

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

   11. Taylor expanded in x around 0 45.0%

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

       1. mul-1-neg 45.0%

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

       2. associate-/r* 45.1%

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

       3. distribute-neg-frac 45.1%

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

   13. Simplified 45.1%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-110}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 14000000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]

Alternative 10: 74.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.2e-29)
   (/ x (* y (- t z)))
   (if (<= y 5.4e-196) (* (/ x (- t z)) (/ -1.0 z)) (/ (/ x (- y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.2e-29) {
		tmp = x / (y * (t - z));
	} else if (y <= 5.4e-196) {
		tmp = (x / (t - z)) * (-1.0 / 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 <= (-9.2d-29)) then
        tmp = x / (y * (t - z))
    else if (y <= 5.4d-196) then
        tmp = (x / (t - z)) * ((-1.0d0) / 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 <= -9.2e-29) {
		tmp = x / (y * (t - z));
	} else if (y <= 5.4e-196) {
		tmp = (x / (t - z)) * (-1.0 / z);
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.2e-29:
		tmp = x / (y * (t - z))
	elif y <= 5.4e-196:
		tmp = (x / (t - z)) * (-1.0 / z)
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.2e-29)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 5.4e-196)
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(-1.0 / 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 <= -9.2e-29)
		tmp = x / (y * (t - z));
	elseif (y <= 5.4e-196)
		tmp = (x / (t - z)) * (-1.0 / z);
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.2e-29], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-196], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.19999999999999965e-29

   1. Initial program 94.4%

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

   2. Taylor expanded in y around inf 87.4%

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

      1. *-commutative 87.4%

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

   4. Simplified 87.4%

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

   if -9.19999999999999965e-29 < y < 5.39999999999999963e-196

   1. Initial program 96.1%

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

      1. *-un-lft-identity 96.1%

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

      2. times-frac 95.9%

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

   3. Applied egg-rr 95.9%

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

   4. Taylor expanded in y around 0 86.9%

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

   if 5.39999999999999963e-196 < y

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-/r* 61.0%

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

   4. Simplified 61.0%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]

Alternative 11: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+34}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t - z}{x}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e+34)
   (/ 1.0 (* y (/ (- t z) x)))
   (if (<= y 5.4e-196) (* (/ x (- t z)) (/ -1.0 z)) (/ (/ x (- y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e+34) {
		tmp = 1.0 / (y * ((t - z) / x));
	} else if (y <= 5.4e-196) {
		tmp = (x / (t - z)) * (-1.0 / 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 <= (-5d+34)) then
        tmp = 1.0d0 / (y * ((t - z) / x))
    else if (y <= 5.4d-196) then
        tmp = (x / (t - z)) * ((-1.0d0) / 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 <= -5e+34) {
		tmp = 1.0 / (y * ((t - z) / x));
	} else if (y <= 5.4e-196) {
		tmp = (x / (t - z)) * (-1.0 / z);
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5e+34:
		tmp = 1.0 / (y * ((t - z) / x))
	elif y <= 5.4e-196:
		tmp = (x / (t - z)) * (-1.0 / z)
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e+34)
		tmp = Float64(1.0 / Float64(y * Float64(Float64(t - z) / x)));
	elseif (y <= 5.4e-196)
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(-1.0 / 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 <= -5e+34)
		tmp = 1.0 / (y * ((t - z) / x));
	elseif (y <= 5.4e-196)
		tmp = (x / (t - z)) * (-1.0 / z);
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5e+34], N[(1.0 / N[(y * N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-196], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999998e34

   1. Initial program 94.6%

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

      1. *-un-lft-identity 94.6%

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

      2. times-frac 97.0%

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

   3. Applied egg-rr 97.0%

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

      1. *-commutative 97.0%

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

      2. clear-num 97.0%

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

      3. frac-times 97.5%

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

      4. metadata-eval 97.5%

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

   5. Applied egg-rr 97.5%

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

   6. Taylor expanded in y around inf 90.5%

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

      1. associate-*r/ 92.2%

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

   8. Simplified 92.2%

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

   if -4.9999999999999998e34 < y < 5.39999999999999963e-196

   1. Initial program 95.6%

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

      1. *-un-lft-identity 95.6%

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

      2. times-frac 96.5%

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

   3. Applied egg-rr 96.5%

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

   4. Taylor expanded in y around 0 83.5%

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

   if 5.39999999999999963e-196 < y

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-/r* 61.0%

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

   4. Simplified 61.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+34}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t - z}{x}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]

Alternative 12: 72.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.42e-39)
   (/ x (* y (- t z)))
   (if (<= y 5.4e-196) (/ (- x) (* z (- t z))) (/ (/ x (- y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.42e-39) {
		tmp = x / (y * (t - z));
	} else if (y <= 5.4e-196) {
		tmp = -x / (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 (y <= (-1.42d-39)) then
        tmp = x / (y * (t - z))
    else if (y <= 5.4d-196) then
        tmp = -x / (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 (y <= -1.42e-39) {
		tmp = x / (y * (t - z));
	} else if (y <= 5.4e-196) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.42e-39:
		tmp = x / (y * (t - z))
	elif y <= 5.4e-196:
		tmp = -x / (z * (t - z))
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.42e-39)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 5.4e-196)
		tmp = Float64(Float64(-x) / Float64(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 (y <= -1.42e-39)
		tmp = x / (y * (t - z));
	elseif (y <= 5.4e-196)
		tmp = -x / (z * (t - z));
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.42e-39], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-196], N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.42000000000000005e-39

   1. Initial program 94.4%

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

   2. Taylor expanded in y around inf 87.4%

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

      1. *-commutative 87.4%

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

   4. Simplified 87.4%

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

   if -1.42000000000000005e-39 < y < 5.39999999999999963e-196

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 85.1%

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

      1. associate-*r/ 85.1%

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

      2. neg-mul-1 85.1%

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

   4. Simplified 85.1%

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

   if 5.39999999999999963e-196 < y

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-/r* 61.0%

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

   4. Simplified 61.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]

Alternative 13: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-196}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.12e-35)
   (/ x (* y (- t z)))
   (if (<= y 1.6e-196) (/ (/ (- x) z) (- t z)) (/ (/ x (- y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.12e-35) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.6e-196) {
		tmp = (-x / 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 (y <= (-1.12d-35)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.6d-196) then
        tmp = (-x / 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 (y <= -1.12e-35) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.6e-196) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.12e-35:
		tmp = x / (y * (t - z))
	elif y <= 1.6e-196:
		tmp = (-x / z) / (t - z)
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.12e-35)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.6e-196)
		tmp = Float64(Float64(Float64(-x) / 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 (y <= -1.12e-35)
		tmp = x / (y * (t - z));
	elseif (y <= 1.6e-196)
		tmp = (-x / z) / (t - z);
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.12e-35], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-196], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e-35

   1. Initial program 94.4%

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

   2. Taylor expanded in y around inf 87.4%

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

      1. *-commutative 87.4%

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

   4. Simplified 87.4%

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

   if -1.12e-35 < y < 1.6e-196

   1. Initial program 96.1%

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

      1. *-un-lft-identity 96.1%

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

      2. times-frac 95.9%

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

   3. Applied egg-rr 95.9%

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

   4. Taylor expanded in y around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. associate-/r* 87.5%

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

      3. distribute-neg-frac 87.5%

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

   6. Simplified 87.5%

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

   if 1.6e-196 < y

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-/r* 61.0%

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

   4. Simplified 61.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-196}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]

Alternative 14: 73.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+58}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 50000000000:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.9e+58)
   (/ 1.0 (/ z (/ x z)))
   (if (<= z 50000000000.0) (/ x (* (- y z) t)) (* (/ x z) (/ 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.9e+58) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= 50000000000.0) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.9d+58)) then
        tmp = 1.0d0 / (z / (x / z))
    else if (z <= 50000000000.0d0) then
        tmp = x / ((y - z) * t)
    else
        tmp = (x / z) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.9e+58) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= 50000000000.0) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.9e+58:
		tmp = 1.0 / (z / (x / z))
	elif z <= 50000000000.0:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.9e+58)
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	elseif (z <= 50000000000.0)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.9e+58)
		tmp = 1.0 / (z / (x / z));
	elseif (z <= 50000000000.0)
		tmp = x / ((y - z) * t);
	else
		tmp = (x / z) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.9e+58], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 50000000000.0], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.90000000000000018e58

   1. Initial program 86.3%

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

   2. Taylor expanded in z around inf 80.9%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 80.9%

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

   4. Simplified 80.9%

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

      1. clear-num 80.9%

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

      2. inv-pow 80.9%

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

      3. associate-/l* 82.9%

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

   6. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

   8. Simplified 82.9%

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

   if -4.90000000000000018e58 < z < 5e10

   1. Initial program 93.8%

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

   2. Taylor expanded in t around inf 69.7%

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

   if 5e10 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in z around inf 82.9%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 82.9%

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

   4. Simplified 82.9%

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

      1. associate-/r* 89.8%

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

      2. div-inv 89.8%

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

   6. Applied egg-rr 89.8%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+58}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 50000000000:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 15: 90.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.6 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.6e+180) (/ x (* (- y z) (- t z))) (/ (/ x t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.6e+180) {
		tmp = x / ((y - z) * (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 <= 3.6d+180) then
        tmp = x / ((y - z) * (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 <= 3.6e+180) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 3.6e+180:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3.6e+180)
		tmp = Float64(x / Float64(Float64(y - z) * 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 <= 3.6e+180)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 3.6e+180], N[(x / N[(N[(y - z), $MachinePrecision] * 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 < 3.6000000000000002e180

   1. Initial program 92.8%

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

   if 3.6000000000000002e180 < t

   1. Initial program 79.6%

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

   2. Taylor expanded in t around inf 79.6%

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

      1. associate-/r* 95.8%

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

   4. Simplified 95.8%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.6 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 16: 96.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (1.0 / (y - z)) * (x / (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 = (1.0d0 / (y - z)) * (x / (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.6%

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

   1. *-un-lft-identity 91.6%

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

   2. times-frac 96.5%

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

3. Applied egg-rr 96.5%

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

4. Final simplification 96.5%

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

Alternative 17: 46.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+101} \lor \neg \left(z \leq 6 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.1e+101) (not (<= z 6e+67))) (/ x (* y z)) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+101) || !(z <= 6e+67)) {
		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 <= (-3.1d+101)) .or. (.not. (z <= 6d+67))) 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 <= -3.1e+101) || !(z <= 6e+67)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.1e+101) or not (z <= 6e+67):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.1e+101) || !(z <= 6e+67))
		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 <= -3.1e+101) || ~((z <= 6e+67)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.1e+101], N[Not[LessEqual[z, 6e+67]], $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 < -3.09999999999999999e101 or 6.0000000000000002e67 < z

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 45.1%

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

      1. *-commutative 45.1%

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

   4. Simplified 45.1%

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

   5. Taylor expanded in t around 0 44.1%

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

      1. associate-*r/ 44.1%

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

      2. neg-mul-1 44.1%

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

      3. *-commutative 44.1%

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

   7. Simplified 44.1%

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

      1. expm1-log1p-u 43.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-x}{z \cdot y}\right)\right)} \]

      2. expm1-udef 69.9%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{-x}{z \cdot y}\right)} - 1} \]

      3. add-sqr-sqrt 37.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot y}\right)} - 1 \]

      4. sqrt-unprod 67.5%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot y}\right)} - 1 \]

      5. sqr-neg 67.5%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot y}\right)} - 1 \]

      6. sqrt-unprod 31.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot y}\right)} - 1 \]

      7. add-sqr-sqrt 69.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot y}\right)} - 1 \]

      8. associate-/r* 69.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\frac{x}{z}}{y}}\right)} - 1 \]

   9. Applied egg-rr 69.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{x}{z}}{y}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 52.6%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{x}{z}}{y}\right)\right)} \]

       2. expm1-log1p 52.9%

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

       3. associate-/l/ 43.0%

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

       4. *-commutative 43.0%

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

   11. Simplified 43.0%

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

   if -3.09999999999999999e101 < z < 6.0000000000000002e67

   1. Initial program 93.2%

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

   2. Taylor expanded in z around 0 53.7%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+101} \lor \neg \left(z \leq 6 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 18: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9000000000000 \lor \neg \left(z \leq 9.2 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9000000000000.0) (not (<= z 9.2e-110)))
   (/ x (* z z))
   (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9000000000000.0) || !(z <= 9.2e-110)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9000000000000.0d0)) .or. (.not. (z <= 9.2d-110))) then
        tmp = x / (z * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9000000000000.0) || !(z <= 9.2e-110)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9000000000000.0) or not (z <= 9.2e-110):
		tmp = x / (z * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9000000000000.0) || !(z <= 9.2e-110))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9000000000000.0) || ~((z <= 9.2e-110)))
		tmp = x / (z * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9000000000000.0], N[Not[LessEqual[z, 9.2e-110]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9e12 or 9.2000000000000006e-110 < z

   1. Initial program 89.3%

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

   2. Taylor expanded in z around inf 69.7%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 69.7%

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

   4. Simplified 69.7%

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

   if -9e12 < z < 9.2000000000000006e-110

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 70.7%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9000000000000 \lor \neg \left(z \leq 9.2 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 19: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+58} \lor \neg \left(z \leq 9.2 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.15e+58) (not (<= z 9.2e-110))) (/ x (* z z)) (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+58) || !(z <= 9.2e-110)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.15d+58)) .or. (.not. (z <= 9.2d-110))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+58) || !(z <= 9.2e-110)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.15e+58) or not (z <= 9.2e-110):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.15e+58) || !(z <= 9.2e-110))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.15e+58) || ~((z <= 9.2e-110)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.15e+58], N[Not[LessEqual[z, 9.2e-110]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000001e58 or 9.2000000000000006e-110 < z

   1. Initial program 89.7%

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

   2. Taylor expanded in z around inf 74.2%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 74.2%

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

   4. Simplified 74.2%

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

   if -1.15000000000000001e58 < z < 9.2000000000000006e-110

   1. Initial program 93.6%

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

      1. *-un-lft-identity 93.6%

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

      2. times-frac 94.4%

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

   3. Applied egg-rr 94.4%

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

      1. *-commutative 94.4%

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

      2. clear-num 93.6%

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

      3. frac-times 93.5%

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

      4. metadata-eval 93.5%

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

   5. Applied egg-rr 93.5%

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

   6. Taylor expanded in z around 0 65.5%

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

      1. associate-/r* 68.6%

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

   8. Simplified 68.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+58} \lor \neg \left(z \leq 9.2 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 20: 39.7% 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 91.6%

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

2. Taylor expanded in z around 0 41.4%

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

3. Final simplification 41.4%

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

Developer target: 88.3% 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 2023275 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (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))))