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

Percentage Accurate: 89.2% → 96.8%

Time: 12.3s

Alternatives: 22

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.2%

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

3. Taylor expanded in x around 0 88.2%

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

   1. associate-/l/ 98.4%

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

5. Simplified 98.4%

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

6. Final simplification 98.4%

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

Alternative 2: 93.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x y) (- t z))
     (if (<= t_1 5e+302) (/ x t_1) (/ (/ x z) (- z t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x / y) / (t - z);
	} else if (t_1 <= 5e+302) {
		tmp = x / t_1;
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / y) / (t - z);
	} else if (t_1 <= 5e+302) {
		tmp = x / t_1;
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x / y) / (t - z)
	elif t_1 <= 5e+302:
		tmp = x / t_1
	else:
		tmp = (x / z) / (z - t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t_1 <= 5e+302)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / z) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x / y) / (t - z);
	elseif (t_1 <= 5e+302)
		tmp = x / t_1;
	else
		tmp = (x / z) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+302], N[(x / t$95$1), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 62.3%

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

   3. Taylor expanded in x around 0 62.3%

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

      1. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf 81.6%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 5e302

   1. Initial program 98.5%

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

   if 5e302 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 70.4%

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

   3. Taylor expanded in x around 0 70.4%

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

      1. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 87.3%

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

      1. associate-*r/ 87.3%

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

      2. mul-1-neg 87.3%

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

   8. Simplified 87.3%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(-t\right)}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- t)))))
   (if (<= z -2.25e-115)
     t_1
     (if (<= z 1.1e-23)
       (/ (/ x t) y)
       (if (<= z 2.45e+125) t_1 (/ x (* y z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * -t);
	double tmp;
	if (z <= -2.25e-115) {
		tmp = t_1;
	} else if (z <= 1.1e-23) {
		tmp = (x / t) / y;
	} else if (z <= 2.45e+125) {
		tmp = t_1;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z * -t)
    if (z <= (-2.25d-115)) then
        tmp = t_1
    else if (z <= 1.1d-23) then
        tmp = (x / t) / y
    else if (z <= 2.45d+125) then
        tmp = t_1
    else
        tmp = x / (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 * -t);
	double tmp;
	if (z <= -2.25e-115) {
		tmp = t_1;
	} else if (z <= 1.1e-23) {
		tmp = (x / t) / y;
	} else if (z <= 2.45e+125) {
		tmp = t_1;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * -t)
	tmp = 0
	if z <= -2.25e-115:
		tmp = t_1
	elif z <= 1.1e-23:
		tmp = (x / t) / y
	elif z <= 2.45e+125:
		tmp = t_1
	else:
		tmp = x / (y * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(-t)))
	tmp = 0.0
	if (z <= -2.25e-115)
		tmp = t_1;
	elseif (z <= 1.1e-23)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 2.45e+125)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * -t);
	tmp = 0.0;
	if (z <= -2.25e-115)
		tmp = t_1;
	elseif (z <= 1.1e-23)
		tmp = (x / t) / y;
	elseif (z <= 2.45e+125)
		tmp = t_1;
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e-115], t$95$1, If[LessEqual[z, 1.1e-23], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 2.45e+125], t$95$1, N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.25000000000000011e-115 or 1.1e-23 < z < 2.45000000000000008e125

   1. Initial program 88.8%

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

      1. associate-/l/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 51.1%

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

   6. Taylor expanded in y around 0 40.2%

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

      1. associate-*r/ 40.2%

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

      2. mul-1-neg 40.2%

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

   8. Simplified 40.2%

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

   if -2.25000000000000011e-115 < z < 1.1e-23

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 93.5%

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

      1. associate-/l/ 95.9%

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

   5. Simplified 95.9%

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

      1. clear-num 95.6%

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

      2. associate-/r/ 95.8%

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

      3. associate-*l/ 93.5%

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

   7. Applied egg-rr 93.5%

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

      1. associate-*l/ 95.8%

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

      2. clear-num 95.8%

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

      3. associate-*l/ 95.8%

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

      4. *-un-lft-identity 95.8%

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

   9. Applied egg-rr 95.8%

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

   10. Taylor expanded in z around 0 72.0%

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

       1. associate-/r* 73.5%

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

   12. Simplified 73.5%

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

   if 2.45000000000000008e125 < z

   1. Initial program 72.3%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 91.8%

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

      1. associate-*r/ 91.8%

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

      2. neg-mul-1 91.8%

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

   7. Simplified 91.8%

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

      1. div-inv 91.8%

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

      2. associate-/l* 67.3%

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

      3. add-sqr-sqrt 23.5%

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

      4. sqrt-unprod 62.0%

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

      5. sqr-neg 62.0%

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

      6. sqrt-unprod 41.1%

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

      7. add-sqr-sqrt 64.7%

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

   9. Applied egg-rr 64.7%

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

       1. associate-/r* 64.9%

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

       2. associate-*r/ 64.9%

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

       3. times-frac 64.2%

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

       4. associate-*r/ 64.2%

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

       5. associate-*l/ 64.2%

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

       6. *-rgt-identity 64.2%

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

       7. associate-/r* 64.9%

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

   11. Simplified 64.9%

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

   12. Taylor expanded in z around 0 34.8%

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

       1. *-commutative 34.8%

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

   14. Simplified 34.8%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.2e-41)
   (/ (/ x t) y)
   (if (<= t 1.02e-18)
     (/ (/ x y) (- z))
     (if (<= t 3e+130) (/ x (* y t)) (/ (/ x t) (- z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-41) {
		tmp = (x / t) / y;
	} else if (t <= 1.02e-18) {
		tmp = (x / y) / -z;
	} else if (t <= 3e+130) {
		tmp = x / (y * t);
	} else {
		tmp = (x / t) / -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4.2d-41)) then
        tmp = (x / t) / y
    else if (t <= 1.02d-18) then
        tmp = (x / y) / -z
    else if (t <= 3d+130) then
        tmp = x / (y * t)
    else
        tmp = (x / t) / -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-41) {
		tmp = (x / t) / y;
	} else if (t <= 1.02e-18) {
		tmp = (x / y) / -z;
	} else if (t <= 3e+130) {
		tmp = x / (y * t);
	} else {
		tmp = (x / t) / -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.2e-41:
		tmp = (x / t) / y
	elif t <= 1.02e-18:
		tmp = (x / y) / -z
	elif t <= 3e+130:
		tmp = x / (y * t)
	else:
		tmp = (x / t) / -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.2e-41)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 1.02e-18)
		tmp = Float64(Float64(x / y) / Float64(-z));
	elseif (t <= 3e+130)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = Float64(Float64(x / t) / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.2e-41)
		tmp = (x / t) / y;
	elseif (t <= 1.02e-18)
		tmp = (x / y) / -z;
	elseif (t <= 3e+130)
		tmp = x / (y * t);
	else
		tmp = (x / t) / -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.2e-41], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.02e-18], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[t, 3e+130], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.20000000000000025e-41

   1. Initial program 90.2%

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

   3. Taylor expanded in x around 0 90.2%

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

      1. associate-/l/ 96.7%

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

   5. Simplified 96.7%

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

      1. clear-num 96.6%

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

      2. associate-/r/ 96.6%

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

      3. associate-*l/ 91.1%

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

   7. Applied egg-rr 91.1%

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

      1. associate-*l/ 96.6%

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

      2. clear-num 95.6%

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

      3. associate-*l/ 95.6%

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

      4. *-un-lft-identity 95.6%

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

   9. Applied egg-rr 95.6%

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

   10. Taylor expanded in z around 0 49.8%

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

       1. associate-/r* 56.5%

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

   12. Simplified 56.5%

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

   if -4.20000000000000025e-41 < t < 1.02e-18

   1. Initial program 88.3%

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

   3. Taylor expanded in y around inf 50.4%

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

      1. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in t around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. associate-/r* 38.8%

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

      3. distribute-neg-frac2 38.8%

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

   8. Simplified 38.8%

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

   if 1.02e-18 < t < 2.9999999999999999e130

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0 65.4%

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

   if 2.9999999999999999e130 < t

   1. Initial program 73.9%

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

      1. associate-/l/ 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around inf 91.8%

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

   6. Taylor expanded in y around 0 49.9%

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

      1. associate-*r/ 49.9%

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

      2. mul-1-neg 49.9%

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

   8. Simplified 49.9%

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

      1. neg-mul-1 49.9%

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

      2. *-commutative 49.9%

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

      3. times-frac 67.3%

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

   10. Applied egg-rr 67.3%

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

       1. associate-*l/ 67.3%

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

       2. associate-*r/ 67.3%

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

       3. neg-mul-1 67.3%

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

   12. Applied egg-rr 67.3%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+121} \lor \neg \left(z \leq 1.4 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9e+121) (not (<= z 1.4e+122)))
   (/ x (* z (- y z)))
   (/ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+121) || !(z <= 1.4e+122)) {
		tmp = x / (z * (y - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.9d+121)) .or. (.not. (z <= 1.4d+122))) then
        tmp = x / (z * (y - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+121) || !(z <= 1.4e+122)) {
		tmp = x / (z * (y - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.9e+121) or not (z <= 1.4e+122):
		tmp = x / (z * (y - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.9e+121) || !(z <= 1.4e+122))
		tmp = Float64(x / Float64(z * Float64(y - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.9e+121) || ~((z <= 1.4e+122)))
		tmp = x / (z * (y - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.9e+121], N[Not[LessEqual[z, 1.4e+122]], $MachinePrecision]], N[(x / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8999999999999999e121 or 1.4e122 < z

   1. Initial program 71.3%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 88.7%

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

      1. associate-*r/ 88.7%

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

      2. neg-mul-1 88.7%

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

   7. Simplified 88.7%

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

      1. div-inv 88.6%

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

      2. associate-/l* 69.9%

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

      3. add-sqr-sqrt 26.7%

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

      4. sqrt-unprod 60.1%

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

      5. sqr-neg 60.1%

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

      6. sqrt-unprod 40.7%

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

      7. add-sqr-sqrt 65.0%

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

   9. Applied egg-rr 65.0%

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

       1. associate-/r* 65.1%

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

       2. associate-*r/ 65.1%

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

       3. times-frac 64.6%

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

       4. associate-*r/ 64.6%

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

       5. associate-*l/ 64.6%

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

       6. *-rgt-identity 64.6%

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

       7. associate-/r* 65.1%

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

   11. Simplified 65.1%

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

   if -2.8999999999999999e121 < z < 1.4e122

   1. Initial program 95.1%

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

   3. Taylor expanded in t around inf 65.3%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+121} \lor \neg \left(z \leq 1.4 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-115}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e-115)
   (/ (/ x (- z)) t)
   (if (<= z 4.2e-24) (* (/ x y) (/ 1.0 t)) (/ (/ x y) (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e-115) {
		tmp = (x / -z) / t;
	} else if (z <= 4.2e-24) {
		tmp = (x / y) * (1.0 / t);
	} else {
		tmp = (x / y) / -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5d-115)) then
        tmp = (x / -z) / t
    else if (z <= 4.2d-24) then
        tmp = (x / y) * (1.0d0 / t)
    else
        tmp = (x / y) / -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e-115) {
		tmp = (x / -z) / t;
	} else if (z <= 4.2e-24) {
		tmp = (x / y) * (1.0 / t);
	} else {
		tmp = (x / y) / -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5e-115:
		tmp = (x / -z) / t
	elif z <= 4.2e-24:
		tmp = (x / y) * (1.0 / t)
	else:
		tmp = (x / y) / -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e-115)
		tmp = Float64(Float64(x / Float64(-z)) / t);
	elseif (z <= 4.2e-24)
		tmp = Float64(Float64(x / y) * Float64(1.0 / t));
	else
		tmp = Float64(Float64(x / y) / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5e-115)
		tmp = (x / -z) / t;
	elseif (z <= 4.2e-24)
		tmp = (x / y) * (1.0 / t);
	else
		tmp = (x / y) / -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5e-115], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.2e-24], N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.0000000000000003e-115

   1. Initial program 85.6%

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

      1. associate-/l/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf 51.0%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. associate-*r/ 39.4%

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

      2. mul-1-neg 39.4%

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

   8. Simplified 39.4%

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

   9. Taylor expanded in x around 0 39.4%

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

       1. associate-/l/ 45.8%

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

       2. associate-*r/ 45.8%

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

       3. associate-*r/ 45.8%

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

       4. mul-1-neg 45.8%

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

   11. Simplified 45.8%

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

   if -5.0000000000000003e-115 < z < 4.1999999999999999e-24

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 71.6%

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

      1. *-un-lft-identity 71.6%

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

      2. times-frac 73.8%

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

   5. Applied egg-rr 73.8%

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

   if 4.1999999999999999e-24 < z

   1. Initial program 85.0%

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

   3. Taylor expanded in y around inf 35.2%

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

      1. *-commutative 35.2%

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

   5. Simplified 35.2%

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

   6. Taylor expanded in t around 0 31.6%

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

      1. mul-1-neg 31.6%

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

      2. associate-/r* 33.6%

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

      3. distribute-neg-frac2 33.6%

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

   8. Simplified 33.6%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-115}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-115}:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e-115)
   (/ -1.0 (* t (/ z x)))
   (if (<= z 4.2e-24) (* (/ x y) (/ 1.0 t)) (/ (/ x y) (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e-115) {
		tmp = -1.0 / (t * (z / x));
	} else if (z <= 4.2e-24) {
		tmp = (x / y) * (1.0 / t);
	} else {
		tmp = (x / y) / -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.1d-115)) then
        tmp = (-1.0d0) / (t * (z / x))
    else if (z <= 4.2d-24) then
        tmp = (x / y) * (1.0d0 / t)
    else
        tmp = (x / y) / -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e-115) {
		tmp = -1.0 / (t * (z / x));
	} else if (z <= 4.2e-24) {
		tmp = (x / y) * (1.0 / t);
	} else {
		tmp = (x / y) / -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e-115:
		tmp = -1.0 / (t * (z / x))
	elif z <= 4.2e-24:
		tmp = (x / y) * (1.0 / t)
	else:
		tmp = (x / y) / -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e-115)
		tmp = Float64(-1.0 / Float64(t * Float64(z / x)));
	elseif (z <= 4.2e-24)
		tmp = Float64(Float64(x / y) * Float64(1.0 / t));
	else
		tmp = Float64(Float64(x / y) / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.1e-115)
		tmp = -1.0 / (t * (z / x));
	elseif (z <= 4.2e-24)
		tmp = (x / y) * (1.0 / t);
	else
		tmp = (x / y) / -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.1e-115], N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-24], N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e-115

   1. Initial program 85.6%

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

      1. associate-/l/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf 51.0%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. associate-*r/ 39.4%

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

      2. mul-1-neg 39.4%

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

   8. Simplified 39.4%

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

      1. neg-mul-1 39.4%

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

      2. *-commutative 39.4%

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

      3. times-frac 43.7%

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

   10. Applied egg-rr 43.7%

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

       1. clear-num 43.7%

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

       2. frac-times 42.9%

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

       3. metadata-eval 42.9%

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

       4. associate-/l* 38.6%

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

       5. *-commutative 38.6%

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

       6. associate-/l* 44.9%

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

   12. Applied egg-rr 44.9%

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

   if -1.1e-115 < z < 4.1999999999999999e-24

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 71.6%

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

      1. *-un-lft-identity 71.6%

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

      2. times-frac 73.8%

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

   5. Applied egg-rr 73.8%

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

   if 4.1999999999999999e-24 < z

   1. Initial program 85.0%

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

   3. Taylor expanded in y around inf 35.2%

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

      1. *-commutative 35.2%

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

   5. Simplified 35.2%

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

   6. Taylor expanded in t around 0 31.6%

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

      1. mul-1-neg 31.6%

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

      2. associate-/r* 33.6%

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

      3. distribute-neg-frac2 33.6%

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

   8. Simplified 33.6%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-115}:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-140}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-137}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6e-140)
   (* (/ x y) (/ 1.0 t))
   (if (<= t 3.7e-137) (/ (/ x y) (- z)) (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6e-140) {
		tmp = (x / y) * (1.0 / t);
	} else if (t <= 3.7e-137) {
		tmp = (x / y) / -z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-6d-140)) then
        tmp = (x / y) * (1.0d0 / t)
    else if (t <= 3.7d-137) then
        tmp = (x / y) / -z
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6e-140) {
		tmp = (x / y) * (1.0 / t);
	} else if (t <= 3.7e-137) {
		tmp = (x / y) / -z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6e-140:
		tmp = (x / y) * (1.0 / t)
	elif t <= 3.7e-137:
		tmp = (x / y) / -z
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6e-140)
		tmp = Float64(Float64(x / y) * Float64(1.0 / t));
	elseif (t <= 3.7e-137)
		tmp = Float64(Float64(x / y) / Float64(-z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6e-140)
		tmp = (x / y) * (1.0 / t);
	elseif (t <= 3.7e-137)
		tmp = (x / y) / -z;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6e-140], N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-137], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.00000000000000037e-140

   1. Initial program 89.7%

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

   3. Taylor expanded in z around 0 45.7%

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

      1. *-un-lft-identity 45.7%

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

      2. times-frac 45.8%

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

   5. Applied egg-rr 45.8%

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

   if -6.00000000000000037e-140 < t < 3.7e-137

   1. Initial program 90.9%

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

   3. Taylor expanded in y around inf 54.4%

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

      1. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in t around 0 41.7%

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

      1. mul-1-neg 41.7%

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

      2. associate-/r* 42.7%

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

      3. distribute-neg-frac2 42.7%

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

   8. Simplified 42.7%

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

   if 3.7e-137 < t

   1. Initial program 84.1%

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

   3. Taylor expanded in t around inf 64.4%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-140}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-137}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 10^{-60}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.4e-88)
   (/ (/ x y) (- t z))
   (if (<= y 1e-60) (/ x (* z (- z t))) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-88) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1e-60) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.4d-88)) then
        tmp = (x / y) / (t - z)
    else if (y <= 1d-60) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-88) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1e-60) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e-88:
		tmp = (x / y) / (t - z)
	elif y <= 1e-60:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e-88)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 1e-60)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.4e-88)
		tmp = (x / y) / (t - z);
	elseif (y <= 1e-60)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.4e-88], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-60], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e-88

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0 87.0%

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

      1. associate-/l/ 96.3%

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

   5. Simplified 96.3%

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

   6. Taylor expanded in y around inf 78.9%

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

   if -2.4e-88 < y < 9.9999999999999997e-61

   1. Initial program 91.2%

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

   3. Taylor expanded in y around 0 77.2%

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

      1. associate-*r/ 77.2%

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

      2. neg-mul-1 77.2%

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

   5. Simplified 77.2%

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

   if 9.9999999999999997e-61 < y

   1. Initial program 85.6%

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

      1. associate-/l/ 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in t around inf 58.8%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 10^{-60}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 24000000000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e-88)
   (/ (/ x y) (- t z))
   (if (<= y 24000000000000.0) (/ (/ x z) (- z t)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-88) {
		tmp = (x / y) / (t - z);
	} else if (y <= 24000000000000.0) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d-88)) then
        tmp = (x / y) / (t - z)
    else if (y <= 24000000000000.0d0) then
        tmp = (x / z) / (z - t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-88) {
		tmp = (x / y) / (t - z);
	} else if (y <= 24000000000000.0) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e-88:
		tmp = (x / y) / (t - z)
	elif y <= 24000000000000.0:
		tmp = (x / z) / (z - t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e-88)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 24000000000000.0)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e-88)
		tmp = (x / y) / (t - z);
	elseif (y <= 24000000000000.0)
		tmp = (x / z) / (z - t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e-88], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 24000000000000.0], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000004e-88

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0 87.0%

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

      1. associate-/l/ 96.3%

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

   5. Simplified 96.3%

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

   6. Taylor expanded in y around inf 78.9%

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

   if -2.50000000000000004e-88 < y < 2.4e13

   1. Initial program 89.5%

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

   3. Taylor expanded in x around 0 89.5%

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

      1. associate-/l/ 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in y around 0 83.0%

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

      1. associate-*r/ 83.0%

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

      2. mul-1-neg 83.0%

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

   8. Simplified 83.0%

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

   if 2.4e13 < y

   1. Initial program 87.2%

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

      1. associate-/l/ 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in t around inf 59.9%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 24000000000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-115}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.6e-115)
   (/ (/ x y) (- t z))
   (if (<= t 6.2e+32) (/ (/ x z) (- z y)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e-115) {
		tmp = (x / y) / (t - z);
	} else if (t <= 6.2e+32) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.6d-115)) then
        tmp = (x / y) / (t - z)
    else if (t <= 6.2d+32) then
        tmp = (x / z) / (z - y)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e-115) {
		tmp = (x / y) / (t - z);
	} else if (t <= 6.2e+32) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.6e-115:
		tmp = (x / y) / (t - z)
	elif t <= 6.2e+32:
		tmp = (x / z) / (z - y)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.6e-115)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 6.2e+32)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.6e-115)
		tmp = (x / y) / (t - z);
	elseif (t <= 6.2e+32)
		tmp = (x / z) / (z - y);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.6e-115], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+32], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6e-115

   1. Initial program 89.5%

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

   3. Taylor expanded in x around 0 89.5%

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

      1. associate-/l/ 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in y around inf 55.7%

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

   if -1.6e-115 < t < 6.19999999999999986e32

   1. Initial program 89.8%

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

      1. associate-/l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in t around 0 81.2%

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

      1. associate-*r/ 81.2%

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

      2. neg-mul-1 81.2%

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

   7. Simplified 81.2%

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

   if 6.19999999999999986e32 < t

   1. Initial program 81.4%

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

      1. associate-/l/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in t around inf 90.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-115}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e-115)
   (/ x (* z (- t)))
   (if (<= z 4.6e-24) (/ (/ x t) y) (/ x (* y (- z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e-115) {
		tmp = x / (z * -t);
	} else if (z <= 4.6e-24) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (y * -z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5d-115)) then
        tmp = x / (z * -t)
    else if (z <= 4.6d-24) then
        tmp = (x / t) / y
    else
        tmp = x / (y * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e-115) {
		tmp = x / (z * -t);
	} else if (z <= 4.6e-24) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (y * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5e-115:
		tmp = x / (z * -t)
	elif z <= 4.6e-24:
		tmp = (x / t) / y
	else:
		tmp = x / (y * -z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e-115)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (z <= 4.6e-24)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x / Float64(y * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5e-115)
		tmp = x / (z * -t);
	elseif (z <= 4.6e-24)
		tmp = (x / t) / y;
	else
		tmp = x / (y * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5e-115], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-24], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.0000000000000003e-115

   1. Initial program 85.6%

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

      1. associate-/l/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf 51.0%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. associate-*r/ 39.4%

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

      2. mul-1-neg 39.4%

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

   8. Simplified 39.4%

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

   if -5.0000000000000003e-115 < z < 4.6000000000000002e-24

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 93.5%

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

      1. associate-/l/ 95.8%

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

   5. Simplified 95.8%

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

      1. clear-num 95.6%

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

      2. associate-/r/ 95.7%

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

      3. associate-*l/ 93.4%

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

   7. Applied egg-rr 93.4%

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

      1. associate-*l/ 95.7%

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

      2. clear-num 95.7%

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

      3. associate-*l/ 95.8%

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

      4. *-un-lft-identity 95.8%

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

   9. Applied egg-rr 95.8%

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

   10. Taylor expanded in z around 0 71.6%

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

       1. associate-/r* 73.2%

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

   12. Simplified 73.2%

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

   if 4.6000000000000002e-24 < z

   1. Initial program 85.0%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 78.8%

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

      1. associate-*r/ 78.8%

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

      2. neg-mul-1 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in z around 0 31.6%

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

      1. associate-*r/ 31.6%

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

      2. mul-1-neg 31.6%

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

      3. *-commutative 31.6%

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

   10. Simplified 31.6%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.5e-118)
   (/ x (* z (- t)))
   (if (<= z 5.5e-24) (/ (/ x t) y) (/ (/ x y) (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-118) {
		tmp = x / (z * -t);
	} else if (z <= 5.5e-24) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / y) / -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.5d-118)) then
        tmp = x / (z * -t)
    else if (z <= 5.5d-24) then
        tmp = (x / t) / y
    else
        tmp = (x / y) / -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-118) {
		tmp = x / (z * -t);
	} else if (z <= 5.5e-24) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / y) / -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e-118:
		tmp = x / (z * -t)
	elif z <= 5.5e-24:
		tmp = (x / t) / y
	else:
		tmp = (x / y) / -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.5e-118)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (z <= 5.5e-24)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(x / y) / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.5e-118)
		tmp = x / (z * -t);
	elseif (z <= 5.5e-24)
		tmp = (x / t) / y;
	else
		tmp = (x / y) / -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.5e-118], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-24], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.49999999999999978e-118

   1. Initial program 85.6%

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

      1. associate-/l/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf 51.0%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. associate-*r/ 39.4%

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

      2. mul-1-neg 39.4%

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

   8. Simplified 39.4%

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

   if -7.49999999999999978e-118 < z < 5.4999999999999999e-24

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 93.5%

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

      1. associate-/l/ 95.8%

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

   5. Simplified 95.8%

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

      1. clear-num 95.6%

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

      2. associate-/r/ 95.7%

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

      3. associate-*l/ 93.4%

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

   7. Applied egg-rr 93.4%

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

      1. associate-*l/ 95.7%

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

      2. clear-num 95.7%

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

      3. associate-*l/ 95.8%

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

      4. *-un-lft-identity 95.8%

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

   9. Applied egg-rr 95.8%

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

   10. Taylor expanded in z around 0 71.6%

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

       1. associate-/r* 73.2%

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

   12. Simplified 73.2%

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

   if 5.4999999999999999e-24 < z

   1. Initial program 85.0%

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

   3. Taylor expanded in y around inf 35.2%

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

      1. *-commutative 35.2%

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

   5. Simplified 35.2%

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

   6. Taylor expanded in t around 0 31.6%

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

      1. mul-1-neg 31.6%

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

      2. associate-/r* 33.6%

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

      3. distribute-neg-frac2 33.6%

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

   8. Simplified 33.6%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-115}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.4e-115)
   (/ (/ x (- z)) t)
   (if (<= z 3.8e-24) (/ (/ x t) y) (/ (/ x y) (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.4e-115) {
		tmp = (x / -z) / t;
	} else if (z <= 3.8e-24) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / y) / -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.4d-115)) then
        tmp = (x / -z) / t
    else if (z <= 3.8d-24) then
        tmp = (x / t) / y
    else
        tmp = (x / y) / -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.4e-115) {
		tmp = (x / -z) / t;
	} else if (z <= 3.8e-24) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / y) / -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.4e-115:
		tmp = (x / -z) / t
	elif z <= 3.8e-24:
		tmp = (x / t) / y
	else:
		tmp = (x / y) / -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.4e-115)
		tmp = Float64(Float64(x / Float64(-z)) / t);
	elseif (z <= 3.8e-24)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(x / y) / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.4e-115)
		tmp = (x / -z) / t;
	elseif (z <= 3.8e-24)
		tmp = (x / t) / y;
	else
		tmp = (x / y) / -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.4e-115], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.8e-24], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3999999999999999e-115

   1. Initial program 85.6%

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

      1. associate-/l/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf 51.0%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. associate-*r/ 39.4%

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

      2. mul-1-neg 39.4%

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

   8. Simplified 39.4%

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

   9. Taylor expanded in x around 0 39.4%

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

       1. associate-/l/ 45.8%

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

       2. associate-*r/ 45.8%

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

       3. associate-*r/ 45.8%

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

       4. mul-1-neg 45.8%

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

   11. Simplified 45.8%

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

   if -4.3999999999999999e-115 < z < 3.80000000000000026e-24

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 93.5%

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

      1. associate-/l/ 95.8%

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

   5. Simplified 95.8%

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

      1. clear-num 95.6%

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

      2. associate-/r/ 95.7%

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

      3. associate-*l/ 93.4%

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

   7. Applied egg-rr 93.4%

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

      1. associate-*l/ 95.7%

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

      2. clear-num 95.7%

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

      3. associate-*l/ 95.8%

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

      4. *-un-lft-identity 95.8%

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

   9. Applied egg-rr 95.8%

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

   10. Taylor expanded in z around 0 71.6%

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

       1. associate-/r* 73.2%

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

   12. Simplified 73.2%

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

   if 3.80000000000000026e-24 < z

   1. Initial program 85.0%

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

   3. Taylor expanded in y around inf 35.2%

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

      1. *-commutative 35.2%

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

   5. Simplified 35.2%

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

   6. Taylor expanded in t around 0 31.6%

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

      1. mul-1-neg 31.6%

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

      2. associate-/r* 33.6%

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

      3. distribute-neg-frac2 33.6%

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

   8. Simplified 33.6%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-115}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+121} \lor \neg \left(z \leq 1.9 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.6e+121) (not (<= z 1.9e+75))) (/ x (* z t)) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.6e+121) || !(z <= 1.9e+75)) {
		tmp = x / (z * t);
	} 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 <= (-3.6d+121)) .or. (.not. (z <= 1.9d+75))) then
        tmp = x / (z * t)
    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 <= -3.6e+121) || !(z <= 1.9e+75)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.6e+121) or not (z <= 1.9e+75):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.6e+121) || !(z <= 1.9e+75))
		tmp = Float64(x / Float64(z * t));
	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 <= -3.6e+121) || ~((z <= 1.9e+75)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.6e+121], N[Not[LessEqual[z, 1.9e+75]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.59999999999999981e121 or 1.9000000000000001e75 < z

   1. Initial program 75.8%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 47.3%

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

   6. Taylor expanded in y around 0 43.0%

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

      1. associate-*r/ 43.0%

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

      2. mul-1-neg 43.0%

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

   8. Simplified 43.0%

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

      1. add-sqr-sqrt 17.5%

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

      2. sqrt-unprod 43.6%

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

      3. sqr-neg 43.6%

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

      4. sqrt-unprod 24.4%

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

      5. add-sqr-sqrt 40.4%

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

      6. *-un-lft-identity 40.4%

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

      7. *-commutative 40.4%

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

      8. associate-/r* 42.6%

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

   10. Applied egg-rr 42.6%

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

       1. *-lft-identity 42.6%

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

       2. associate-/l/ 40.4%

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

       3. *-commutative 40.4%

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

   12. Simplified 40.4%

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

   if -3.59999999999999981e121 < z < 1.9000000000000001e75

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 51.1%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+121} \lor \neg \left(z \leq 1.9 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+122}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.56e+122)
   (/ x (* z t))
   (if (<= z 5.2e+29) (/ x (* y t)) (/ x (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.56e+122) {
		tmp = x / (z * t);
	} else if (z <= 5.2e+29) {
		tmp = x / (y * t);
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.56d+122)) then
        tmp = x / (z * t)
    else if (z <= 5.2d+29) then
        tmp = x / (y * t)
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.56e+122) {
		tmp = x / (z * t);
	} else if (z <= 5.2e+29) {
		tmp = x / (y * t);
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.56e+122:
		tmp = x / (z * t)
	elif z <= 5.2e+29:
		tmp = x / (y * t)
	else:
		tmp = x / (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.56e+122)
		tmp = Float64(x / Float64(z * t));
	elseif (z <= 5.2e+29)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.56e+122)
		tmp = x / (z * t);
	elseif (z <= 5.2e+29)
		tmp = x / (y * t);
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.56e+122], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+29], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55999999999999993e122

   1. Initial program 70.3%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 48.3%

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

   6. Taylor expanded in y around 0 39.8%

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

      1. associate-*r/ 39.8%

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

      2. mul-1-neg 39.8%

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

   8. Simplified 39.8%

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

      1. add-sqr-sqrt 14.7%

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

      2. sqrt-unprod 38.6%

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

      3. sqr-neg 38.6%

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

      4. sqrt-unprod 25.1%

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

      5. add-sqr-sqrt 40.0%

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

      6. *-un-lft-identity 40.0%

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

      7. *-commutative 40.0%

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

      8. associate-/r* 39.7%

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

   10. Applied egg-rr 39.7%

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

       1. *-lft-identity 39.7%

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

       2. associate-/l/ 40.0%

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

       3. *-commutative 40.0%

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

   12. Simplified 40.0%

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

   if -1.55999999999999993e122 < z < 5.2e29

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0 52.9%

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

   if 5.2e29 < z

   1. Initial program 81.2%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. neg-mul-1 86.5%

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

   7. Simplified 86.5%

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

      1. div-inv 86.4%

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

      2. associate-/l* 69.7%

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

      3. add-sqr-sqrt 28.4%

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

      4. sqrt-unprod 53.1%

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

      5. sqr-neg 53.1%

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

      6. sqrt-unprod 31.3%

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

      7. add-sqr-sqrt 51.6%

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

   9. Applied egg-rr 51.6%

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

       1. associate-/r* 51.7%

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

       2. associate-*r/ 51.7%

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

       3. times-frac 51.3%

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

       4. associate-*r/ 51.3%

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

       5. associate-*l/ 51.3%

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

       6. *-rgt-identity 51.3%

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

       7. associate-/r* 51.7%

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

   11. Simplified 51.7%

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

   12. Taylor expanded in z around 0 27.9%

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

       1. *-commutative 27.9%

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

   14. Simplified 27.9%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+122}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+30}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.5e+121)
   (/ x (* z t))
   (if (<= z 6.5e+30) (/ (/ x t) y) (/ x (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e+121) {
		tmp = x / (z * t);
	} else if (z <= 6.5e+30) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.5d+121)) then
        tmp = x / (z * t)
    else if (z <= 6.5d+30) then
        tmp = (x / t) / y
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e+121) {
		tmp = x / (z * t);
	} else if (z <= 6.5e+30) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.5e+121:
		tmp = x / (z * t)
	elif z <= 6.5e+30:
		tmp = (x / t) / y
	else:
		tmp = x / (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.5e+121)
		tmp = Float64(x / Float64(z * t));
	elseif (z <= 6.5e+30)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.5e+121)
		tmp = x / (z * t);
	elseif (z <= 6.5e+30)
		tmp = (x / t) / y;
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.5e+121], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+30], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5e121

   1. Initial program 70.3%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 48.3%

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

   6. Taylor expanded in y around 0 39.8%

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

      1. associate-*r/ 39.8%

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

      2. mul-1-neg 39.8%

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

   8. Simplified 39.8%

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

      1. add-sqr-sqrt 14.7%

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

      2. sqrt-unprod 38.6%

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

      3. sqr-neg 38.6%

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

      4. sqrt-unprod 25.1%

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

      5. add-sqr-sqrt 40.0%

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

      6. *-un-lft-identity 40.0%

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

      7. *-commutative 40.0%

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

      8. associate-/r* 39.7%

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

   10. Applied egg-rr 39.7%

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

       1. *-lft-identity 39.7%

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

       2. associate-/l/ 40.0%

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

       3. *-commutative 40.0%

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

   12. Simplified 40.0%

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

   if -3.5e121 < z < 6.5e30

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0 95.0%

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

      1. associate-/l/ 97.5%

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

   5. Simplified 97.5%

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

      1. clear-num 97.3%

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

      2. associate-/r/ 97.4%

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

      3. associate-*l/ 95.5%

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

   7. Applied egg-rr 95.5%

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

      1. associate-*l/ 97.4%

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

      2. clear-num 96.9%

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

      3. associate-*l/ 97.0%

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

      4. *-un-lft-identity 97.0%

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

   9. Applied egg-rr 97.0%

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

   10. Taylor expanded in z around 0 52.9%

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

       1. associate-/r* 53.8%

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

   12. Simplified 53.8%

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

   if 6.5e30 < z

   1. Initial program 81.2%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. neg-mul-1 86.5%

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

   7. Simplified 86.5%

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

      1. div-inv 86.4%

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

      2. associate-/l* 69.7%

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

      3. add-sqr-sqrt 28.4%

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

      4. sqrt-unprod 53.1%

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

      5. sqr-neg 53.1%

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

      6. sqrt-unprod 31.3%

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

      7. add-sqr-sqrt 51.6%

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

   9. Applied egg-rr 51.6%

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

       1. associate-/r* 51.7%

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

       2. associate-*r/ 51.7%

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

       3. times-frac 51.3%

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

       4. associate-*r/ 51.3%

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

       5. associate-*l/ 51.3%

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

       6. *-rgt-identity 51.3%

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

       7. associate-/r* 51.7%

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

   11. Simplified 51.7%

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

   12. Taylor expanded in z around 0 27.9%

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

       1. *-commutative 27.9%

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

   14. Simplified 27.9%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+30}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e-90) (/ x (* y (- t z))) (/ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-90) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.3d-90)) then
        tmp = x / (y * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-90) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e-90:
		tmp = x / (y * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e-90)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e-90)
		tmp = x / (y * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e-90], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e-90

   1. Initial program 87.3%

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

   3. Taylor expanded in y around inf 73.9%

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

      1. *-commutative 73.9%

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

   5. Simplified 73.9%

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

   if -1.3e-90 < y

   1. Initial program 88.6%

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

   3. Taylor expanded in t around inf 56.9%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 64.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.2 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 4.2e-29) (/ x (* y (- t z))) (/ (/ x t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.2e-29) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 4.2d-29) then
        tmp = x / (y * (t - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.2e-29) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 4.2e-29:
		tmp = x / (y * (t - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 4.2e-29)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 4.2e-29)
		tmp = x / (y * (t - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 4.2e-29], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.19999999999999979e-29

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 53.8%

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

      1. *-commutative 53.8%

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

   5. Simplified 53.8%

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

   if 4.19999999999999979e-29 < t

   1. Initial program 85.5%

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

      1. associate-/l/ 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in t around inf 87.1%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.2 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-90}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e-90) (/ (/ x y) (- t z)) (/ (/ x t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-90) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.3d-90)) then
        tmp = (x / y) / (t - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-90) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e-90:
		tmp = (x / y) / (t - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e-90)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e-90)
		tmp = (x / y) / (t - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e-90], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e-90

   1. Initial program 87.3%

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

   3. Taylor expanded in x around 0 87.3%

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

      1. associate-/l/ 96.4%

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

   5. Simplified 96.4%

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

   6. Taylor expanded in y around inf 76.9%

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

   if -1.3e-90 < y

   1. Initial program 88.6%

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

      1. associate-/l/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 58.3%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-90}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.2%

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

   1. associate-/l/ 97.3%

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

3. Simplified 97.3%

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

5. Final simplification 97.3%

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

Alternative 22: 39.0% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.2%

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

3. Taylor expanded in z around 0 38.8%

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

4. Final simplification 38.8%

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

Developer target: 88.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

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 2024055 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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