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

Percentage Accurate: 89.2% → 96.7%

Time: 12.0s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / (y - z)) * ((-1.0d0) / (z - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.2%

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

   1. associate-/r* 98.4%

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

   2. div-inv 98.3%

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

4. Applied egg-rr 98.3%

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

5. Final simplification 98.3%

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

Alternative 2: 93.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 62.3%

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

   3. Taylor expanded in y around inf 57.6%

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

      1. associate-/r* 81.6%

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

   5. Simplified 81.6%

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

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

   1. Initial program 98.5%

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

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

   1. Initial program 70.4%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. un-div-inv 99.9%

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

      2. clear-num 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t around 0 62.0%

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

      1. associate-*r/ 62.0%

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

      2. times-frac 85.7%

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

      3. associate-*l/ 85.8%

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

      4. mul-1-neg 85.8%

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

   9. Simplified 85.8%

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

4. Final simplification 93.8%

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

Alternative 3: 48.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(-t\right)}\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-23}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- t)))))
   (if (<= z -1.32e-117)
     t_1
     (if (<= z 1e-23) (/ (/ x t) y) (if (<= z 1.5e+123) t_1 (/ x (* y z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * -t);
	double tmp;
	if (z <= -1.32e-117) {
		tmp = t_1;
	} else if (z <= 1e-23) {
		tmp = (x / t) / y;
	} else if (z <= 1.5e+123) {
		tmp = t_1;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z * -t)
    if (z <= (-1.32d-117)) then
        tmp = t_1
    else if (z <= 1d-23) then
        tmp = (x / t) / y
    else if (z <= 1.5d+123) then
        tmp = t_1
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * -t);
	double tmp;
	if (z <= -1.32e-117) {
		tmp = t_1;
	} else if (z <= 1e-23) {
		tmp = (x / t) / y;
	} else if (z <= 1.5e+123) {
		tmp = t_1;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * -t)
	tmp = 0
	if z <= -1.32e-117:
		tmp = t_1
	elif z <= 1e-23:
		tmp = (x / t) / y
	elif z <= 1.5e+123:
		tmp = t_1
	else:
		tmp = x / (y * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(-t)))
	tmp = 0.0
	if (z <= -1.32e-117)
		tmp = t_1;
	elseif (z <= 1e-23)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 1.5e+123)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * -t);
	tmp = 0.0;
	if (z <= -1.32e-117)
		tmp = t_1;
	elseif (z <= 1e-23)
		tmp = (x / t) / y;
	elseif (z <= 1.5e+123)
		tmp = t_1;
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.32e-117], t$95$1, If[LessEqual[z, 1e-23], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.5e+123], t$95$1, N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.32e-117 or 9.9999999999999996e-24 < z < 1.50000000000000004e123

   1. Initial program 88.8%

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

      1. associate-/l/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 51.1%

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

   6. Taylor expanded in y around 0 40.2%

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

      1. associate-*r/ 40.2%

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

      2. mul-1-neg 40.2%

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

   8. Simplified 40.2%

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

   if -1.32e-117 < z < 9.9999999999999996e-24

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 72.0%

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

      1. associate-/r* 73.5%

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

   5. Simplified 73.5%

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

   if 1.50000000000000004e123 < z

   1. Initial program 72.3%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 91.8%

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

      1. associate-*r/ 91.8%

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

      2. neg-mul-1 91.8%

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

   7. Simplified 91.8%

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

      1. div-inv 91.8%

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

      2. associate-/l* 67.3%

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

      3. add-sqr-sqrt 23.5%

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

      4. sqrt-unprod 62.0%

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

      5. sqr-neg 62.0%

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

      6. sqrt-unprod 41.1%

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

      7. add-sqr-sqrt 64.7%

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

   9. Applied egg-rr 64.7%

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

       1. associate-/r* 64.9%

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

       2. associate-*r/ 64.9%

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

       3. associate-*l/ 64.9%

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

       4. *-rgt-identity 64.9%

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

   11. Simplified 64.9%

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

   12. Taylor expanded in z around 0 34.8%

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

       1. *-commutative 34.8%

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

   14. Simplified 34.8%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 10^{-23}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+20} \lor \neg \left(z \leq 4.6 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e+20) (not (<= z 4.6e-24)))
   (/ (/ x z) (- y))
   (* (/ x y) (/ 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+20) || !(z <= 4.6e-24)) {
		tmp = (x / z) / -y;
	} else {
		tmp = (x / y) * (1.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8d+20)) .or. (.not. (z <= 4.6d-24))) then
        tmp = (x / z) / -y
    else
        tmp = (x / y) * (1.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+20) || !(z <= 4.6e-24)) {
		tmp = (x / z) / -y;
	} else {
		tmp = (x / y) * (1.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8e+20) or not (z <= 4.6e-24):
		tmp = (x / z) / -y
	else:
		tmp = (x / y) * (1.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e+20) || !(z <= 4.6e-24))
		tmp = Float64(Float64(x / z) / Float64(-y));
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8e+20) || ~((z <= 4.6e-24)))
		tmp = (x / z) / -y;
	else
		tmp = (x / y) * (1.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8e+20], N[Not[LessEqual[z, 4.6e-24]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / (-y)), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8e20 or 4.6000000000000002e-24 < z

   1. Initial program 82.8%

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

   3. Taylor expanded in t around 0 69.1%

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

      1. associate-*r/ 69.1%

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

      2. neg-mul-1 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in z around 0 35.8%

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

      1. mul-1-neg 35.8%

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

      2. associate-/l/ 41.7%

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

      3. distribute-neg-frac2 41.7%

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

   8. Simplified 41.7%

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

   if -8e20 < z < 4.6000000000000002e-24

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0 61.7%

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

      1. *-un-lft-identity 61.7%

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

      2. times-frac 63.4%

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

   5. Applied egg-rr 63.4%

      \[\leadsto \color{blue}{\frac{1}{t} \cdot \frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+20} \lor \neg \left(z \leq 4.6 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{x}{z}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.1e-135)
   (* (/ x y) (/ 1.0 t))
   (if (<= t 3.7e-135) (/ (/ x z) (- y)) (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.1e-135) {
		tmp = (x / y) * (1.0 / t);
	} else if (t <= 3.7e-135) {
		tmp = (x / z) / -y;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.1d-135)) then
        tmp = (x / y) * (1.0d0 / t)
    else if (t <= 3.7d-135) then
        tmp = (x / z) / -y
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.1e-135) {
		tmp = (x / y) * (1.0 / t);
	} else if (t <= 3.7e-135) {
		tmp = (x / z) / -y;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.1e-135:
		tmp = (x / y) * (1.0 / t)
	elif t <= 3.7e-135:
		tmp = (x / z) / -y
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.1e-135)
		tmp = Float64(Float64(x / y) * Float64(1.0 / t));
	elseif (t <= 3.7e-135)
		tmp = Float64(Float64(x / z) / Float64(-y));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.1e-135)
		tmp = (x / y) * (1.0 / t);
	elseif (t <= 3.7e-135)
		tmp = (x / z) / -y;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.1e-135], N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-135], N[(N[(x / z), $MachinePrecision] / (-y)), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.1000000000000001e-135

   1. Initial program 89.7%

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

   3. Taylor expanded in z around 0 45.7%

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

      1. *-un-lft-identity 45.7%

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

      2. times-frac 45.8%

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

   5. Applied egg-rr 45.8%

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

   if -5.1000000000000001e-135 < t < 3.6999999999999997e-135

   1. Initial program 90.9%

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

   3. Taylor expanded in t around 0 78.1%

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

      1. associate-*r/ 78.1%

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

      2. neg-mul-1 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in z around 0 41.7%

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

      1. mul-1-neg 41.7%

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

      2. associate-/l/ 45.1%

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

      3. distribute-neg-frac2 45.1%

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

   8. Simplified 45.1%

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

   if 3.6999999999999997e-135 < t

   1. Initial program 84.1%

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

   3. Taylor expanded in t around inf 64.4%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{x}{z}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e-88)
   (/ (/ x y) (- t z))
   (if (<= y 6.4e-61) (/ x (* z (- z t))) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-88) {
		tmp = (x / y) / (t - z);
	} else if (y <= 6.4e-61) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d-88)) then
        tmp = (x / y) / (t - z)
    else if (y <= 6.4d-61) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-88) {
		tmp = (x / y) / (t - z);
	} else if (y <= 6.4e-61) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e-88:
		tmp = (x / y) / (t - z)
	elif y <= 6.4e-61:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e-88)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 6.4e-61)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e-88)
		tmp = (x / y) / (t - z);
	elseif (y <= 6.4e-61)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e-88], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-61], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000004e-88

   1. Initial program 87.0%

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

   3. Taylor expanded in y around inf 75.8%

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

      1. associate-/r* 78.9%

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

   5. Simplified 78.9%

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

   if -2.50000000000000004e-88 < y < 6.4000000000000003e-61

   1. Initial program 91.2%

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

   3. Taylor expanded in y around 0 77.2%

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

      1. associate-*r/ 77.2%

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

      2. neg-mul-1 77.2%

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

   5. Simplified 77.2%

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

   if 6.4000000000000003e-61 < y

   1. Initial program 85.6%

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

      1. associate-/l/ 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in t around inf 58.8%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if t < -1.6e-115

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 55.7%

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

      1. associate-/r* 55.7%

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

   5. Simplified 55.7%

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

   if -1.6e-115 < t < 6.19999999999999986e32

   1. Initial program 89.8%

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

      1. associate-/r* 99.0%

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

      2. div-inv 98.9%

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

   4. Applied egg-rr 98.9%

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

      1. un-div-inv 99.0%

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

      2. clear-num 98.5%

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

   6. Applied egg-rr 98.5%

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

   7. Taylor expanded in t around 0 73.1%

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

      1. associate-*r/ 73.1%

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

      2. times-frac 82.2%

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

      3. associate-*l/ 82.2%

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

      4. mul-1-neg 82.2%

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

   9. Simplified 82.2%

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

   if 6.19999999999999986e32 < t

   1. Initial program 81.4%

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

      1. associate-/l/ 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in t around inf 90.9%

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

4. Final simplification 73.3%

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

Alternative 8: 52.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+20} \lor \neg \left(z \leq 5 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.12e+20) (not (<= z 5e-24))) (/ (/ x z) (- y)) (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.12e+20) || !(z <= 5e-24)) {
		tmp = (x / z) / -y;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.12d+20)) .or. (.not. (z <= 5d-24))) then
        tmp = (x / z) / -y
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.12e+20) || !(z <= 5e-24)) {
		tmp = (x / z) / -y;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.12e+20) or not (z <= 5e-24):
		tmp = (x / z) / -y
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.12e+20) || !(z <= 5e-24))
		tmp = Float64(Float64(x / z) / Float64(-y));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.12e+20) || ~((z <= 5e-24)))
		tmp = (x / z) / -y;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.12e+20], N[Not[LessEqual[z, 5e-24]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / (-y)), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12e20 or 4.9999999999999998e-24 < z

   1. Initial program 82.8%

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

   3. Taylor expanded in t around 0 69.1%

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

      1. associate-*r/ 69.1%

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

      2. neg-mul-1 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in z around 0 35.8%

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

      1. mul-1-neg 35.8%

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

      2. associate-/l/ 41.7%

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

      3. distribute-neg-frac2 41.7%

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

   8. Simplified 41.7%

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

   if -1.12e20 < z < 4.9999999999999998e-24

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0 61.7%

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

      1. associate-/r* 62.9%

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

   5. Simplified 62.9%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+20} \lor \neg \left(z \leq 5 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-115}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e-115)
   (/ (- x) (* z t))
   (if (<= z 5e-24) (/ (/ x t) y) (/ x (* z (- y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e-115) {
		tmp = -x / (z * t);
	} else if (z <= 5e-24) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (z * -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.3d-115)) then
        tmp = -x / (z * t)
    else if (z <= 5d-24) then
        tmp = (x / t) / y
    else
        tmp = x / (z * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e-115) {
		tmp = -x / (z * t);
	} else if (z <= 5e-24) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (z * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e-115:
		tmp = -x / (z * t)
	elif z <= 5e-24:
		tmp = (x / t) / y
	else:
		tmp = x / (z * -y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e-115)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 5e-24)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x / Float64(z * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.3e-115)
		tmp = -x / (z * t);
	elseif (z <= 5e-24)
		tmp = (x / t) / y;
	else
		tmp = x / (z * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e-115], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-24], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.29999999999999985e-115

   1. Initial program 85.6%

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

      1. associate-/l/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf 51.0%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. associate-*r/ 39.4%

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

      2. mul-1-neg 39.4%

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

   8. Simplified 39.4%

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

   if -2.29999999999999985e-115 < z < 4.9999999999999998e-24

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 71.6%

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

      1. associate-/r* 73.2%

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

   5. Simplified 73.2%

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

   if 4.9999999999999998e-24 < z

   1. Initial program 85.0%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 78.8%

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

      1. associate-*r/ 78.8%

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

      2. neg-mul-1 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in z around 0 31.6%

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

      1. associate-*r/ 31.6%

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

      2. mul-1-neg 31.6%

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

      3. *-commutative 31.6%

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

   10. Simplified 31.6%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-115}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+121} \lor \neg \left(z \leq 1.05 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9e+121) (not (<= z 1.05e+30))) (/ x (* y z)) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+121) || !(z <= 1.05e+30)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.9d+121)) .or. (.not. (z <= 1.05d+30))) then
        tmp = x / (y * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+121) || !(z <= 1.05e+30)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.9e+121) or not (z <= 1.05e+30):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.9e+121) || !(z <= 1.05e+30))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.9e+121) || ~((z <= 1.05e+30)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.9e+121], N[Not[LessEqual[z, 1.05e+30]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8999999999999999e121 or 1.05e30 < z

   1. Initial program 76.9%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 86.2%

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

      1. associate-*r/ 86.2%

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

      2. neg-mul-1 86.2%

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

   7. Simplified 86.2%

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

      1. div-inv 86.1%

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

      2. associate-/l* 70.7%

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

      3. add-sqr-sqrt 28.9%

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

      4. sqrt-unprod 55.2%

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

      5. sqr-neg 55.2%

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

      6. sqrt-unprod 34.9%

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

      7. add-sqr-sqrt 57.0%

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

   9. Applied egg-rr 57.0%

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

       1. associate-/r* 57.1%

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

       2. associate-*r/ 57.1%

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

       3. associate-*l/ 57.1%

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

       4. *-rgt-identity 57.1%

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

   11. Simplified 57.1%

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

   12. Taylor expanded in z around 0 33.5%

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

       1. *-commutative 33.5%

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

   14. Simplified 33.5%

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

   if -2.8999999999999999e121 < z < 1.05e30

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0 52.9%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+121} \lor \neg \left(z \leq 1.05 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+121} \lor \neg \left(z \leq 4.2 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9e+121) (not (<= z 4.2e+30))) (/ x (* y z)) (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+121) || !(z <= 4.2e+30)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.9d+121)) .or. (.not. (z <= 4.2d+30))) then
        tmp = x / (y * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+121) || !(z <= 4.2e+30)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.9e+121) or not (z <= 4.2e+30):
		tmp = x / (y * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.9e+121) || !(z <= 4.2e+30))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.9e+121) || ~((z <= 4.2e+30)))
		tmp = x / (y * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.9e+121], N[Not[LessEqual[z, 4.2e+30]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8999999999999999e121 or 4.2e30 < z

   1. Initial program 76.9%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 86.2%

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

      1. associate-*r/ 86.2%

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

      2. neg-mul-1 86.2%

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

   7. Simplified 86.2%

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

      1. div-inv 86.1%

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

      2. associate-/l* 70.7%

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

      3. add-sqr-sqrt 28.9%

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

      4. sqrt-unprod 55.2%

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

      5. sqr-neg 55.2%

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

      6. sqrt-unprod 34.9%

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

      7. add-sqr-sqrt 57.0%

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

   9. Applied egg-rr 57.0%

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

       1. associate-/r* 57.1%

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

       2. associate-*r/ 57.1%

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

       3. associate-*l/ 57.1%

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

       4. *-rgt-identity 57.1%

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

   11. Simplified 57.1%

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

   12. Taylor expanded in z around 0 33.5%

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

       1. *-commutative 33.5%

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

   14. Simplified 33.5%

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

   if -2.8999999999999999e121 < z < 4.2e30

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0 52.9%

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

      1. associate-/r* 53.8%

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

   5. Simplified 53.8%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+121} \lor \neg \left(z \leq 4.2 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1.3e-90

   1. Initial program 87.3%

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

   3. Taylor expanded in y around inf 73.9%

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

      1. *-commutative 73.9%

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

   5. Simplified 73.9%

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

   if -1.3e-90 < y

   1. Initial program 88.6%

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

   3. Taylor expanded in t around inf 56.9%

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

4. Final simplification 61.9%

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

Alternative 13: 64.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.15 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.15e-29) (/ x (* y (- t z))) (/ (/ x t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.15e-29) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 2.15d-29) then
        tmp = x / (y * (t - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.15e-29) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 2.15e-29:
		tmp = x / (y * (t - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.15e-29)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 2.15e-29)
		tmp = x / (y * (t - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.15e-29], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.1499999999999999e-29

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 53.8%

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

      1. *-commutative 53.8%

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

   5. Simplified 53.8%

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

   if 2.1499999999999999e-29 < t

   1. Initial program 85.5%

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

      1. associate-/l/ 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in t around inf 87.1%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.15 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1.3e-90

   1. Initial program 87.3%

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

   3. Taylor expanded in y around inf 73.9%

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

      1. associate-/r* 76.9%

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

   5. Simplified 76.9%

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

   if -1.3e-90 < y

   1. Initial program 88.6%

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

      1. associate-/l/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 58.3%

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

4. Final simplification 63.8%

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

Alternative 15: 67.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1.3e-90

   1. Initial program 87.3%

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

   3. Taylor expanded in y around inf 73.9%

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

      1. associate-/r* 76.9%

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

   5. Simplified 76.9%

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

   if -1.3e-90 < y

   1. Initial program 88.6%

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

      1. associate-/r* 99.2%

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

      2. div-inv 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in t around inf 56.9%

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

      1. *-commutative 56.9%

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

      2. associate-/r* 61.4%

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

   7. Simplified 61.4%

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

4. Final simplification 65.9%

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

Alternative 16: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.2%

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

   1. associate-/l/ 97.3%

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

3. Simplified 97.3%

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

5. Final simplification 97.3%

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

Alternative 17: 39.0% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.2%

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

3. Taylor expanded in z around 0 38.8%

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

4. Final simplification 38.8%

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

Developer target: 88.1% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

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

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

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