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

Percentage Accurate: 89.2% → 96.2%

Time: 13.6s

Alternatives: 14

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t\_1 \leq 1.5 \cdot 10^{+285}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 1.5e+285) (/ x t_1) (/ (/ x (- t z)) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 1.5e+285) {
		tmp = x / t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 = (y - z) * (t - z)
    if (t_1 <= 1.5d+285) then
        tmp = x / t_1
    else
        tmp = (x / (t - z)) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 1.5e+285) {
		tmp = x / t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= 1.5e+285:
		tmp = x / t_1
	else:
		tmp = (x / (t - z)) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= 1.5e+285)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / Float64(t - z)) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= 1.5e+285)
		tmp = x / t_1;
	else
		tmp = (x / (t - z)) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1.5e+285], N[(x / t$95$1), $MachinePrecision], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 1.5000000000000001e285

   1. Initial program 95.9%

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

   if 1.5000000000000001e285 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 68.2%

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

      1. add-sqr-sqrt 27.3%

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

      2. times-frac 38.1%

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

   4. Applied egg-rr 38.1%

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

      1. associate-*l/ 38.1%

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

      2. associate-*r/ 38.1%

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

      3. add-sqr-sqrt 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq 1.5 \cdot 10^{+285}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 48.4% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, 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 = (sqrt(x) / (y - z)) * (sqrt(x) / (t - z))
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return (Math.sqrt(x) / (y - z)) * (Math.sqrt(x) / (t - z));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.2%

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

   1. add-sqr-sqrt 40.3%

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

   2. times-frac 43.3%

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

4. Applied egg-rr 43.3%

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

5. Final simplification 43.3%

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

Alternative 3: 51.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-137}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-57}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -8.2e-137)
   (/ (/ x y) t)
   (if (<= t 2.3e-57)
     (/ (- x) (* y z))
     (if (<= t 5.5e+123) (/ (- x) (* z t)) (/ (/ x t) y)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.2e-137) {
		tmp = (x / y) / t;
	} else if (t <= 2.3e-57) {
		tmp = -x / (y * z);
	} else if (t <= 5.5e+123) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-8.2d-137)) then
        tmp = (x / y) / t
    else if (t <= 2.3d-57) then
        tmp = -x / (y * z)
    else if (t <= 5.5d+123) then
        tmp = -x / (z * t)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.2e-137) {
		tmp = (x / y) / t;
	} else if (t <= 2.3e-57) {
		tmp = -x / (y * z);
	} else if (t <= 5.5e+123) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -8.2e-137:
		tmp = (x / y) / t
	elif t <= 2.3e-57:
		tmp = -x / (y * z)
	elif t <= 5.5e+123:
		tmp = -x / (z * t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8.2e-137)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 2.3e-57)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (t <= 5.5e+123)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8.2e-137)
		tmp = (x / y) / t;
	elseif (t <= 2.3e-57)
		tmp = -x / (y * z);
	elseif (t <= 5.5e+123)
		tmp = -x / (z * t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -8.2e-137], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.3e-57], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+123], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.1999999999999997e-137

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 53.1%

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

      1. frac-2neg 53.1%

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

      2. neg-sub0 53.1%

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

      3. div-sub 53.0%

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

      4. *-commutative 53.0%

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

      5. distribute-rgt-neg-in 53.0%

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

      6. add-sqr-sqrt 28.2%

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

      7. sqrt-unprod 46.4%

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

      8. sqr-neg 46.4%

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

      9. sqrt-unprod 13.3%

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

      10. add-sqr-sqrt 30.5%

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

      11. frac-2neg 30.5%

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

      12. *-commutative 30.5%

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

   5. Applied egg-rr 30.5%

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

      1. div0 30.5%

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

      2. neg-sub0 30.5%

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

      3. distribute-neg-frac 30.5%

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

      4. *-commutative 30.5%

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

   7. Simplified 30.5%

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

      1. div-inv 30.5%

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

      2. add-sqr-sqrt 13.3%

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

      3. sqrt-unprod 46.5%

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

      4. sqr-neg 46.5%

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

      5. sqrt-unprod 28.2%

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

      6. add-sqr-sqrt 53.1%

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

      7. associate-/r* 53.1%

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

   9. Applied egg-rr 53.1%

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

       1. associate-*r/ 59.7%

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

       2. associate-*l/ 52.3%

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

       3. associate-*r/ 52.3%

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

       4. *-rgt-identity 52.3%

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

   11. Simplified 52.3%

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

   if -8.1999999999999997e-137 < t < 2.3e-57

   1. Initial program 76.8%

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

   3. Taylor expanded in t around 0 70.4%

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

      1. associate-*r/ 70.4%

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

      2. neg-mul-1 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in z around 0 43.4%

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

      1. associate-*r/ 43.4%

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

      2. neg-mul-1 43.4%

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

      3. *-commutative 43.4%

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

   8. Simplified 43.4%

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

   if 2.3e-57 < t < 5.5000000000000002e123

   1. Initial program 91.4%

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

   3. Taylor expanded in t around inf 62.5%

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

      1. associate-/r* 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in y around 0 39.2%

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

      1. associate-*r/ 39.2%

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

      2. neg-mul-1 39.2%

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

   8. Simplified 39.2%

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

   if 5.5000000000000002e123 < t

   1. Initial program 95.4%

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

   3. Taylor expanded in z around 0 62.8%

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

      1. frac-2neg 62.8%

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

      2. neg-sub0 62.8%

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

      3. div-sub 62.8%

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

      4. *-commutative 62.8%

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

      5. distribute-rgt-neg-in 62.8%

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

      6. add-sqr-sqrt 23.0%

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

      7. sqrt-unprod 59.7%

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

      8. sqr-neg 59.7%

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

      9. sqrt-unprod 33.5%

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

      10. add-sqr-sqrt 49.2%

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

      11. frac-2neg 49.2%

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

      12. *-commutative 49.2%

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

   5. Applied egg-rr 49.2%

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

      1. div0 49.2%

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

      2. neg-sub0 49.2%

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

      3. distribute-neg-frac 49.2%

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

      4. *-commutative 49.2%

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

   7. Simplified 49.2%

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

      1. *-commutative 49.2%

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

      2. associate-/r* 49.0%

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

      3. add-sqr-sqrt 33.4%

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

      4. sqrt-unprod 58.8%

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

      5. sqr-neg 58.8%

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

      6. sqrt-unprod 22.2%

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

      7. add-sqr-sqrt 60.6%

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

      8. clear-num 60.6%

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

      9. div-inv 60.6%

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

      10. clear-num 60.6%

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

   9. Applied egg-rr 60.6%

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

       1. associate-*l/ 72.8%

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

       2. div-inv 72.8%

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

   11. Applied egg-rr 72.8%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-137}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-57}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-1}{z}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+123}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.7e-135)
   (/ (/ x y) t)
   (if (<= t 4.3e-60)
     (* (/ x y) (/ -1.0 z))
     (if (<= t 4.6e+123) (/ (- x) (* z t)) (/ (/ x t) y)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.7e-135) {
		tmp = (x / y) / t;
	} else if (t <= 4.3e-60) {
		tmp = (x / y) * (-1.0 / z);
	} else if (t <= 4.6e+123) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-2.7d-135)) then
        tmp = (x / y) / t
    else if (t <= 4.3d-60) then
        tmp = (x / y) * ((-1.0d0) / z)
    else if (t <= 4.6d+123) then
        tmp = -x / (z * t)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.7e-135) {
		tmp = (x / y) / t;
	} else if (t <= 4.3e-60) {
		tmp = (x / y) * (-1.0 / z);
	} else if (t <= 4.6e+123) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.7e-135:
		tmp = (x / y) / t
	elif t <= 4.3e-60:
		tmp = (x / y) * (-1.0 / z)
	elif t <= 4.6e+123:
		tmp = -x / (z * t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.7e-135)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 4.3e-60)
		tmp = Float64(Float64(x / y) * Float64(-1.0 / z));
	elseif (t <= 4.6e+123)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.7e-135)
		tmp = (x / y) / t;
	elseif (t <= 4.3e-60)
		tmp = (x / y) * (-1.0 / z);
	elseif (t <= 4.6e+123)
		tmp = -x / (z * t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -2.7e-135], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 4.3e-60], N[(N[(x / y), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+123], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.69999999999999999e-135

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 53.1%

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

      1. frac-2neg 53.1%

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

      2. neg-sub0 53.1%

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

      3. div-sub 53.0%

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

      4. *-commutative 53.0%

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

      5. distribute-rgt-neg-in 53.0%

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

      6. add-sqr-sqrt 28.2%

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

      7. sqrt-unprod 46.4%

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

      8. sqr-neg 46.4%

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

      9. sqrt-unprod 13.3%

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

      10. add-sqr-sqrt 30.5%

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

      11. frac-2neg 30.5%

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

      12. *-commutative 30.5%

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

   5. Applied egg-rr 30.5%

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

      1. div0 30.5%

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

      2. neg-sub0 30.5%

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

      3. distribute-neg-frac 30.5%

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

      4. *-commutative 30.5%

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

   7. Simplified 30.5%

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

      1. div-inv 30.5%

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

      2. add-sqr-sqrt 13.3%

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

      3. sqrt-unprod 46.5%

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

      4. sqr-neg 46.5%

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

      5. sqrt-unprod 28.2%

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

      6. add-sqr-sqrt 53.1%

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

      7. associate-/r* 53.1%

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

   9. Applied egg-rr 53.1%

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

       1. associate-*r/ 59.7%

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

       2. associate-*l/ 52.3%

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

       3. associate-*r/ 52.3%

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

       4. *-rgt-identity 52.3%

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

   11. Simplified 52.3%

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

   if -2.69999999999999999e-135 < t < 4.3000000000000001e-60

   1. Initial program 76.8%

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

      1. associate-/r* 95.0%

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

      2. div-inv 94.9%

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in t around 0 89.2%

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

   6. Taylor expanded in y around inf 45.7%

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

   if 4.3000000000000001e-60 < t < 4.59999999999999981e123

   1. Initial program 91.4%

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

   3. Taylor expanded in t around inf 62.5%

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

      1. associate-/r* 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in y around 0 39.2%

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

      1. associate-*r/ 39.2%

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

      2. neg-mul-1 39.2%

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

   8. Simplified 39.2%

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

   if 4.59999999999999981e123 < t

   1. Initial program 95.4%

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

   3. Taylor expanded in z around 0 62.8%

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

      1. frac-2neg 62.8%

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

      2. neg-sub0 62.8%

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

      3. div-sub 62.8%

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

      4. *-commutative 62.8%

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

      5. distribute-rgt-neg-in 62.8%

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

      6. add-sqr-sqrt 23.0%

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

      7. sqrt-unprod 59.7%

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

      8. sqr-neg 59.7%

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

      9. sqrt-unprod 33.5%

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

      10. add-sqr-sqrt 49.2%

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

      11. frac-2neg 49.2%

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

      12. *-commutative 49.2%

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

   5. Applied egg-rr 49.2%

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

      1. div0 49.2%

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

      2. neg-sub0 49.2%

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

      3. distribute-neg-frac 49.2%

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

      4. *-commutative 49.2%

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

   7. Simplified 49.2%

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

      1. *-commutative 49.2%

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

      2. associate-/r* 49.0%

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

      3. add-sqr-sqrt 33.4%

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

      4. sqrt-unprod 58.8%

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

      5. sqr-neg 58.8%

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

      6. sqrt-unprod 22.2%

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

      7. add-sqr-sqrt 60.6%

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

      8. clear-num 60.6%

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

      9. div-inv 60.6%

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

      10. clear-num 60.6%

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

   9. Applied egg-rr 60.6%

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

       1. associate-*l/ 72.8%

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

       2. div-inv 72.8%

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

   11. Applied egg-rr 72.8%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-1}{z}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+123}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 2e+286) (/ x t_1) (/ (/ (- x) (- y z)) z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 2e+286) {
		tmp = x / t_1;
	} else {
		tmp = (-x / (y - z)) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 = (y - z) * (t - z)
    if (t_1 <= 2d+286) then
        tmp = x / t_1
    else
        tmp = (-x / (y - z)) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 2e+286) {
		tmp = x / t_1;
	} else {
		tmp = (-x / (y - z)) / z;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= 2e+286:
		tmp = x / t_1
	else:
		tmp = (-x / (y - z)) / z
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= 2e+286)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(Float64(-x) / Float64(y - z)) / z);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= 2e+286)
		tmp = x / t_1;
	else
		tmp = (-x / (y - z)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+286], N[(x / t$95$1), $MachinePrecision], N[(N[((-x) / N[(y - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 2.00000000000000007e286

   1. Initial program 95.9%

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

   if 2.00000000000000007e286 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 67.4%

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

   3. Taylor expanded in t around 0 63.0%

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

      1. associate-*r/ 63.0%

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

      2. neg-mul-1 63.0%

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

   5. Simplified 63.0%

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

      1. distribute-frac-neg 63.0%

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

      2. *-commutative 63.0%

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

      3. associate-/r* 93.2%

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

   7. Applied egg-rr 93.2%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -7.5e-135)
   (/ (/ x y) (- t z))
   (if (<= t 6.8e+72) (/ (/ (- x) (- y z)) z) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.5e-135) {
		tmp = (x / y) / (t - z);
	} else if (t <= 6.8e+72) {
		tmp = (-x / (y - z)) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-7.5d-135)) then
        tmp = (x / y) / (t - z)
    else if (t <= 6.8d+72) then
        tmp = (-x / (y - z)) / z
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.5e-135) {
		tmp = (x / y) / (t - z);
	} else if (t <= 6.8e+72) {
		tmp = (-x / (y - z)) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -7.5e-135:
		tmp = (x / y) / (t - z)
	elif t <= 6.8e+72:
		tmp = (-x / (y - z)) / z
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7.5e-135)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 6.8e+72)
		tmp = Float64(Float64(Float64(-x) / Float64(y - z)) / z);
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7.5e-135)
		tmp = (x / y) / (t - z);
	elseif (t <= 6.8e+72)
		tmp = (-x / (y - z)) / z;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -7.5e-135], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+72], N[(N[((-x) / N[(y - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5e-135

   1. Initial program 87.8%

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

      1. add-sqr-sqrt 48.4%

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

      2. times-frac 51.0%

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

   4. Applied egg-rr 51.0%

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

   5. Taylor expanded in y around inf 63.2%

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

      1. associate-/r* 60.5%

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

   7. Simplified 60.5%

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

   if -7.5e-135 < t < 6.7999999999999997e72

   1. Initial program 80.5%

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

   3. Taylor expanded in t around 0 66.6%

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

      1. associate-*r/ 66.6%

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

      2. neg-mul-1 66.6%

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

   5. Simplified 66.6%

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

      1. distribute-frac-neg 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-/r* 83.6%

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

   7. Applied egg-rr 83.6%

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

   if 6.7999999999999997e72 < t

   1. Initial program 95.0%

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

   3. Taylor expanded in t around inf 90.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-137}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.4e-137)
   (/ (/ x y) t)
   (if (<= t 5.2e-61) (* (/ x y) (/ -1.0 z)) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.4e-137) {
		tmp = (x / y) / t;
	} else if (t <= 5.2e-61) {
		tmp = (x / y) * (-1.0 / z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-3.4d-137)) then
        tmp = (x / y) / t
    else if (t <= 5.2d-61) then
        tmp = (x / y) * ((-1.0d0) / z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.4e-137) {
		tmp = (x / y) / t;
	} else if (t <= 5.2e-61) {
		tmp = (x / y) * (-1.0 / z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -3.4e-137:
		tmp = (x / y) / t
	elif t <= 5.2e-61:
		tmp = (x / y) * (-1.0 / z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.4e-137)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 5.2e-61)
		tmp = Float64(Float64(x / y) * Float64(-1.0 / z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.4e-137)
		tmp = (x / y) / t;
	elseif (t <= 5.2e-61)
		tmp = (x / y) * (-1.0 / z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -3.4e-137], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 5.2e-61], N[(N[(x / y), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.40000000000000014e-137

   1. Initial program 87.3%

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

   3. Taylor expanded in z around 0 52.9%

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

      1. frac-2neg 52.9%

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

      2. neg-sub0 52.9%

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

      3. div-sub 52.8%

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

      4. *-commutative 52.8%

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

      5. distribute-rgt-neg-in 52.8%

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

      6. add-sqr-sqrt 28.2%

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

      7. sqrt-unprod 45.9%

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

      8. sqr-neg 45.9%

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

      9. sqrt-unprod 13.2%

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

      10. add-sqr-sqrt 30.2%

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

      11. frac-2neg 30.2%

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

      12. *-commutative 30.2%

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

   5. Applied egg-rr 30.2%

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

      1. div0 30.2%

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

      2. neg-sub0 30.2%

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

      3. distribute-neg-frac 30.2%

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

      4. *-commutative 30.2%

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

   7. Simplified 30.2%

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

      1. div-inv 30.2%

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

      2. add-sqr-sqrt 13.2%

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

      3. sqrt-unprod 45.9%

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

      4. sqr-neg 45.9%

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

      5. sqrt-unprod 27.9%

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

      6. add-sqr-sqrt 52.6%

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

      7. associate-/r* 52.5%

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

   9. Applied egg-rr 52.5%

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

       1. associate-*r/ 60.2%

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

       2. associate-*l/ 52.8%

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

       3. associate-*r/ 52.8%

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

       4. *-rgt-identity 52.8%

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

   11. Simplified 52.8%

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

   if -3.40000000000000014e-137 < t < 5.20000000000000021e-61

   1. Initial program 77.3%

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

      1. associate-/r* 94.9%

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

      2. div-inv 94.9%

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in t around 0 90.3%

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

   6. Taylor expanded in y around inf 46.3%

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

   if 5.20000000000000021e-61 < t

   1. Initial program 93.3%

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

   3. Taylor expanded in t around inf 78.2%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-137}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-121}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.5e-141)
   (/ (/ x y) t)
   (if (<= y 3.2e-121) (/ (- x) (* z t)) (/ (/ x t) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e-141) {
		tmp = (x / y) / t;
	} else if (y <= 3.2e-121) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-8.5d-141)) then
        tmp = (x / y) / t
    else if (y <= 3.2d-121) then
        tmp = -x / (z * t)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e-141) {
		tmp = (x / y) / t;
	} else if (y <= 3.2e-121) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -8.5e-141:
		tmp = (x / y) / t
	elif y <= 3.2e-121:
		tmp = -x / (z * t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.5e-141)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= 3.2e-121)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.5e-141)
		tmp = (x / y) / t;
	elseif (y <= 3.2e-121)
		tmp = -x / (z * t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -8.5e-141], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 3.2e-121], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.50000000000000021e-141

   1. Initial program 85.9%

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

   3. Taylor expanded in z around 0 48.2%

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

      1. frac-2neg 48.2%

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

      2. neg-sub0 48.2%

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

      3. div-sub 48.1%

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

      4. *-commutative 48.1%

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

      5. distribute-rgt-neg-in 48.1%

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

      6. add-sqr-sqrt 24.0%

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

      7. sqrt-unprod 36.6%

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

      8. sqr-neg 36.6%

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

      9. sqrt-unprod 15.3%

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

      10. add-sqr-sqrt 29.4%

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

      11. frac-2neg 29.4%

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

      12. *-commutative 29.4%

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

   5. Applied egg-rr 29.4%

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

      1. div0 29.6%

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

      2. neg-sub0 29.6%

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

      3. distribute-neg-frac 29.6%

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

      4. *-commutative 29.6%

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

   7. Simplified 29.6%

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

      1. div-inv 29.6%

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

      2. add-sqr-sqrt 15.5%

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

      3. sqrt-unprod 36.8%

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

      4. sqr-neg 36.8%

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

      5. sqrt-unprod 24.1%

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

      6. add-sqr-sqrt 48.2%

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

      7. associate-/r* 49.1%

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

   9. Applied egg-rr 49.1%

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

       1. associate-*r/ 51.3%

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

       2. associate-*l/ 51.1%

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

       3. associate-*r/ 51.1%

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

       4. *-rgt-identity 51.1%

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

   11. Simplified 51.1%

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

   if -8.50000000000000021e-141 < y < 3.20000000000000019e-121

   1. Initial program 90.0%

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

   3. Taylor expanded in t around inf 57.1%

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

      1. associate-/r* 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in y around 0 48.4%

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

      1. associate-*r/ 48.4%

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

      2. neg-mul-1 48.4%

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

   8. Simplified 48.4%

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

   if 3.20000000000000019e-121 < y

   1. Initial program 82.6%

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

   3. Taylor expanded in z around 0 49.1%

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

      1. frac-2neg 49.1%

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

      2. neg-sub0 49.1%

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

      3. div-sub 49.1%

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

      4. *-commutative 49.1%

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

      5. distribute-rgt-neg-in 49.1%

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

      6. add-sqr-sqrt 26.1%

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

      7. sqrt-unprod 40.7%

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

      8. sqr-neg 40.7%

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

      9. sqrt-unprod 15.3%

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

      10. add-sqr-sqrt 28.5%

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

      11. frac-2neg 28.5%

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

      12. *-commutative 28.5%

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

   5. Applied egg-rr 28.5%

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

      1. div0 28.5%

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

      2. neg-sub0 28.5%

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

      3. distribute-neg-frac 28.5%

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

      4. *-commutative 28.5%

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

   7. Simplified 28.5%

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

      1. *-commutative 28.5%

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

      2. associate-/r* 32.4%

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

      3. add-sqr-sqrt 18.5%

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

      4. sqrt-unprod 42.7%

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

      5. sqr-neg 42.7%

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

      6. sqrt-unprod 24.4%

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

      7. add-sqr-sqrt 50.6%

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

      8. clear-num 50.6%

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

      9. div-inv 50.5%

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

      10. clear-num 50.5%

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

   9. Applied egg-rr 50.5%

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

       1. associate-*l/ 48.0%

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

       2. div-inv 48.0%

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

   11. Applied egg-rr 48.0%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-121}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.15 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.15e-57) (/ x (* y (- t z))) (/ x (* (- y z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.15e-57) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= 1.15d-57) then
        tmp = x / (y * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.15e-57) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.15e-57:
		tmp = x / (y * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.15e-57)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.15e-57)
		tmp = x / (y * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.15e-57], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.15e-57

   1. Initial program 82.5%

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

   3. Taylor expanded in y around inf 56.3%

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

      1. *-commutative 56.3%

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

   5. Simplified 56.3%

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

   if 1.15e-57 < t

   1. Initial program 93.3%

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

   3. Taylor expanded in t around inf 78.2%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.15 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.2e-57) (/ (/ x y) (- t z)) (/ x (* (- y z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.2e-57) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= 1.2d-57) then
        tmp = (x / y) / (t - z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.2e-57) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.2e-57:
		tmp = (x / y) / (t - z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.2e-57)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.2e-57)
		tmp = (x / y) / (t - z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.2e-57], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.20000000000000003e-57

   1. Initial program 82.5%

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

      1. add-sqr-sqrt 40.0%

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

      2. times-frac 43.9%

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

   4. Applied egg-rr 43.9%

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

   5. Taylor expanded in y around inf 56.3%

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

      1. associate-/r* 55.8%

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

   7. Simplified 55.8%

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

   if 1.20000000000000003e-57 < t

   1. Initial program 93.3%

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

   3. Taylor expanded in t around inf 78.2%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 96.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{y - z} \cdot \frac{1}{t - z} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (* (/ x (- y z)) (/ 1.0 (- t z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (x / (y - z)) * (1.0 / (t - z));
}

Fortran

NOTE: x, y, z, 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 / (y - z)) * (1.0d0 / (t - z))
end function

Java

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

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return (x / (y - z)) * (1.0 / (t - z))

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (y - z)) * (1.0 / (t - z));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.2%

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

   1. associate-/r* 94.3%

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

   2. div-inv 94.3%

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

4. Applied egg-rr 94.3%

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

5. Final simplification 94.3%

   \[\leadsto \frac{x}{y - z} \cdot \frac{1}{t - z} \]
6. Add Preprocessing

Alternative 12: 44.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1e-102) (/ (/ x y) t) (/ (/ x t) y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e-102) {
		tmp = (x / y) / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-1d-102)) then
        tmp = (x / y) / t
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e-102) {
		tmp = (x / y) / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1e-102:
		tmp = (x / y) / t
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1e-102)
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1e-102)
		tmp = (x / y) / t;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1e-102], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999933e-103

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 48.5%

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

      1. frac-2neg 48.5%

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

      2. neg-sub0 48.5%

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

      3. div-sub 48.5%

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

      4. *-commutative 48.5%

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

      5. distribute-rgt-neg-in 48.5%

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

      6. add-sqr-sqrt 24.8%

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

      7. sqrt-unprod 38.3%

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

      8. sqr-neg 38.3%

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

      9. sqrt-unprod 16.5%

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

      10. add-sqr-sqrt 31.6%

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

      11. frac-2neg 31.6%

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

      12. *-commutative 31.6%

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

   5. Applied egg-rr 31.6%

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

      1. div0 31.7%

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

      2. neg-sub0 31.7%

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

      3. distribute-neg-frac 31.7%

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

      4. *-commutative 31.7%

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

   7. Simplified 31.7%

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

      1. div-inv 31.7%

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

      2. add-sqr-sqrt 16.6%

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

      3. sqrt-unprod 38.4%

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

      4. sqr-neg 38.4%

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

      5. sqrt-unprod 24.8%

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

      6. add-sqr-sqrt 48.5%

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

      7. associate-/r* 49.5%

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

   9. Applied egg-rr 49.5%

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

       1. associate-*r/ 50.7%

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

       2. associate-*l/ 50.6%

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

       3. associate-*r/ 50.6%

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

       4. *-rgt-identity 50.6%

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

   11. Simplified 50.6%

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

   if -9.99999999999999933e-103 < y

   1. Initial program 85.3%

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

   3. Taylor expanded in z around 0 32.5%

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

      1. frac-2neg 32.5%

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

      2. neg-sub0 32.5%

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

      3. div-sub 31.0%

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

      4. *-commutative 31.0%

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

      5. distribute-rgt-neg-in 31.0%

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

      6. add-sqr-sqrt 14.7%

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

      7. sqrt-unprod 29.3%

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

      8. sqr-neg 29.3%

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

      9. sqrt-unprod 8.6%

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

      10. add-sqr-sqrt 15.2%

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

      11. frac-2neg 15.2%

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

      12. *-commutative 15.2%

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

   5. Applied egg-rr 15.2%

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

      1. div0 16.1%

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

      2. neg-sub0 16.1%

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

      3. distribute-neg-frac 16.1%

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

      4. *-commutative 16.1%

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

   7. Simplified 16.1%

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

      1. *-commutative 16.1%

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

      2. associate-/r* 17.9%

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

      3. add-sqr-sqrt 10.8%

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

      4. sqrt-unprod 32.1%

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

      5. sqr-neg 32.1%

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

      6. sqrt-unprod 14.7%

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

      7. add-sqr-sqrt 33.5%

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

      8. clear-num 33.6%

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

      9. div-inv 33.5%

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

      10. clear-num 33.6%

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

   9. Applied egg-rr 33.6%

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

       1. associate-*l/ 38.9%

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

       2. div-inv 38.9%

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

   11. Applied egg-rr 38.9%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, 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 / (y * t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.2%

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

3. Taylor expanded in z around 0 38.3%

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

4. Final simplification 38.3%

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

Alternative 14: 43.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, 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 x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return (x / t) / y;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.2%

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

3. Taylor expanded in z around 0 38.3%

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

   1. frac-2neg 38.3%

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

   2. neg-sub0 38.3%

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

   3. div-sub 37.3%

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

   4. *-commutative 37.3%

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

   5. distribute-rgt-neg-in 37.3%

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

   6. add-sqr-sqrt 18.3%

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

   7. sqrt-unprod 32.5%

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

   8. sqr-neg 32.5%

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

   9. sqrt-unprod 11.4%

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

   10. add-sqr-sqrt 21.1%

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

   11. frac-2neg 21.1%

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

   12. *-commutative 21.1%

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

5. Applied egg-rr 21.1%

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

   1. div0 21.7%

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

   2. neg-sub0 21.7%

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

   3. distribute-neg-frac 21.7%

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

   4. *-commutative 21.7%

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

7. Simplified 21.7%

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

   1. *-commutative 21.7%

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

   2. associate-/r* 23.9%

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

   3. add-sqr-sqrt 13.2%

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

   4. sqrt-unprod 35.4%

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

   5. sqr-neg 35.4%

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

   6. sqrt-unprod 19.5%

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

   7. add-sqr-sqrt 39.7%

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

   8. clear-num 39.4%

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

   9. div-inv 39.3%

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

   10. clear-num 39.7%

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

9. Applied egg-rr 39.7%

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

    1. associate-*l/ 43.2%

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

    2. div-inv 43.2%

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

11. Applied egg-rr 43.2%

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

12. Final simplification 43.2%

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

Developer target: 88.0% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024096 
(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))))