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

Percentage Accurate: 89.0% → 96.9%

Time: 11.6s

Alternatives: 17

Speedup: 1.0×

• Unsound rule application detected in e-graph. Results may not be sound.

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: 89.0% 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: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \frac{\frac{x}{t - z}}{y - z} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x (- t z)) (- y z)))

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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

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

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return (x / (t - z)) / (y - z)

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(t - z)) / Float64(y - z))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (t - z)) / (y - z);
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.1%

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

   1. associate-/l/ 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 2: 93.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot \left(y - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t z) (- y z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x (- t z)) y)
     (if (<= t_1 5e+307) (/ x t_1) (/ (/ (- x) z) (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x / (t - z)) / y;
	} else if (t_1 <= 5e+307) {
		tmp = x / t_1;
	} else {
		tmp = (-x / z) / (y - z);
	}
	return tmp;
}

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / (t - z)) / y;
	} else if (t_1 <= 5e+307) {
		tmp = x / t_1;
	} else {
		tmp = (-x / z) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (t - z) * (y - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x / (t - z)) / y
	elif t_1 <= 5e+307:
		tmp = x / t_1
	else:
		tmp = (-x / z) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(t - z) * Float64(y - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t_1 <= 5e+307)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (t - z) * (y - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x / (t - z)) / y;
	elseif (t_1 <= 5e+307)
		tmp = x / t_1;
	else
		tmp = (-x / z) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 5e+307], N[(x / t$95$1), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 79.8%

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

   2. Taylor expanded in y around inf 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-/r* 86.2%

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

   4. Simplified 86.2%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 5e307

   1. Initial program 99.1%

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

   if 5e307 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 74.3%

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

   2. Taylor expanded in t around 0 71.5%

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

      1. associate-*r/ 71.5%

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

      2. neg-mul-1 71.5%

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

      3. *-commutative 71.5%

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

      4. associate-/r* 89.5%

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

   4. Simplified 89.5%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;\left(t - z\right) \cdot \left(y - z\right) \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \end{array} \]

Alternative 3: 93.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot \left(y - z\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{-1}{z}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t z) (- y z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x (- t z)) y)
     (if (<= t_1 5e+307) (/ x t_1) (/ (* x (/ -1.0 z)) (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x / (t - z)) / y;
	} else if (t_1 <= 5e+307) {
		tmp = x / t_1;
	} else {
		tmp = (x * (-1.0 / z)) / (y - z);
	}
	return tmp;
}

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / (t - z)) / y;
	} else if (t_1 <= 5e+307) {
		tmp = x / t_1;
	} else {
		tmp = (x * (-1.0 / z)) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (t - z) * (y - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x / (t - z)) / y
	elif t_1 <= 5e+307:
		tmp = x / t_1
	else:
		tmp = (x * (-1.0 / z)) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(t - z) * Float64(y - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t_1 <= 5e+307)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x * Float64(-1.0 / z)) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (t - z) * (y - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x / (t - z)) / y;
	elseif (t_1 <= 5e+307)
		tmp = x / t_1;
	else
		tmp = (x * (-1.0 / z)) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 5e+307], N[(x / t$95$1), $MachinePrecision], N[(N[(x * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 79.8%

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

   2. Taylor expanded in y around inf 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-/r* 86.2%

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

   4. Simplified 86.2%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 5e307

   1. Initial program 99.1%

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

   if 5e307 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 74.3%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around 0 89.5%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;\left(t - z\right) \cdot \left(y - z\right) \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{-1}{z}}{y - z}\\ \end{array} \]

Alternative 4: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{if}\;z \leq -5200000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)) (t_2 (/ x (* (- t z) y))))
   (if (<= z -5200000000.0)
     t_1
     (if (<= z -1.25e-135)
       t_2
       (if (<= z 1.9e-119)
         (/ (/ x t) (- y z))
         (if (<= z 1.75e-38)
           t_2
           (if (<= z 1.85e+74) (/ x (* t (- y z))) t_1)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = x / ((t - z) * y);
	double tmp;
	if (z <= -5200000000.0) {
		tmp = t_1;
	} else if (z <= -1.25e-135) {
		tmp = t_2;
	} else if (z <= 1.9e-119) {
		tmp = (x / t) / (y - z);
	} else if (z <= 1.75e-38) {
		tmp = t_2;
	} else if (z <= 1.85e+74) {
		tmp = x / (t * (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) / z
    t_2 = x / ((t - z) * y)
    if (z <= (-5200000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.25d-135)) then
        tmp = t_2
    else if (z <= 1.9d-119) then
        tmp = (x / t) / (y - z)
    else if (z <= 1.75d-38) then
        tmp = t_2
    else if (z <= 1.85d+74) then
        tmp = x / (t * (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = x / ((t - z) * y);
	double tmp;
	if (z <= -5200000000.0) {
		tmp = t_1;
	} else if (z <= -1.25e-135) {
		tmp = t_2;
	} else if (z <= 1.9e-119) {
		tmp = (x / t) / (y - z);
	} else if (z <= 1.75e-38) {
		tmp = t_2;
	} else if (z <= 1.85e+74) {
		tmp = x / (t * (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	t_2 = x / ((t - z) * y)
	tmp = 0
	if z <= -5200000000.0:
		tmp = t_1
	elif z <= -1.25e-135:
		tmp = t_2
	elif z <= 1.9e-119:
		tmp = (x / t) / (y - z)
	elif z <= 1.75e-38:
		tmp = t_2
	elif z <= 1.85e+74:
		tmp = x / (t * (y - z))
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	t_2 = Float64(x / Float64(Float64(t - z) * y))
	tmp = 0.0
	if (z <= -5200000000.0)
		tmp = t_1;
	elseif (z <= -1.25e-135)
		tmp = t_2;
	elseif (z <= 1.9e-119)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (z <= 1.75e-38)
		tmp = t_2;
	elseif (z <= 1.85e+74)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	t_2 = x / ((t - z) * y);
	tmp = 0.0;
	if (z <= -5200000000.0)
		tmp = t_1;
	elseif (z <= -1.25e-135)
		tmp = t_2;
	elseif (z <= 1.9e-119)
		tmp = (x / t) / (y - z);
	elseif (z <= 1.75e-38)
		tmp = t_2;
	elseif (z <= 1.85e+74)
		tmp = x / (t * (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5200000000.0], t$95$1, If[LessEqual[z, -1.25e-135], t$95$2, If[LessEqual[z, 1.9e-119], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-38], t$95$2, If[LessEqual[z, 1.85e+74], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.2e9 or 1.8500000000000001e74 < z

   1. Initial program 84.5%

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

   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%

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

      2. associate-/r* 83.9%

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

   4. Simplified 83.9%

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

   if -5.2e9 < z < -1.25000000000000005e-135 or 1.89999999999999987e-119 < z < 1.7500000000000001e-38

   1. Initial program 97.7%

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

   2. Taylor expanded in y around inf 58.1%

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

      1. *-commutative 58.1%

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

   4. Simplified 58.1%

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

   if -1.25000000000000005e-135 < z < 1.89999999999999987e-119

   1. Initial program 91.5%

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

      1. associate-/l/ 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in t around inf 81.5%

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

   if 1.7500000000000001e-38 < z < 1.8500000000000001e74

   1. Initial program 99.7%

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

   2. Taylor expanded in t around inf 49.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5200000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 5: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{t \cdot \left(y - z\right)}\\ t_2 := \frac{\frac{x}{z}}{z}\\ t_3 := \frac{\frac{x}{t - z}}{y}\\ \mathbf{if}\;z \leq -5200000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-291}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* t (- y z))))
        (t_2 (/ (/ x z) z))
        (t_3 (/ (/ x (- t z)) y)))
   (if (<= z -5200000000.0)
     t_2
     (if (<= z -5e-291)
       t_3
       (if (<= z 1.05e-120)
         t_1
         (if (<= z 1.85e-41) t_3 (if (<= z 2.3e+70) t_1 t_2)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (t * (y - z));
	double t_2 = (x / z) / z;
	double t_3 = (x / (t - z)) / y;
	double tmp;
	if (z <= -5200000000.0) {
		tmp = t_2;
	} else if (z <= -5e-291) {
		tmp = t_3;
	} else if (z <= 1.05e-120) {
		tmp = t_1;
	} else if (z <= 1.85e-41) {
		tmp = t_3;
	} else if (z <= 2.3e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x / (t * (y - z))
    t_2 = (x / z) / z
    t_3 = (x / (t - z)) / y
    if (z <= (-5200000000.0d0)) then
        tmp = t_2
    else if (z <= (-5d-291)) then
        tmp = t_3
    else if (z <= 1.05d-120) then
        tmp = t_1
    else if (z <= 1.85d-41) then
        tmp = t_3
    else if (z <= 2.3d+70) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t * (y - z));
	double t_2 = (x / z) / z;
	double t_3 = (x / (t - z)) / y;
	double tmp;
	if (z <= -5200000000.0) {
		tmp = t_2;
	} else if (z <= -5e-291) {
		tmp = t_3;
	} else if (z <= 1.05e-120) {
		tmp = t_1;
	} else if (z <= 1.85e-41) {
		tmp = t_3;
	} else if (z <= 2.3e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / (t * (y - z))
	t_2 = (x / z) / z
	t_3 = (x / (t - z)) / y
	tmp = 0
	if z <= -5200000000.0:
		tmp = t_2
	elif z <= -5e-291:
		tmp = t_3
	elif z <= 1.05e-120:
		tmp = t_1
	elif z <= 1.85e-41:
		tmp = t_3
	elif z <= 2.3e+70:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(t * Float64(y - z)))
	t_2 = Float64(Float64(x / z) / z)
	t_3 = Float64(Float64(x / Float64(t - z)) / y)
	tmp = 0.0
	if (z <= -5200000000.0)
		tmp = t_2;
	elseif (z <= -5e-291)
		tmp = t_3;
	elseif (z <= 1.05e-120)
		tmp = t_1;
	elseif (z <= 1.85e-41)
		tmp = t_3;
	elseif (z <= 2.3e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (t * (y - z));
	t_2 = (x / z) / z;
	t_3 = (x / (t - z)) / y;
	tmp = 0.0;
	if (z <= -5200000000.0)
		tmp = t_2;
	elseif (z <= -5e-291)
		tmp = t_3;
	elseif (z <= 1.05e-120)
		tmp = t_1;
	elseif (z <= 1.85e-41)
		tmp = t_3;
	elseif (z <= 2.3e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -5200000000.0], t$95$2, If[LessEqual[z, -5e-291], t$95$3, If[LessEqual[z, 1.05e-120], t$95$1, If[LessEqual[z, 1.85e-41], t$95$3, If[LessEqual[z, 2.3e+70], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2e9 or 2.29999999999999994e70 < z

   1. Initial program 84.5%

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

   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%

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

      2. associate-/r* 83.9%

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

   4. Simplified 83.9%

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

   if -5.2e9 < z < -5.0000000000000003e-291 or 1.05e-120 < z < 1.8500000000000001e-41

   1. Initial program 90.8%

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

   2. Taylor expanded in y around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. associate-/r* 70.7%

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

   4. Simplified 70.7%

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

   if -5.0000000000000003e-291 < z < 1.05e-120 or 1.8500000000000001e-41 < z < 2.29999999999999994e70

   1. Initial program 99.6%

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

   2. Taylor expanded in t around inf 72.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5200000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-291}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-41}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 6: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-304} \lor \neg \left(y \leq 5.2 \cdot 10^{-181}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e-16)
   (/ (/ x y) (- t z))
   (if (<= y -9.2e-138)
     (/ (/ x z) z)
     (if (or (<= y -5.4e-304) (not (<= y 5.2e-181)))
       (/ (/ x t) (- y z))
       (/ 1.0 (/ z (/ x z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-16) {
		tmp = (x / y) / (t - z);
	} else if (y <= -9.2e-138) {
		tmp = (x / z) / z;
	} else if ((y <= -5.4e-304) || !(y <= 5.2e-181)) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = 1.0 / (z / (x / z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-3.4d-16)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-9.2d-138)) then
        tmp = (x / z) / z
    else if ((y <= (-5.4d-304)) .or. (.not. (y <= 5.2d-181))) then
        tmp = (x / t) / (y - z)
    else
        tmp = 1.0d0 / (z / (x / z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-16) {
		tmp = (x / y) / (t - z);
	} else if (y <= -9.2e-138) {
		tmp = (x / z) / z;
	} else if ((y <= -5.4e-304) || !(y <= 5.2e-181)) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = 1.0 / (z / (x / z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e-16:
		tmp = (x / y) / (t - z)
	elif y <= -9.2e-138:
		tmp = (x / z) / z
	elif (y <= -5.4e-304) or not (y <= 5.2e-181):
		tmp = (x / t) / (y - z)
	else:
		tmp = 1.0 / (z / (x / z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e-16)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -9.2e-138)
		tmp = Float64(Float64(x / z) / z);
	elseif ((y <= -5.4e-304) || !(y <= 5.2e-181))
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e-16)
		tmp = (x / y) / (t - z);
	elseif (y <= -9.2e-138)
		tmp = (x / z) / z;
	elseif ((y <= -5.4e-304) || ~((y <= 5.2e-181)))
		tmp = (x / t) / (y - z);
	else
		tmp = 1.0 / (z / (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e-16], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.2e-138], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[y, -5.4e-304], N[Not[LessEqual[y, 5.2e-181]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.4e-16

   1. Initial program 91.9%

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

      1. associate-/r* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in y around inf 81.0%

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

   if -3.4e-16 < y < -9.1999999999999996e-138

   1. Initial program 92.6%

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

   2. Taylor expanded in z around inf 44.8%

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

      1. unpow2 44.8%

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

      2. associate-/r* 51.9%

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

   4. Simplified 51.9%

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

   if -9.1999999999999996e-138 < y < -5.40000000000000021e-304 or 5.19999999999999998e-181 < y

   1. Initial program 89.3%

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

      1. associate-/l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in t around inf 57.6%

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

   if -5.40000000000000021e-304 < y < 5.19999999999999998e-181

   1. Initial program 86.7%

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

      1. associate-/l/ 95.5%

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

   3. Simplified 95.5%

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

      1. clear-num 95.4%

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

      2. associate-/r/ 95.6%

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

   5. Applied egg-rr 95.6%

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

      1. clear-num 95.5%

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

      2. inv-pow 95.5%

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

      3. *-un-lft-identity 95.5%

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

      4. times-frac 95.2%

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

      5. clear-num 95.1%

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

      6. /-rgt-identity 95.1%

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

   7. Applied egg-rr 95.1%

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

      1. unpow-1 95.1%

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

   9. Simplified 95.1%

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

   10. Taylor expanded in z around inf 51.2%

       \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   11. Step-by-step derivation

       1. unpow2 51.2%

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

       2. associate-/l* 59.7%

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

   12. Simplified 59.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-304} \lor \neg \left(y \leq 5.2 \cdot 10^{-181}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \]

Alternative 7: 67.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -2800000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-81}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -2800000000.0)
     t_1
     (if (<= z 1e-81)
       (/ (/ x t) y)
       (if (<= z 4.2e-42)
         (/ (/ (- x) y) z)
         (if (<= z 3.8e+17) (/ (- x) (* t z)) t_1))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -2800000000.0) {
		tmp = t_1;
	} else if (z <= 1e-81) {
		tmp = (x / t) / y;
	} else if (z <= 4.2e-42) {
		tmp = (-x / y) / z;
	} else if (z <= 3.8e+17) {
		tmp = -x / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-2800000000.0d0)) then
        tmp = t_1
    else if (z <= 1d-81) then
        tmp = (x / t) / y
    else if (z <= 4.2d-42) then
        tmp = (-x / y) / z
    else if (z <= 3.8d+17) then
        tmp = -x / (t * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -2800000000.0) {
		tmp = t_1;
	} else if (z <= 1e-81) {
		tmp = (x / t) / y;
	} else if (z <= 4.2e-42) {
		tmp = (-x / y) / z;
	} else if (z <= 3.8e+17) {
		tmp = -x / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -2800000000.0:
		tmp = t_1
	elif z <= 1e-81:
		tmp = (x / t) / y
	elif z <= 4.2e-42:
		tmp = (-x / y) / z
	elif z <= 3.8e+17:
		tmp = -x / (t * z)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -2800000000.0)
		tmp = t_1;
	elseif (z <= 1e-81)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 4.2e-42)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (z <= 3.8e+17)
		tmp = Float64(Float64(-x) / Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -2800000000.0)
		tmp = t_1;
	elseif (z <= 1e-81)
		tmp = (x / t) / y;
	elseif (z <= 4.2e-42)
		tmp = (-x / y) / z;
	elseif (z <= 3.8e+17)
		tmp = -x / (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -2800000000.0], t$95$1, If[LessEqual[z, 1e-81], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 4.2e-42], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.8e+17], N[((-x) / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8e9 or 3.8e17 < z

   1. Initial program 85.6%

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

   2. Taylor expanded in z around inf 72.3%

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

      1. unpow2 72.3%

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

      2. associate-/r* 80.1%

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

   4. Simplified 80.1%

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

   if -2.8e9 < z < 9.9999999999999996e-82

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 63.7%

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

      1. div-inv 63.7%

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

      2. associate-/r* 65.0%

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

   4. Applied egg-rr 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*l/ 69.7%

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

      3. associate-*r/ 65.5%

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

      4. associate-*l/ 65.5%

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

      5. *-lft-identity 65.5%

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

   6. Simplified 65.5%

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

   if 9.9999999999999996e-82 < z < 4.20000000000000013e-42

   1. Initial program 99.8%

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

      1. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 61.4%

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

   5. Taylor expanded in t around 0 51.8%

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

      1. associate-*r/ 51.8%

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

      2. neg-mul-1 51.8%

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

   7. Simplified 51.8%

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

      1. distribute-frac-neg 51.8%

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

      2. add-sqr-sqrt 40.2%

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

      3. sqrt-unprod 43.5%

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

      4. sqr-neg 43.5%

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

      5. sqrt-unprod 11.0%

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

      6. add-sqr-sqrt 12.5%

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

      7. associate-/r* 12.5%

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

      8. add-sqr-sqrt 11.0%

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

      9. sqrt-unprod 43.6%

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

      10. sqr-neg 43.6%

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

      11. sqrt-unprod 40.4%

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

      12. add-sqr-sqrt 51.8%

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

   9. Applied egg-rr 51.8%

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

   if 4.20000000000000013e-42 < z < 3.8e17

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 56.5%

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

   3. Taylor expanded in y around 0 40.7%

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

      1. associate-*r/ 40.7%

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

      2. neg-mul-1 40.7%

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

      3. *-commutative 40.7%

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

   5. Simplified 40.7%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2800000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 10^{-81}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 8: 66.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -760000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -760000000.0)
     t_1
     (if (<= z 4.7e-79)
       (/ (/ x t) y)
       (if (<= z 1.9e-39)
         (/ (/ (- x) y) z)
         (if (<= z 2.7e+15) (/ x (* t y)) t_1))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -760000000.0) {
		tmp = t_1;
	} else if (z <= 4.7e-79) {
		tmp = (x / t) / y;
	} else if (z <= 1.9e-39) {
		tmp = (-x / y) / z;
	} else if (z <= 2.7e+15) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-760000000.0d0)) then
        tmp = t_1
    else if (z <= 4.7d-79) then
        tmp = (x / t) / y
    else if (z <= 1.9d-39) then
        tmp = (-x / y) / z
    else if (z <= 2.7d+15) then
        tmp = x / (t * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -760000000.0) {
		tmp = t_1;
	} else if (z <= 4.7e-79) {
		tmp = (x / t) / y;
	} else if (z <= 1.9e-39) {
		tmp = (-x / y) / z;
	} else if (z <= 2.7e+15) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -760000000.0:
		tmp = t_1
	elif z <= 4.7e-79:
		tmp = (x / t) / y
	elif z <= 1.9e-39:
		tmp = (-x / y) / z
	elif z <= 2.7e+15:
		tmp = x / (t * y)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -760000000.0)
		tmp = t_1;
	elseif (z <= 4.7e-79)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 1.9e-39)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (z <= 2.7e+15)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -760000000.0)
		tmp = t_1;
	elseif (z <= 4.7e-79)
		tmp = (x / t) / y;
	elseif (z <= 1.9e-39)
		tmp = (-x / y) / z;
	elseif (z <= 2.7e+15)
		tmp = x / (t * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -760000000.0], t$95$1, If[LessEqual[z, 4.7e-79], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.9e-39], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.7e+15], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.6e8 or 2.7e15 < z

   1. Initial program 85.6%

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

   2. Taylor expanded in z around inf 72.3%

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

      1. unpow2 72.3%

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

      2. associate-/r* 80.1%

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

   4. Simplified 80.1%

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

   if -7.6e8 < z < 4.7000000000000002e-79

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 63.7%

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

      1. div-inv 63.7%

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

      2. associate-/r* 65.0%

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

   4. Applied egg-rr 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*l/ 69.7%

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

      3. associate-*r/ 65.5%

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

      4. associate-*l/ 65.5%

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

      5. *-lft-identity 65.5%

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

   6. Simplified 65.5%

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

   if 4.7000000000000002e-79 < z < 1.9000000000000001e-39

   1. Initial program 99.8%

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

      1. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 61.4%

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

   5. Taylor expanded in t around 0 51.8%

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

      1. associate-*r/ 51.8%

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

      2. neg-mul-1 51.8%

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

   7. Simplified 51.8%

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

      1. distribute-frac-neg 51.8%

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

      2. add-sqr-sqrt 40.2%

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

      3. sqrt-unprod 43.5%

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

      4. sqr-neg 43.5%

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

      5. sqrt-unprod 11.0%

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

      6. add-sqr-sqrt 12.5%

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

      7. associate-/r* 12.5%

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

      8. add-sqr-sqrt 11.0%

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

      9. sqrt-unprod 43.6%

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

      10. sqr-neg 43.6%

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

      11. sqrt-unprod 40.4%

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

      12. add-sqr-sqrt 51.8%

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

   9. Applied egg-rr 51.8%

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

   if 1.9000000000000001e-39 < z < 2.7e15

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 33.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -760000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 9: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -4600000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -4600000000.0)
     t_1
     (if (<= z 8.6e-42)
       (/ x (* (- t z) y))
       (if (<= z 6.2e+66) (/ x (* t (- y z))) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -4600000000.0) {
		tmp = t_1;
	} else if (z <= 8.6e-42) {
		tmp = x / ((t - z) * y);
	} else if (z <= 6.2e+66) {
		tmp = x / (t * (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-4600000000.0d0)) then
        tmp = t_1
    else if (z <= 8.6d-42) then
        tmp = x / ((t - z) * y)
    else if (z <= 6.2d+66) then
        tmp = x / (t * (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -4600000000.0) {
		tmp = t_1;
	} else if (z <= 8.6e-42) {
		tmp = x / ((t - z) * y);
	} else if (z <= 6.2e+66) {
		tmp = x / (t * (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -4600000000.0:
		tmp = t_1
	elif z <= 8.6e-42:
		tmp = x / ((t - z) * y)
	elif z <= 6.2e+66:
		tmp = x / (t * (y - z))
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -4600000000.0)
		tmp = t_1;
	elseif (z <= 8.6e-42)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (z <= 6.2e+66)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -4600000000.0)
		tmp = t_1;
	elseif (z <= 8.6e-42)
		tmp = x / ((t - z) * y);
	elseif (z <= 6.2e+66)
		tmp = x / (t * (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -4600000000.0], t$95$1, If[LessEqual[z, 8.6e-42], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+66], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e9 or 6.20000000000000037e66 < z

   1. Initial program 84.5%

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

   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%

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

      2. associate-/r* 83.9%

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

   4. Simplified 83.9%

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

   if -4.6e9 < z < 8.6000000000000002e-42

   1. Initial program 94.0%

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

   2. Taylor expanded in y around inf 74.3%

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

      1. *-commutative 74.3%

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

   4. Simplified 74.3%

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

   if 8.6000000000000002e-42 < z < 6.20000000000000037e66

   1. Initial program 99.7%

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

   2. Taylor expanded in t around inf 49.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4600000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 10: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-101}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e-16)
   (/ (/ x (- t z)) y)
   (if (<= y 6e-101) (/ (/ (- x) z) (- t z)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-16) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 6e-101) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-1.7d-16)) then
        tmp = (x / (t - z)) / y
    else if (y <= 6d-101) then
        tmp = (-x / z) / (t - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-16) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 6e-101) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e-16:
		tmp = (x / (t - z)) / y
	elif y <= 6e-101:
		tmp = (-x / z) / (t - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e-16)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 6e-101)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e-16)
		tmp = (x / (t - z)) / y;
	elseif (y <= 6e-101)
		tmp = (-x / z) / (t - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e-16], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 6e-101], 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 3 regimes

2. if y < -1.7e-16

   1. Initial program 91.9%

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

   2. Taylor expanded in y around inf 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/r* 82.2%

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

   4. Simplified 82.2%

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

   if -1.7e-16 < y < 6.0000000000000006e-101

   1. Initial program 92.0%

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

   2. Taylor expanded in y around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-frac-neg 76.2%

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

      3. associate-/r* 81.9%

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

   4. Simplified 81.9%

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

   if 6.0000000000000006e-101 < y

   1. Initial program 87.0%

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

      1. associate-/l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around inf 57.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-101}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 11: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.5e-87)
   (/ (/ x y) (- t z))
   (if (<= t 3.8e-35) (/ (/ (- x) z) (- y z)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.5e-87) {
		tmp = (x / y) / (t - z);
	} else if (t <= 3.8e-35) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-2.5d-87)) then
        tmp = (x / y) / (t - z)
    else if (t <= 3.8d-35) then
        tmp = (-x / z) / (y - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.5e-87) {
		tmp = (x / y) / (t - z);
	} else if (t <= 3.8e-35) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.5e-87:
		tmp = (x / y) / (t - z)
	elif t <= 3.8e-35:
		tmp = (-x / z) / (y - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.5e-87)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 3.8e-35)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.5e-87)
		tmp = (x / y) / (t - z);
	elseif (t <= 3.8e-35)
		tmp = (-x / z) / (y - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -2.5e-87], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-35], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.50000000000000021e-87

   1. Initial program 87.5%

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

      1. associate-/r* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around inf 58.7%

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

   if -2.50000000000000021e-87 < t < 3.8000000000000001e-35

   1. Initial program 90.1%

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

   2. Taylor expanded in t around 0 72.4%

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

      1. associate-*r/ 72.4%

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

      2. neg-mul-1 72.4%

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

      3. *-commutative 72.4%

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

      4. associate-/r* 79.5%

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

   4. Simplified 79.5%

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

   if 3.8000000000000001e-35 < t

   1. Initial program 93.5%

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

      1. associate-/l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 91.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 12: 69.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.2e-88)
   (/ (/ x y) t)
   (if (<= t 4.2e-35) (/ (/ x z) z) (/ x (* t (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-88) {
		tmp = (x / y) / t;
	} else if (t <= 4.2e-35) {
		tmp = (x / z) / z;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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-88)) then
        tmp = (x / y) / t
    else if (t <= 4.2d-35) then
        tmp = (x / z) / z
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-88) {
		tmp = (x / y) / t;
	} else if (t <= 4.2e-35) {
		tmp = (x / z) / z;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4.2e-88:
		tmp = (x / y) / t
	elif t <= 4.2e-35:
		tmp = (x / z) / z
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.2e-88)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 4.2e-35)
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.2e-88)
		tmp = (x / y) / t;
	elseif (t <= 4.2e-35)
		tmp = (x / z) / z;
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -4.2e-88], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 4.2e-35], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1999999999999999e-88

   1. Initial program 87.5%

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

   2. Taylor expanded in z around 0 50.0%

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

      1. clear-num 49.1%

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

      2. associate-/r/ 49.9%

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

      3. associate-/r* 50.3%

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

   4. Applied egg-rr 50.3%

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

      1. associate-*l/ 52.2%

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

      2. associate-*l/ 52.3%

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

      3. *-un-lft-identity 52.3%

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

   6. Applied egg-rr 52.3%

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

   if -4.1999999999999999e-88 < t < 4.2e-35

   1. Initial program 90.1%

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

   2. Taylor expanded in z around inf 49.1%

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

      1. unpow2 49.1%

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

      2. associate-/r* 57.1%

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

   4. Simplified 57.1%

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

   if 4.2e-35 < t

   1. Initial program 93.5%

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

   2. Taylor expanded in t around inf 90.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 13: 45.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+93} \lor \neg \left(z \leq 3.05 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e+93) (not (<= z 3.05e+88))) (/ x (* z y)) (/ x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+93) || !(z <= 3.05e+88)) {
		tmp = x / (z * y);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-1.6d+93)) .or. (.not. (z <= 3.05d+88))) then
        tmp = x / (z * y)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+93) || !(z <= 3.05e+88)) {
		tmp = x / (z * y);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e+93) or not (z <= 3.05e+88):
		tmp = x / (z * y)
	else:
		tmp = x / (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e+93) || !(z <= 3.05e+88))
		tmp = Float64(x / Float64(z * y));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e+93) || ~((z <= 3.05e+88)))
		tmp = x / (z * y);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e+93], N[Not[LessEqual[z, 3.05e+88]], $MachinePrecision]], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e93 or 3.0499999999999999e88 < z

   1. Initial program 83.9%

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

      1. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 50.2%

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

   5. Taylor expanded in t around 0 49.1%

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

      1. associate-*r/ 49.1%

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

      2. neg-mul-1 49.1%

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

   7. Simplified 49.1%

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

      1. expm1-log1p-u 48.8%

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

      2. expm1-udef 66.0%

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

      3. associate-/r* 65.9%

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

      4. add-sqr-sqrt 22.6%

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

      5. sqrt-unprod 61.5%

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

      6. sqr-neg 61.5%

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

      7. sqrt-unprod 42.5%

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

      8. add-sqr-sqrt 65.1%

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

   9. Applied egg-rr 65.1%

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

       1. expm1-def 44.1%

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

       2. expm1-log1p 44.4%

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

       3. associate-/r* 48.1%

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

   11. Simplified 48.1%

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

   if -1.6000000000000001e93 < z < 3.0499999999999999e88

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 49.7%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+93} \lor \neg \left(z \leq 3.05 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]

Alternative 14: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1800000000 \lor \neg \left(z \leq 1.2 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1800000000.0) (not (<= z 1.2e-81)))
   (/ x (* z z))
   (/ x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1800000000.0) || !(z <= 1.2e-81)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-1800000000.0d0)) .or. (.not. (z <= 1.2d-81))) then
        tmp = x / (z * z)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1800000000.0) || !(z <= 1.2e-81)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1800000000.0) or not (z <= 1.2e-81):
		tmp = x / (z * z)
	else:
		tmp = x / (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1800000000.0) || !(z <= 1.2e-81))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1800000000.0) || ~((z <= 1.2e-81)))
		tmp = x / (z * z);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1800000000.0], N[Not[LessEqual[z, 1.2e-81]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e9 or 1.2e-81 < z

   1. Initial program 87.8%

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

   2. Taylor expanded in z around inf 65.1%

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

      1. unpow2 65.1%

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

   4. Simplified 65.1%

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

   if -1.8e9 < z < 1.2e-81

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 63.7%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1800000000 \lor \neg \left(z \leq 1.2 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]

Alternative 15: 62.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4100000000 \lor \neg \left(z \leq 2.05 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4100000000.0) (not (<= z 2.05e-78)))
   (/ x (* z z))
   (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4100000000.0) || !(z <= 2.05e-78)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-4100000000.0d0)) .or. (.not. (z <= 2.05d-78))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4100000000.0) || !(z <= 2.05e-78)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -4100000000.0) or not (z <= 2.05e-78):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4100000000.0) || !(z <= 2.05e-78))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4100000000.0) || ~((z <= 2.05e-78)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4100000000.0], N[Not[LessEqual[z, 2.05e-78]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1e9 or 2.0499999999999999e-78 < z

   1. Initial program 87.8%

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

   2. Taylor expanded in z around inf 65.1%

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

      1. unpow2 65.1%

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

   4. Simplified 65.1%

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

   if -4.1e9 < z < 2.0499999999999999e-78

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 63.7%

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

      1. div-inv 63.7%

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

      2. associate-/r* 65.0%

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

   4. Applied egg-rr 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*l/ 69.7%

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

      3. associate-*r/ 65.5%

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

      4. associate-*l/ 65.5%

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

      5. *-lft-identity 65.5%

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

   6. Simplified 65.5%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4100000000 \lor \neg \left(z \leq 2.05 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 16: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4200000000 \lor \neg \left(z \leq 2.05 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4200000000.0) (not (<= z 2.05e-78)))
   (/ (/ x z) z)
   (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4200000000.0) || !(z <= 2.05e-78)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= (-4200000000.0d0)) .or. (.not. (z <= 2.05d-78))) then
        tmp = (x / z) / z
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4200000000.0) || !(z <= 2.05e-78)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -4200000000.0) or not (z <= 2.05e-78):
		tmp = (x / z) / z
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4200000000.0) || !(z <= 2.05e-78))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4200000000.0) || ~((z <= 2.05e-78)))
		tmp = (x / z) / z;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4200000000.0], N[Not[LessEqual[z, 2.05e-78]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e9 or 2.0499999999999999e-78 < z

   1. Initial program 87.8%

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

   2. Taylor expanded in z around inf 65.1%

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

      1. unpow2 65.1%

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

      2. associate-/r* 71.7%

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

   4. Simplified 71.7%

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

   if -4.2e9 < z < 2.0499999999999999e-78

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 63.7%

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

      1. div-inv 63.7%

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

      2. associate-/r* 65.0%

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

   4. Applied egg-rr 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*l/ 69.7%

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

      3. associate-*r/ 65.5%

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

      4. associate-*l/ 65.5%

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

      5. *-lft-identity 65.5%

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

   6. Simplified 65.5%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4200000000 \lor \neg \left(z \leq 2.05 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 17: 38.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \frac{x}{t \cdot y} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (* t y)))

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 * y)
end function

Java

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

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return x / (t * y)

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(x / Float64(t * y))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / (t * y);
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.1%

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

2. Taylor expanded in z around 0 42.7%

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

3. Final simplification 42.7%

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

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 2023171 
(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))))