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

Percentage Accurate: 89.2% → 98.1%

Time: 10.9s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 0.0) (/ (/ x (- t z)) (- y z)) t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (x / (t - z)) / (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (t - z))
    if (t_1 <= 0.0d0) then
        tmp = (x / (t - z)) / (y - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (x / (t - z)) / (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= 0.0:
		tmp = (x / (t - z)) / (y - z)
	else:
		tmp = t_1
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < 0.0

   1. Initial program 83.8%

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

      1. associate-/l/ 98.6%

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

   3. Simplified 98.6%

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

   if 0.0 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 99.5%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 2: 93.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{x}{t - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{t_2}{y}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \frac{-1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))) (t_2 (/ x (- t z))))
   (if (<= t_1 (- INFINITY))
     (/ t_2 y)
     (if (<= t_1 4e+305) (/ x t_1) (* t_2 (/ -1.0 z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double t_2 = x / (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2 / y;
	} else if (t_1 <= 4e+305) {
		tmp = x / t_1;
	} else {
		tmp = t_2 * (-1.0 / z);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double t_2 = x / (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2 / y;
	} else if (t_1 <= 4e+305) {
		tmp = x / t_1;
	} else {
		tmp = t_2 * (-1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	t_2 = x / (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2 / y
	elif t_1 <= 4e+305:
		tmp = x / t_1
	else:
		tmp = t_2 * (-1.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	t_2 = Float64(x / Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t_2 / y);
	elseif (t_1 <= 4e+305)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(t_2 * Float64(-1.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	t_2 = x / (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2 / y;
	elseif (t_1 <= 4e+305)
		tmp = x / t_1;
	else
		tmp = t_2 * (-1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t$95$2 / y), $MachinePrecision], If[LessEqual[t$95$1, 4e+305], N[(x / t$95$1), $MachinePrecision], N[(t$95$2 * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.5%

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

   2. Taylor expanded in y around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. associate-/r* 86.0%

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

   4. Simplified 86.0%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 3.9999999999999998e305

   1. Initial program 99.1%

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

   if 3.9999999999999998e305 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 68.8%

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

   2. Taylor expanded in y around 0 61.8%

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

      1. associate-*r/ 61.8%

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

      2. neg-mul-1 61.8%

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

   4. Simplified 61.8%

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

      1. neg-mul-1 61.8%

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

      2. times-frac 84.3%

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

   6. Applied egg-rr 84.3%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \end{array} \]

Alternative 3: 93.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x (- t z)) y)
     (if (<= t_1 4e+305) (/ x t_1) (/ (/ -1.0 z) (/ (- t z) x))))))

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 / (t - z)) / y;
	} else if (t_1 <= 4e+305) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / z) / ((t - z) / x);
	}
	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 / (t - z)) / y;
	} else if (t_1 <= 4e+305) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / z) / ((t - z) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x / (t - z)) / y
	elif t_1 <= 4e+305:
		tmp = x / t_1
	else:
		tmp = (-1.0 / z) / ((t - z) / x)
	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 / Float64(t - z)) / y);
	elseif (t_1 <= 4e+305)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(-1.0 / z) / Float64(Float64(t - z) / x));
	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 / (t - z)) / y;
	elseif (t_1 <= 4e+305)
		tmp = x / t_1;
	else
		tmp = (-1.0 / z) / ((t - z) / x);
	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 / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 4e+305], N[(x / t$95$1), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.5%

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

   2. Taylor expanded in y around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. associate-/r* 86.0%

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

   4. Simplified 86.0%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 3.9999999999999998e305

   1. Initial program 99.1%

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

   if 3.9999999999999998e305 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 68.8%

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

   2. Taylor expanded in y around 0 61.8%

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

      1. associate-*r/ 61.8%

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

      2. neg-mul-1 61.8%

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

   4. Simplified 61.8%

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

      1. neg-mul-1 61.8%

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

      2. times-frac 84.3%

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

   6. Applied egg-rr 84.3%

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

      1. clear-num 85.6%

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

      2. un-div-inv 85.6%

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

   8. Applied egg-rr 85.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x}}\\ \end{array} \]

Alternative 4: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+210}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-112}:\\ \;\;\;\;\frac{t_1}{y - z}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-133} \lor \neg \left(y \leq 1.12 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) z)))
   (if (<= y -1.15e+210)
     (/ (/ x (- t z)) y)
     (if (<= y -2.4e-5)
       (/ x (* y (- t z)))
       (if (<= y -1.15e-112)
         (/ t_1 (- y z))
         (if (or (<= y -5.6e-133) (not (<= y 1.12e-98)))
           (/ (/ x t) (- y z))
           (/ t_1 (- t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / z;
	double tmp;
	if (y <= -1.15e+210) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -2.4e-5) {
		tmp = x / (y * (t - z));
	} else if (y <= -1.15e-112) {
		tmp = t_1 / (y - z);
	} else if ((y <= -5.6e-133) || !(y <= 1.12e-98)) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = t_1 / (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) :: t_1
    real(8) :: tmp
    t_1 = -x / z
    if (y <= (-1.15d+210)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-2.4d-5)) then
        tmp = x / (y * (t - z))
    else if (y <= (-1.15d-112)) then
        tmp = t_1 / (y - z)
    else if ((y <= (-5.6d-133)) .or. (.not. (y <= 1.12d-98))) then
        tmp = (x / t) / (y - z)
    else
        tmp = t_1 / (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -x / z;
	double tmp;
	if (y <= -1.15e+210) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -2.4e-5) {
		tmp = x / (y * (t - z));
	} else if (y <= -1.15e-112) {
		tmp = t_1 / (y - z);
	} else if ((y <= -5.6e-133) || !(y <= 1.12e-98)) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = t_1 / (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / z
	tmp = 0
	if y <= -1.15e+210:
		tmp = (x / (t - z)) / y
	elif y <= -2.4e-5:
		tmp = x / (y * (t - z))
	elif y <= -1.15e-112:
		tmp = t_1 / (y - z)
	elif (y <= -5.6e-133) or not (y <= 1.12e-98):
		tmp = (x / t) / (y - z)
	else:
		tmp = t_1 / (t - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (y <= -1.15e+210)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -2.4e-5)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= -1.15e-112)
		tmp = Float64(t_1 / Float64(y - z));
	elseif ((y <= -5.6e-133) || !(y <= 1.12e-98))
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = Float64(t_1 / Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / z;
	tmp = 0.0;
	if (y <= -1.15e+210)
		tmp = (x / (t - z)) / y;
	elseif (y <= -2.4e-5)
		tmp = x / (y * (t - z));
	elseif (y <= -1.15e-112)
		tmp = t_1 / (y - z);
	elseif ((y <= -5.6e-133) || ~((y <= 1.12e-98)))
		tmp = (x / t) / (y - z);
	else
		tmp = t_1 / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[y, -1.15e+210], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2.4e-5], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-112], N[(t$95$1 / N[(y - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5.6e-133], N[Not[LessEqual[y, 1.12e-98]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.1499999999999999e210

   1. Initial program 77.6%

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

   2. Taylor expanded in y around inf 77.6%

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

      1. *-commutative 77.6%

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

      2. associate-/r* 95.9%

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

   4. Simplified 95.9%

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

   if -1.1499999999999999e210 < y < -2.4000000000000001e-5

   1. Initial program 91.6%

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

   2. Taylor expanded in y around inf 83.2%

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

      1. *-commutative 83.2%

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

   4. Simplified 83.2%

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

   if -2.4000000000000001e-5 < y < -1.14999999999999995e-112

   1. Initial program 94.1%

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

   2. Taylor expanded in t around 0 50.2%

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

      1. associate-*r/ 50.2%

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

      2. neg-mul-1 50.2%

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

      3. *-commutative 50.2%

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

      4. associate-/r* 52.2%

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

   4. Simplified 52.2%

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

   if -1.14999999999999995e-112 < y < -5.5999999999999997e-133 or 1.12e-98 < y

   1. Initial program 83.9%

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

      1. associate-/l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 60.4%

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

   if -5.5999999999999997e-133 < y < 1.12e-98

   1. Initial program 91.5%

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

   2. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-frac-neg 84.6%

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

      3. associate-/r* 90.3%

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

   4. Simplified 90.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+210}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-112}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-133} \lor \neg \left(y \leq 1.12 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \end{array} \]

Alternative 5: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+210}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq -0.00012:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-110}:\\ \;\;\;\;\frac{t_1}{y - z}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-132} \lor \neg \left(y \leq 2.2 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) z)))
   (if (<= y -1.3e+210)
     (* (/ x (- t z)) (/ 1.0 y))
     (if (<= y -0.00012)
       (/ x (* y (- t z)))
       (if (<= y -2.3e-110)
         (/ t_1 (- y z))
         (if (or (<= y -3e-132) (not (<= y 2.2e-93)))
           (/ (/ x t) (- y z))
           (/ t_1 (- t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / z;
	double tmp;
	if (y <= -1.3e+210) {
		tmp = (x / (t - z)) * (1.0 / y);
	} else if (y <= -0.00012) {
		tmp = x / (y * (t - z));
	} else if (y <= -2.3e-110) {
		tmp = t_1 / (y - z);
	} else if ((y <= -3e-132) || !(y <= 2.2e-93)) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = t_1 / (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) :: t_1
    real(8) :: tmp
    t_1 = -x / z
    if (y <= (-1.3d+210)) then
        tmp = (x / (t - z)) * (1.0d0 / y)
    else if (y <= (-0.00012d0)) then
        tmp = x / (y * (t - z))
    else if (y <= (-2.3d-110)) then
        tmp = t_1 / (y - z)
    else if ((y <= (-3d-132)) .or. (.not. (y <= 2.2d-93))) then
        tmp = (x / t) / (y - z)
    else
        tmp = t_1 / (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -x / z;
	double tmp;
	if (y <= -1.3e+210) {
		tmp = (x / (t - z)) * (1.0 / y);
	} else if (y <= -0.00012) {
		tmp = x / (y * (t - z));
	} else if (y <= -2.3e-110) {
		tmp = t_1 / (y - z);
	} else if ((y <= -3e-132) || !(y <= 2.2e-93)) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = t_1 / (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / z
	tmp = 0
	if y <= -1.3e+210:
		tmp = (x / (t - z)) * (1.0 / y)
	elif y <= -0.00012:
		tmp = x / (y * (t - z))
	elif y <= -2.3e-110:
		tmp = t_1 / (y - z)
	elif (y <= -3e-132) or not (y <= 2.2e-93):
		tmp = (x / t) / (y - z)
	else:
		tmp = t_1 / (t - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (y <= -1.3e+210)
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(1.0 / y));
	elseif (y <= -0.00012)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= -2.3e-110)
		tmp = Float64(t_1 / Float64(y - z));
	elseif ((y <= -3e-132) || !(y <= 2.2e-93))
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = Float64(t_1 / Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / z;
	tmp = 0.0;
	if (y <= -1.3e+210)
		tmp = (x / (t - z)) * (1.0 / y);
	elseif (y <= -0.00012)
		tmp = x / (y * (t - z));
	elseif (y <= -2.3e-110)
		tmp = t_1 / (y - z);
	elseif ((y <= -3e-132) || ~((y <= 2.2e-93)))
		tmp = (x / t) / (y - z);
	else
		tmp = t_1 / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[y, -1.3e+210], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.00012], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-110], N[(t$95$1 / N[(y - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3e-132], N[Not[LessEqual[y, 2.2e-93]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.29999999999999995e210

   1. Initial program 77.6%

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

   2. Taylor expanded in y around inf 77.6%

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

      1. *-commutative 77.6%

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

   4. Simplified 77.6%

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

      1. associate-/r* 95.9%

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

      2. *-un-lft-identity 95.9%

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

      3. associate-*l/ 95.9%

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

      4. div-inv 95.9%

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

      5. associate-*l/ 95.9%

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

      6. *-un-lft-identity 95.9%

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

   6. Applied egg-rr 95.9%

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

   if -1.29999999999999995e210 < y < -1.20000000000000003e-4

   1. Initial program 91.6%

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

   2. Taylor expanded in y around inf 83.2%

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

      1. *-commutative 83.2%

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

   4. Simplified 83.2%

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

   if -1.20000000000000003e-4 < y < -2.3000000000000001e-110

   1. Initial program 94.1%

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

   2. Taylor expanded in t around 0 50.2%

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

      1. associate-*r/ 50.2%

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

      2. neg-mul-1 50.2%

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

      3. *-commutative 50.2%

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

      4. associate-/r* 52.2%

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

   4. Simplified 52.2%

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

   if -2.3000000000000001e-110 < y < -3e-132 or 2.19999999999999996e-93 < y

   1. Initial program 84.7%

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

      1. associate-/l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 61.0%

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

   if -3e-132 < y < 2.19999999999999996e-93

   1. Initial program 90.3%

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

   2. Taylor expanded in y around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. distribute-frac-neg 83.6%

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

      3. associate-/r* 90.4%

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

   4. Simplified 90.4%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+210}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq -0.00012:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-110}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-132} \lor \neg \left(y \leq 2.2 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \end{array} \]

Alternative 6: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{if}\;z \leq -3.05:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2050000000000:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* t (/ y x)))))
   (if (<= z -3.05)
     (* (/ x z) (/ 1.0 z))
     (if (<= z 2.35e-48)
       t_1
       (if (<= z 2050000000000.0)
         (/ (- x) (* y z))
         (if (<= z 1.02e+61) t_1 (/ (/ x z) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (t * (y / x));
	double tmp;
	if (z <= -3.05) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 2.35e-48) {
		tmp = t_1;
	} else if (z <= 2050000000000.0) {
		tmp = -x / (y * z);
	} else if (z <= 1.02e+61) {
		tmp = t_1;
	} else {
		tmp = (x / z) / 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 = 1.0d0 / (t * (y / x))
    if (z <= (-3.05d0)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= 2.35d-48) then
        tmp = t_1
    else if (z <= 2050000000000.0d0) then
        tmp = -x / (y * z)
    else if (z <= 1.02d+61) then
        tmp = t_1
    else
        tmp = (x / z) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (t * (y / x));
	double tmp;
	if (z <= -3.05) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 2.35e-48) {
		tmp = t_1;
	} else if (z <= 2050000000000.0) {
		tmp = -x / (y * z);
	} else if (z <= 1.02e+61) {
		tmp = t_1;
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 / (t * (y / x))
	tmp = 0
	if z <= -3.05:
		tmp = (x / z) * (1.0 / z)
	elif z <= 2.35e-48:
		tmp = t_1
	elif z <= 2050000000000.0:
		tmp = -x / (y * z)
	elif z <= 1.02e+61:
		tmp = t_1
	else:
		tmp = (x / z) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(t * Float64(y / x)))
	tmp = 0.0
	if (z <= -3.05)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= 2.35e-48)
		tmp = t_1;
	elseif (z <= 2050000000000.0)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (z <= 1.02e+61)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / (t * (y / x));
	tmp = 0.0;
	if (z <= -3.05)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= 2.35e-48)
		tmp = t_1;
	elseif (z <= 2050000000000.0)
		tmp = -x / (y * z);
	elseif (z <= 1.02e+61)
		tmp = t_1;
	else
		tmp = (x / z) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.05], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e-48], t$95$1, If[LessEqual[z, 2050000000000.0], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+61], t$95$1, N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.0499999999999998

   1. Initial program 87.0%

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

   2. Taylor expanded in z around inf 69.5%

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

      1. unpow2 69.5%

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

   4. Simplified 69.5%

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

      1. associate-/r* 74.4%

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

      2. div-inv 74.4%

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

   6. Applied egg-rr 74.4%

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

   if -3.0499999999999998 < z < 2.3499999999999999e-48 or 2.05e12 < z < 1.01999999999999999e61

   1. Initial program 89.7%

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

   2. Taylor expanded in z around 0 55.7%

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

      1. frac-2neg 55.7%

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

      2. neg-sub0 55.7%

         \[\leadsto \frac{\color{blue}{0 - x}}{-y \cdot t} \]

      3. metadata-eval 55.7%

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

      4. div-sub 53.2%

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

      5. metadata-eval 53.2%

         \[\leadsto \frac{\color{blue}{0}}{-y \cdot t} - \frac{x}{-y \cdot t} \]

      6. distribute-rgt-neg-in 53.2%

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

      7. add-sqr-sqrt 26.5%

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

      8. sqrt-unprod 33.9%

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

      9. sqr-neg 33.9%

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

      10. sqrt-unprod 7.8%

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

      11. add-sqr-sqrt 21.7%

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

      12. frac-2neg 21.7%

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

      13. associate-/r* 23.9%

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

   4. Applied egg-rr 23.9%

      \[\leadsto \color{blue}{\frac{0}{y \cdot \left(-t\right)} - \frac{\frac{x}{y}}{t}} \]
   5. Step-by-step derivation

      1. div0 24.8%

         \[\leadsto \color{blue}{0} - \frac{\frac{x}{y}}{t} \]

      2. neg-sub0 24.8%

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

      3. distribute-neg-frac 24.8%

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

      4. distribute-neg-frac 24.8%

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

   6. Simplified 24.8%

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

      1. clear-num 24.9%

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

      2. inv-pow 24.9%

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

      3. div-inv 24.8%

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

      4. clear-num 24.8%

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

      5. add-sqr-sqrt 10.2%

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

      6. sqrt-unprod 35.0%

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

      7. sqr-neg 35.0%

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

      8. sqrt-unprod 32.8%

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

      9. add-sqr-sqrt 63.3%

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

   8. Applied egg-rr 63.3%

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

      1. unpow-1 63.3%

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

   10. Simplified 63.3%

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

   if 2.3499999999999999e-48 < z < 2.05e12

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 19.6%

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

      1. *-commutative 19.6%

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

   4. Simplified 19.6%

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

   5. Taylor expanded in t around 0 18.6%

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

      1. mul-1-neg 18.6%

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

   7. Simplified 18.6%

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

   if 1.01999999999999999e61 < z

   1. Initial program 80.7%

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

   2. Taylor expanded in z around inf 68.3%

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

      1. unpow2 68.3%

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

      2. associate-/r* 84.4%

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

   4. Simplified 84.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-48}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;z \leq 2050000000000:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+61}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 7: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1400000000000:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) t))))
   (if (<= z -4.3e+55)
     (* (/ x z) (/ 1.0 z))
     (if (<= z 4.2e-48)
       t_1
       (if (<= z 1400000000000.0)
         (/ (- x) (* y z))
         (if (<= z 3.3e+66) t_1 (/ (/ x z) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * t);
	double tmp;
	if (z <= -4.3e+55) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 4.2e-48) {
		tmp = t_1;
	} else if (z <= 1400000000000.0) {
		tmp = -x / (y * z);
	} else if (z <= 3.3e+66) {
		tmp = t_1;
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * t)
    if (z <= (-4.3d+55)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= 4.2d-48) then
        tmp = t_1
    else if (z <= 1400000000000.0d0) then
        tmp = -x / (y * z)
    else if (z <= 3.3d+66) then
        tmp = t_1
    else
        tmp = (x / z) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * t);
	double tmp;
	if (z <= -4.3e+55) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 4.2e-48) {
		tmp = t_1;
	} else if (z <= 1400000000000.0) {
		tmp = -x / (y * z);
	} else if (z <= 3.3e+66) {
		tmp = t_1;
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * t)
	tmp = 0
	if z <= -4.3e+55:
		tmp = (x / z) * (1.0 / z)
	elif z <= 4.2e-48:
		tmp = t_1
	elif z <= 1400000000000.0:
		tmp = -x / (y * z)
	elif z <= 3.3e+66:
		tmp = t_1
	else:
		tmp = (x / z) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * t))
	tmp = 0.0
	if (z <= -4.3e+55)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= 4.2e-48)
		tmp = t_1;
	elseif (z <= 1400000000000.0)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (z <= 3.3e+66)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * t);
	tmp = 0.0;
	if (z <= -4.3e+55)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= 4.2e-48)
		tmp = t_1;
	elseif (z <= 1400000000000.0)
		tmp = -x / (y * z);
	elseif (z <= 3.3e+66)
		tmp = t_1;
	else
		tmp = (x / z) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+55], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-48], t$95$1, If[LessEqual[z, 1400000000000.0], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+66], t$95$1, N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.2999999999999999e55

   1. Initial program 84.3%

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

   2. Taylor expanded in z around inf 75.5%

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

      1. unpow2 75.5%

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

   4. Simplified 75.5%

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

      1. associate-/r* 81.3%

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

      2. div-inv 81.4%

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

   6. Applied egg-rr 81.4%

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

   if -4.2999999999999999e55 < z < 4.19999999999999977e-48 or 1.4e12 < z < 3.3000000000000001e66

   1. Initial program 90.7%

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

   2. Taylor expanded in t around inf 67.4%

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

   if 4.19999999999999977e-48 < z < 1.4e12

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 19.6%

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

      1. *-commutative 19.6%

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

   4. Simplified 19.6%

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

   5. Taylor expanded in t around 0 18.6%

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

      1. mul-1-neg 18.6%

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

   7. Simplified 18.6%

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

   if 3.3000000000000001e66 < z

   1. Initial program 80.4%

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

   2. Taylor expanded in z around inf 69.7%

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

      1. unpow2 69.7%

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

      2. associate-/r* 86.2%

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

   4. Simplified 86.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 1400000000000:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 8: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+210}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-94}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1e+210)
   (/ (/ x (- t z)) y)
   (if (<= y -1.35e-27)
     (/ x (* y (- t z)))
     (if (<= y 4.8e-94) (/ (- x) (* z (- t z))) (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e+210) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -1.35e-27) {
		tmp = x / (y * (t - z));
	} else if (y <= 4.8e-94) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1d+210)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-1.35d-27)) then
        tmp = x / (y * (t - z))
    else if (y <= 4.8d-94) then
        tmp = -x / (z * (t - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e+210) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -1.35e-27) {
		tmp = x / (y * (t - z));
	} else if (y <= 4.8e-94) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1e+210:
		tmp = (x / (t - z)) / y
	elif y <= -1.35e-27:
		tmp = x / (y * (t - z))
	elif y <= 4.8e-94:
		tmp = -x / (z * (t - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1e+210)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -1.35e-27)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 4.8e-94)
		tmp = Float64(Float64(-x) / Float64(z * Float64(t - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1e+210)
		tmp = (x / (t - z)) / y;
	elseif (y <= -1.35e-27)
		tmp = x / (y * (t - z));
	elseif (y <= 4.8e-94)
		tmp = -x / (z * (t - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1e+210], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1.35e-27], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-94], N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.99999999999999927e209

   1. Initial program 77.6%

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

   2. Taylor expanded in y around inf 77.6%

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

      1. *-commutative 77.6%

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

      2. associate-/r* 95.9%

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

   4. Simplified 95.9%

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

   if -9.99999999999999927e209 < y < -1.34999999999999994e-27

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 80.8%

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

      1. *-commutative 80.8%

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

   4. Simplified 80.8%

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

   if -1.34999999999999994e-27 < y < 4.8e-94

   1. Initial program 91.5%

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

   2. Taylor expanded in y around 0 76.6%

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

      1. associate-*r/ 76.6%

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

      2. neg-mul-1 76.6%

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

   4. Simplified 76.6%

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

   if 4.8e-94 < y

   1. Initial program 83.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. Taylor expanded in t around inf 59.2%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+210}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-94}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 9: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+210}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.1e+210)
   (/ (/ x (- t z)) y)
   (if (<= y -6e-28)
     (/ x (* y (- t z)))
     (if (<= y 8e-95) (/ (/ (- x) z) (- t z)) (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.1e+210) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -6e-28) {
		tmp = x / (y * (t - z));
	} else if (y <= 8e-95) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.1d+210)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-6d-28)) then
        tmp = x / (y * (t - z))
    else if (y <= 8d-95) then
        tmp = (-x / z) / (t - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.1e+210) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -6e-28) {
		tmp = x / (y * (t - z));
	} else if (y <= 8e-95) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.1e+210:
		tmp = (x / (t - z)) / y
	elif y <= -6e-28:
		tmp = x / (y * (t - z))
	elif y <= 8e-95:
		tmp = (-x / z) / (t - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.1e+210)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -6e-28)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 8e-95)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.1e+210)
		tmp = (x / (t - z)) / y;
	elseif (y <= -6e-28)
		tmp = x / (y * (t - z));
	elseif (y <= 8e-95)
		tmp = (-x / z) / (t - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.1e+210], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -6e-28], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-95], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.1000000000000001e210

   1. Initial program 77.6%

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

   2. Taylor expanded in y around inf 77.6%

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

      1. *-commutative 77.6%

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

      2. associate-/r* 95.9%

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

   4. Simplified 95.9%

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

   if -5.1000000000000001e210 < y < -6.00000000000000005e-28

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 80.8%

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

      1. *-commutative 80.8%

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

   4. Simplified 80.8%

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

   if -6.00000000000000005e-28 < y < 7.99999999999999992e-95

   1. Initial program 92.3%

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

   2. Taylor expanded in y around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. distribute-frac-neg 77.3%

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

      3. associate-/r* 82.9%

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

   4. Simplified 82.9%

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

   if 7.99999999999999992e-95 < y

   1. Initial program 82.8%

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

      1. associate-/l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 58.5%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+210}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 10: 62.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.55 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.55e-270)
   (/ x (* y (- t z)))
   (if (<= t 8.2e+24) (/ (/ x z) z) (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.55e-270) {
		tmp = x / (y * (t - z));
	} else if (t <= 8.2e+24) {
		tmp = (x / z) / 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 <= 3.55d-270) then
        tmp = x / (y * (t - z))
    else if (t <= 8.2d+24) then
        tmp = (x / z) / 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 <= 3.55e-270) {
		tmp = x / (y * (t - z));
	} else if (t <= 8.2e+24) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 3.55e-270:
		tmp = x / (y * (t - z))
	elif t <= 8.2e+24:
		tmp = (x / z) / z
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3.55e-270)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 8.2e+24)
		tmp = Float64(Float64(x / z) / 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 <= 3.55e-270)
		tmp = x / (y * (t - z));
	elseif (t <= 8.2e+24)
		tmp = (x / z) / z;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 3.55e-270], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+24], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 3.5500000000000001e-270

   1. Initial program 91.1%

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

   2. Taylor expanded in y around inf 60.3%

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

      1. *-commutative 60.3%

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

   4. Simplified 60.3%

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

   if 3.5500000000000001e-270 < t < 8.2000000000000002e24

   1. Initial program 89.0%

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

   2. Taylor expanded in z around inf 48.4%

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

      1. unpow2 48.4%

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

      2. associate-/r* 57.7%

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

   4. Simplified 57.7%

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

   if 8.2000000000000002e24 < t

   1. Initial program 80.0%

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

   2. Taylor expanded in t around inf 75.5%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.55 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 11: 62.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.7 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.7e-270)
   (/ x (* y (- t z)))
   (if (<= t 4.7e+21) (/ (/ x z) z) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.7e-270) {
		tmp = x / (y * (t - z));
	} else if (t <= 4.7e+21) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 3.7d-270) then
        tmp = x / (y * (t - z))
    else if (t <= 4.7d+21) then
        tmp = (x / z) / z
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.7e-270) {
		tmp = x / (y * (t - z));
	} else if (t <= 4.7e+21) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 3.7e-270:
		tmp = x / (y * (t - z))
	elif t <= 4.7e+21:
		tmp = (x / z) / z
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3.7e-270)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 4.7e+21)
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 3.7e-270)
		tmp = x / (y * (t - z));
	elseif (t <= 4.7e+21)
		tmp = (x / z) / z;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 3.7e-270], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.7e+21], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 3.7000000000000001e-270

   1. Initial program 91.1%

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

   2. Taylor expanded in y around inf 60.3%

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

      1. *-commutative 60.3%

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

   4. Simplified 60.3%

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

   if 3.7000000000000001e-270 < t < 4.7e21

   1. Initial program 89.0%

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

   2. Taylor expanded in z around inf 48.4%

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

      1. unpow2 48.4%

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

      2. associate-/r* 57.7%

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

   4. Simplified 57.7%

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

   if 4.7e21 < t

   1. Initial program 80.0%

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

      1. associate-/l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in t around inf 86.7%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.7 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 12: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-7} \lor \neg \left(z \leq 4.2 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.25e-7) (not (<= z 4.2e-48))) (/ x (* z z)) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.25e-7) || !(z <= 4.2e-48)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.25d-7)) .or. (.not. (z <= 4.2d-48))) then
        tmp = x / (z * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.25e-7) || !(z <= 4.2e-48)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.25e-7) or not (z <= 4.2e-48):
		tmp = x / (z * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.25e-7) || !(z <= 4.2e-48))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.25e-7) || ~((z <= 4.2e-48)))
		tmp = x / (z * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.25e-7], N[Not[LessEqual[z, 4.2e-48]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2499999999999999e-7 or 4.19999999999999977e-48 < z

   1. Initial program 86.6%

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

   2. Taylor expanded in z around inf 62.2%

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

      1. unpow2 62.2%

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

   4. Simplified 62.2%

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

   if -2.2499999999999999e-7 < z < 4.19999999999999977e-48

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 58.0%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-7} \lor \neg \left(z \leq 4.2 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 13: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-8} \lor \neg \left(z \leq 4.2 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.2e-8) (not (<= z 4.2e-48))) (/ (/ x z) z) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e-8) || !(z <= 4.2e-48)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.2d-8)) .or. (.not. (z <= 4.2d-48))) then
        tmp = (x / z) / z
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e-8) || !(z <= 4.2e-48)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.2e-8) or not (z <= 4.2e-48):
		tmp = (x / z) / z
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.2e-8) || !(z <= 4.2e-48))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.2e-8) || ~((z <= 4.2e-48)))
		tmp = (x / z) / z;
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.2e-8], N[Not[LessEqual[z, 4.2e-48]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000002e-8 or 4.19999999999999977e-48 < z

   1. Initial program 86.6%

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

   2. Taylor expanded in z around inf 62.2%

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

      1. unpow2 62.2%

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

      2. associate-/r* 69.9%

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

   4. Simplified 69.9%

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

   if -3.2000000000000002e-8 < z < 4.19999999999999977e-48

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 58.0%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-8} \lor \neg \left(z \leq 4.2 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.25e-8)
   (* (/ x z) (/ 1.0 z))
   (if (<= z 2.1e-48) (/ x (* y t)) (/ (/ x z) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e-8) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 2.1e-48) {
		tmp = x / (y * t);
	} else {
		tmp = (x / z) / 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 <= (-1.25d-8)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= 2.1d-48) then
        tmp = x / (y * t)
    else
        tmp = (x / z) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e-8) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 2.1e-48) {
		tmp = x / (y * t);
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.25e-8:
		tmp = (x / z) * (1.0 / z)
	elif z <= 2.1e-48:
		tmp = x / (y * t)
	else:
		tmp = (x / z) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.25e-8)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= 2.1e-48)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = Float64(Float64(x / z) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.25e-8)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= 2.1e-48)
		tmp = x / (y * t);
	else
		tmp = (x / z) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.25e-8], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-48], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2499999999999999e-8

   1. Initial program 86.1%

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

   2. Taylor expanded in z around inf 67.8%

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

      1. unpow2 67.8%

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

   4. Simplified 67.8%

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

      1. associate-/r* 72.5%

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

      2. div-inv 72.6%

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

   6. Applied egg-rr 72.6%

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

   if -1.2499999999999999e-8 < z < 2.09999999999999989e-48

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 58.0%

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

   if 2.09999999999999989e-48 < z

   1. Initial program 87.1%

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

   2. Taylor expanded in z around inf 56.3%

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

      1. unpow2 56.3%

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

      2. associate-/r* 67.0%

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

   4. Simplified 67.0%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 15: 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 87.7%

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

   1. associate-/r* 96.4%

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

3. Simplified 96.4%

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

4. Final simplification 96.4%

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

Alternative 16: 39.6% 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 87.7%

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

2. Taylor expanded in z around 0 36.4%

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

3. Final simplification 36.4%

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

Developer target: 87.9% 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 2023195 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

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

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