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

Percentage Accurate: 88.7% → 96.8%

Time: 13.1s

Alternatives: 18

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: 88.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.5%

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

   1. associate-/r* 97.7%

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

   2. div-inv 97.6%

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

3. Applied egg-rr 97.6%

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

   1. un-div-inv 97.7%

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

5. Applied egg-rr 97.7%

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

6. Final simplification 97.7%

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

Alternative 2: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-187}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z (- y z)))))
   (if (<= t -8.2e-187)
     (/ (/ x (- t z)) y)
     (if (<= t 2.4e-141)
       t_1
       (if (<= t 5.6e-63)
         (/ (/ x (- y z)) t)
         (if (<= t 2.7e-11)
           t_1
           (if (<= t 2e+220) (/ x (* (- y z) t)) (/ (/ x t) (- y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * (y - z));
	double tmp;
	if (t <= -8.2e-187) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 2.4e-141) {
		tmp = t_1;
	} else if (t <= 5.6e-63) {
		tmp = (x / (y - z)) / t;
	} else if (t <= 2.7e-11) {
		tmp = t_1;
	} else if (t <= 2e+220) {
		tmp = x / ((y - 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) :: t_1
    real(8) :: tmp
    t_1 = -x / (z * (y - z))
    if (t <= (-8.2d-187)) then
        tmp = (x / (t - z)) / y
    else if (t <= 2.4d-141) then
        tmp = t_1
    else if (t <= 5.6d-63) then
        tmp = (x / (y - z)) / t
    else if (t <= 2.7d-11) then
        tmp = t_1
    else if (t <= 2d+220) then
        tmp = x / ((y - 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 t_1 = -x / (z * (y - z));
	double tmp;
	if (t <= -8.2e-187) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 2.4e-141) {
		tmp = t_1;
	} else if (t <= 5.6e-63) {
		tmp = (x / (y - z)) / t;
	} else if (t <= 2.7e-11) {
		tmp = t_1;
	} else if (t <= 2e+220) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / (z * (y - z))
	tmp = 0
	if t <= -8.2e-187:
		tmp = (x / (t - z)) / y
	elif t <= 2.4e-141:
		tmp = t_1
	elif t <= 5.6e-63:
		tmp = (x / (y - z)) / t
	elif t <= 2.7e-11:
		tmp = t_1
	elif t <= 2e+220:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * Float64(y - z)))
	tmp = 0.0
	if (t <= -8.2e-187)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 2.4e-141)
		tmp = t_1;
	elseif (t <= 5.6e-63)
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	elseif (t <= 2.7e-11)
		tmp = t_1;
	elseif (t <= 2e+220)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * (y - z));
	tmp = 0.0;
	if (t <= -8.2e-187)
		tmp = (x / (t - z)) / y;
	elseif (t <= 2.4e-141)
		tmp = t_1;
	elseif (t <= 5.6e-63)
		tmp = (x / (y - z)) / t;
	elseif (t <= 2.7e-11)
		tmp = t_1;
	elseif (t <= 2e+220)
		tmp = x / ((y - z) * t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e-187], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 2.4e-141], t$95$1, If[LessEqual[t, 5.6e-63], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.7e-11], t$95$1, If[LessEqual[t, 2e+220], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.2000000000000004e-187

   1. Initial program 94.3%

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

   2. Taylor expanded in y around inf 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-/r* 77.1%

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

   4. Simplified 77.1%

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

   if -8.2000000000000004e-187 < t < 2.4000000000000001e-141 or 5.6000000000000005e-63 < t < 2.70000000000000005e-11

   1. Initial program 89.3%

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

   2. Taylor expanded in t around 0 77.7%

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

      1. associate-*r/ 77.7%

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

      2. neg-mul-1 77.7%

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

   4. Simplified 77.7%

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

   if 2.4000000000000001e-141 < t < 5.6000000000000005e-63

   1. Initial program 99.9%

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

      1. associate-/r* 92.0%

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

      2. div-inv 91.7%

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

   3. Applied egg-rr 91.7%

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

      1. un-div-inv 92.0%

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

   5. Applied egg-rr 92.0%

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

   6. Taylor expanded in t around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-/r* 68.0%

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

   8. Simplified 68.0%

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

   if 2.70000000000000005e-11 < t < 2e220

   1. Initial program 93.7%

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

   2. Taylor expanded in t around inf 89.6%

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

   if 2e220 < t

   1. Initial program 74.1%

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

      1. associate-/r* 94.3%

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

      2. div-inv 94.4%

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

   3. Applied egg-rr 94.4%

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

   4. Taylor expanded in t around inf 74.1%

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

      1. associate-/r* 92.1%

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

   6. Simplified 92.1%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-187}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-141}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-11}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 3: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-199}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y - z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e-27)
   (/ (/ x (- t z)) y)
   (if (<= y -1.8e-141)
     (/ x (* (- y z) t))
     (if (<= y 2.9e-199)
       (/ (- (/ x z)) (- t z))
       (/ 1.0 (* t (/ (- y z) x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-27) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -1.8e-141) {
		tmp = x / ((y - z) * t);
	} else if (y <= 2.9e-199) {
		tmp = -(x / z) / (t - z);
	} else {
		tmp = 1.0 / (t * ((y - z) / x));
	}
	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 <= (-1.6d-27)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-1.8d-141)) then
        tmp = x / ((y - z) * t)
    else if (y <= 2.9d-199) then
        tmp = -(x / z) / (t - z)
    else
        tmp = 1.0d0 / (t * ((y - z) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-27) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -1.8e-141) {
		tmp = x / ((y - z) * t);
	} else if (y <= 2.9e-199) {
		tmp = -(x / z) / (t - z);
	} else {
		tmp = 1.0 / (t * ((y - z) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e-27:
		tmp = (x / (t - z)) / y
	elif y <= -1.8e-141:
		tmp = x / ((y - z) * t)
	elif y <= 2.9e-199:
		tmp = -(x / z) / (t - z)
	else:
		tmp = 1.0 / (t * ((y - z) / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e-27)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -1.8e-141)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (y <= 2.9e-199)
		tmp = Float64(Float64(-Float64(x / z)) / Float64(t - z));
	else
		tmp = Float64(1.0 / Float64(t * Float64(Float64(y - z) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.6e-27)
		tmp = (x / (t - z)) / y;
	elseif (y <= -1.8e-141)
		tmp = x / ((y - z) * t);
	elseif (y <= 2.9e-199)
		tmp = -(x / z) / (t - z);
	else
		tmp = 1.0 / (t * ((y - z) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e-27], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1.8e-141], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-199], N[((-N[(x / z), $MachinePrecision]) / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(t * N[(N[(y - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.59999999999999995e-27

   1. Initial program 90.5%

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

   2. Taylor expanded in y around inf 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-/r* 89.8%

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

   4. Simplified 89.8%

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

   if -1.59999999999999995e-27 < y < -1.80000000000000007e-141

   1. Initial program 99.5%

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

   2. Taylor expanded in t around inf 96.1%

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

   if -1.80000000000000007e-141 < y < 2.9e-199

   1. Initial program 86.2%

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

      1. associate-/r* 98.3%

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

      2. div-inv 98.1%

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

   3. Applied egg-rr 98.1%

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

      1. un-div-inv 98.3%

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

   5. Applied egg-rr 98.3%

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

   6. Taylor expanded in y around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. neg-mul-1 86.5%

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

   8. Simplified 86.5%

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

   if 2.9e-199 < y

   1. Initial program 93.5%

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

      1. associate-/r* 97.0%

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

      2. div-inv 96.9%

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

   3. Applied egg-rr 96.9%

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

      1. clear-num 96.5%

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

      2. frac-times 96.1%

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

      3. metadata-eval 96.1%

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

   5. Applied egg-rr 96.1%

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

   6. Taylor expanded in t around inf 59.3%

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

      1. associate-*r/ 67.7%

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

   8. Simplified 67.7%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-199}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y - z}{x}}\\ \end{array} \]

Alternative 4: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-203}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.5e-27)
   (/ (/ x (- t z)) y)
   (if (<= y -2.9e-141)
     (/ x (* (- y z) t))
     (if (<= y 4.2e-203) (/ (- (/ x z)) (- t z)) (/ (/ x (- y z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e-27) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -2.9e-141) {
		tmp = x / ((y - z) * t);
	} else if (y <= 4.2e-203) {
		tmp = -(x / z) / (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 <= (-9.5d-27)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-2.9d-141)) then
        tmp = x / ((y - z) * t)
    else if (y <= 4.2d-203) then
        tmp = -(x / z) / (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 <= -9.5e-27) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -2.9e-141) {
		tmp = x / ((y - z) * t);
	} else if (y <= 4.2e-203) {
		tmp = -(x / z) / (t - z);
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.5e-27:
		tmp = (x / (t - z)) / y
	elif y <= -2.9e-141:
		tmp = x / ((y - z) * t)
	elif y <= 4.2e-203:
		tmp = -(x / z) / (t - z)
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.5e-27)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -2.9e-141)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (y <= 4.2e-203)
		tmp = Float64(Float64(-Float64(x / z)) / 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 <= -9.5e-27)
		tmp = (x / (t - z)) / y;
	elseif (y <= -2.9e-141)
		tmp = x / ((y - z) * t);
	elseif (y <= 4.2e-203)
		tmp = -(x / z) / (t - z);
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.5e-27], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2.9e-141], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-203], N[((-N[(x / z), $MachinePrecision]) / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.50000000000000037e-27

   1. Initial program 90.5%

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

   2. Taylor expanded in y around inf 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-/r* 89.8%

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

   4. Simplified 89.8%

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

   if -9.50000000000000037e-27 < y < -2.9e-141

   1. Initial program 99.5%

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

   2. Taylor expanded in t around inf 96.1%

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

   if -2.9e-141 < y < 4.20000000000000004e-203

   1. Initial program 85.7%

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

      1. associate-/r* 98.2%

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

      2. div-inv 98.1%

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

   3. Applied egg-rr 98.1%

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

      1. un-div-inv 98.2%

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

   5. Applied egg-rr 98.2%

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

   6. Taylor expanded in y around 0 86.0%

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

      1. associate-*r/ 86.0%

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

      2. neg-mul-1 86.0%

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

   8. Simplified 86.0%

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

   if 4.20000000000000004e-203 < y

   1. Initial program 93.6%

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

      1. associate-/r* 97.0%

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

      2. div-inv 97.0%

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

   3. Applied egg-rr 97.0%

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

      1. un-div-inv 97.0%

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

   5. Applied egg-rr 97.0%

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

   6. Taylor expanded in t around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. associate-/r* 66.8%

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

   8. Simplified 66.8%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-203}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]

Alternative 5: 48.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-215}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* t (/ y x)))))
   (if (<= t -4.4e-124)
     t_1
     (if (<= t 1.12e-215)
       (/ (- x) (* y z))
       (if (<= t 1.32e+60) t_1 (- (/ x (* z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (t * (y / x));
	double tmp;
	if (t <= -4.4e-124) {
		tmp = t_1;
	} else if (t <= 1.12e-215) {
		tmp = -x / (y * z);
	} else if (t <= 1.32e+60) {
		tmp = t_1;
	} else {
		tmp = -(x / (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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / (t * (y / x))
    if (t <= (-4.4d-124)) then
        tmp = t_1
    else if (t <= 1.12d-215) then
        tmp = -x / (y * z)
    else if (t <= 1.32d+60) then
        tmp = t_1
    else
        tmp = -(x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (t * (y / x));
	double tmp;
	if (t <= -4.4e-124) {
		tmp = t_1;
	} else if (t <= 1.12e-215) {
		tmp = -x / (y * z);
	} else if (t <= 1.32e+60) {
		tmp = t_1;
	} else {
		tmp = -(x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 / (t * (y / x))
	tmp = 0
	if t <= -4.4e-124:
		tmp = t_1
	elif t <= 1.12e-215:
		tmp = -x / (y * z)
	elif t <= 1.32e+60:
		tmp = t_1
	else:
		tmp = -(x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(t * Float64(y / x)))
	tmp = 0.0
	if (t <= -4.4e-124)
		tmp = t_1;
	elseif (t <= 1.12e-215)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (t <= 1.32e+60)
		tmp = t_1;
	else
		tmp = Float64(-Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / (t * (y / x));
	tmp = 0.0;
	if (t <= -4.4e-124)
		tmp = t_1;
	elseif (t <= 1.12e-215)
		tmp = -x / (y * z);
	elseif (t <= 1.32e+60)
		tmp = t_1;
	else
		tmp = -(x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e-124], t$95$1, If[LessEqual[t, 1.12e-215], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.32e+60], t$95$1, (-N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision])]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.3999999999999998e-124 or 1.12e-215 < t < 1.32e60

   1. Initial program 96.9%

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

   2. Taylor expanded in z around 0 53.5%

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

      1. clear-num 54.6%

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

      2. inv-pow 54.6%

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

      3. *-commutative 54.6%

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

      4. associate-/l* 55.8%

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

   4. Applied egg-rr 55.8%

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

      1. unpow-1 55.8%

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

      2. associate-/r/ 56.2%

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

   6. Simplified 56.2%

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

   if -4.3999999999999998e-124 < t < 1.12e-215

   1. Initial program 84.2%

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

   2. Taylor expanded in y around inf 60.8%

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

      1. *-commutative 60.8%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in t around 0 55.6%

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

      1. associate-*r/ 55.6%

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

      2. neg-mul-1 55.6%

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

      3. *-commutative 55.6%

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

   7. Simplified 55.6%

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

   if 1.32e60 < t

   1. Initial program 86.7%

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

      1. associate-/r* 98.0%

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

      2. div-inv 98.0%

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

   3. Applied egg-rr 98.0%

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

   4. Taylor expanded in t around inf 86.6%

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

      1. associate-/r* 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in y around 0 62.6%

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

      1. associate-*r/ 62.6%

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

      2. neg-mul-1 62.6%

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

   9. Simplified 62.6%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-124}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-215}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+60}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \end{array} \]

Alternative 6: 69.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+219}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+268}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 7.5e-78)
   (/ (/ x (- t z)) y)
   (if (<= t 4e+219)
     (/ x (* (- y z) t))
     (if (<= t 7e+268) (/ (/ x t) (- y z)) (/ (/ x (- y z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 7.5e-78) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 4e+219) {
		tmp = x / ((y - z) * t);
	} else if (t <= 7e+268) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 7.5d-78) then
        tmp = (x / (t - z)) / y
    else if (t <= 4d+219) then
        tmp = x / ((y - z) * t)
    else if (t <= 7d+268) then
        tmp = (x / t) / (y - z)
    else
        tmp = (x / (y - z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 7.5e-78) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 4e+219) {
		tmp = x / ((y - z) * t);
	} else if (t <= 7e+268) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 7.5e-78:
		tmp = (x / (t - z)) / y
	elif t <= 4e+219:
		tmp = x / ((y - z) * t)
	elif t <= 7e+268:
		tmp = (x / t) / (y - z)
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 7.5e-78)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 4e+219)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (t <= 7e+268)
		tmp = Float64(Float64(x / t) / Float64(y - 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 (t <= 7.5e-78)
		tmp = (x / (t - z)) / y;
	elseif (t <= 4e+219)
		tmp = x / ((y - z) * t);
	elseif (t <= 7e+268)
		tmp = (x / t) / (y - z);
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 7.5e-78], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4e+219], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+268], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < 7.50000000000000041e-78

   1. Initial program 92.5%

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

   2. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. associate-/r* 73.5%

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

   4. Simplified 73.5%

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

   if 7.50000000000000041e-78 < t < 3.99999999999999986e219

   1. Initial program 93.8%

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

   2. Taylor expanded in t around inf 81.7%

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

   if 3.99999999999999986e219 < t < 6.99999999999999945e268

   1. Initial program 66.4%

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

      1. associate-/r* 91.0%

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

      2. div-inv 91.1%

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

   3. Applied egg-rr 91.1%

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

   4. Taylor expanded in t around inf 66.4%

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

      1. associate-/r* 95.5%

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

   6. Simplified 95.5%

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

   if 6.99999999999999945e268 < t

   1. Initial program 86.3%

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

      1. associate-/r* 99.6%

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

      2. div-inv 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. un-div-inv 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in t around inf 86.3%

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

      1. *-commutative 86.3%

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

      2. associate-/r* 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+219}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+268}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]

Alternative 7: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\frac{x}{z}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+86}:\\ \;\;\;\;\frac{t_1}{y - z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+128}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x z))))
   (if (<= z -4.3e+86)
     (/ t_1 (- y z))
     (if (<= z 6.8e+128) (/ x (* (- y z) (- t z))) (/ t_1 (- t z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -(x / z);
	double tmp;
	if (z <= -4.3e+86) {
		tmp = t_1 / (y - z);
	} else if (z <= 6.8e+128) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = t_1 / (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -(x / z)
    if (z <= (-4.3d+86)) then
        tmp = t_1 / (y - z)
    else if (z <= 6.8d+128) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = t_1 / (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -(x / z);
	double tmp;
	if (z <= -4.3e+86) {
		tmp = t_1 / (y - z);
	} else if (z <= 6.8e+128) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = t_1 / (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -(x / z)
	tmp = 0
	if z <= -4.3e+86:
		tmp = t_1 / (y - z)
	elif z <= 6.8e+128:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = t_1 / (t - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-Float64(x / z))
	tmp = 0.0
	if (z <= -4.3e+86)
		tmp = Float64(t_1 / Float64(y - z));
	elseif (z <= 6.8e+128)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(t_1 / Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -(x / z);
	tmp = 0.0;
	if (z <= -4.3e+86)
		tmp = t_1 / (y - z);
	elseif (z <= 6.8e+128)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = t_1 / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(x / z), $MachinePrecision])}, If[LessEqual[z, -4.3e+86], N[(t$95$1 / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+128], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3000000000000002e86

   1. Initial program 83.7%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in t around 0 83.6%

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

      1. associate-*r/ 83.6%

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

      2. *-commutative 83.6%

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

      3. times-frac 95.6%

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

      4. associate-*l/ 95.6%

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

      5. associate-*r/ 95.6%

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

      6. neg-mul-1 95.6%

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

   6. Simplified 95.6%

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

   if -4.3000000000000002e86 < z < 6.7999999999999997e128

   1. Initial program 94.8%

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

   if 6.7999999999999997e128 < z

   1. Initial program 86.6%

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

      1. associate-/r* 100.0%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 97.9%

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

      1. associate-*r/ 97.9%

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

      2. neg-mul-1 97.9%

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

   8. Simplified 97.9%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+86}:\\ \;\;\;\;\frac{-\frac{x}{z}}{y - z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+128}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \end{array} \]

Alternative 8: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-124}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-219}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.4e-124)
   (/ (/ x t) y)
   (if (<= t 1.12e-219)
     (/ (- x) (* y z))
     (if (<= t 4.8e+58) (/ x (* y t)) (- (/ x (* z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.4e-124) {
		tmp = (x / t) / y;
	} else if (t <= 1.12e-219) {
		tmp = -x / (y * z);
	} else if (t <= 4.8e+58) {
		tmp = x / (y * t);
	} else {
		tmp = -(x / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.4d-124)) then
        tmp = (x / t) / y
    else if (t <= 1.12d-219) then
        tmp = -x / (y * z)
    else if (t <= 4.8d+58) then
        tmp = x / (y * t)
    else
        tmp = -(x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.4e-124) {
		tmp = (x / t) / y;
	} else if (t <= 1.12e-219) {
		tmp = -x / (y * z);
	} else if (t <= 4.8e+58) {
		tmp = x / (y * t);
	} else {
		tmp = -(x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.4e-124:
		tmp = (x / t) / y
	elif t <= 1.12e-219:
		tmp = -x / (y * z)
	elif t <= 4.8e+58:
		tmp = x / (y * t)
	else:
		tmp = -(x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.4e-124)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 1.12e-219)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (t <= 4.8e+58)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = Float64(-Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.4e-124)
		tmp = (x / t) / y;
	elseif (t <= 1.12e-219)
		tmp = -x / (y * z);
	elseif (t <= 4.8e+58)
		tmp = x / (y * t);
	else
		tmp = -(x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.4e-124], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.12e-219], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+58], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], (-N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision])]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.4000000000000001e-124

   1. Initial program 96.4%

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

      1. associate-/r* 98.8%

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

      2. div-inv 98.6%

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

   3. Applied egg-rr 98.6%

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

      1. clear-num 98.7%

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

      2. frac-times 98.6%

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

      3. metadata-eval 98.6%

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

   5. Applied egg-rr 98.6%

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

   6. Taylor expanded in z around 0 59.3%

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

      1. associate-/r* 63.2%

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

   8. Simplified 63.2%

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

   if -3.4000000000000001e-124 < t < 1.12e-219

   1. Initial program 83.7%

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

   2. Taylor expanded in y around inf 59.5%

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

      1. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in t around 0 55.6%

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

      1. associate-*r/ 55.6%

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

      2. neg-mul-1 55.6%

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

      3. *-commutative 55.6%

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

   7. Simplified 55.6%

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

   if 1.12e-219 < t < 4.8e58

   1. Initial program 97.9%

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

   2. Taylor expanded in z around 0 42.9%

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

   if 4.8e58 < t

   1. Initial program 86.7%

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

      1. associate-/r* 98.0%

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

      2. div-inv 98.0%

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

   3. Applied egg-rr 98.0%

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

   4. Taylor expanded in t around inf 86.6%

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

      1. associate-/r* 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in y around 0 62.6%

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

      1. associate-*r/ 62.6%

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

      2. neg-mul-1 62.6%

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

   9. Simplified 62.6%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-124}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-219}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \end{array} \]

Alternative 9: 64.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-124} \lor \neg \left(t \leq 2.5 \cdot 10^{-220}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.8e-124) (not (<= t 2.5e-220)))
   (/ x (* (- y z) t))
   (/ (- x) (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.8e-124) || !(t <= 2.5e-220)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = -x / (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.8d-124)) .or. (.not. (t <= 2.5d-220))) then
        tmp = x / ((y - z) * t)
    else
        tmp = -x / (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.8e-124) || !(t <= 2.5e-220)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = -x / (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.8e-124) or not (t <= 2.5e-220):
		tmp = x / ((y - z) * t)
	else:
		tmp = -x / (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.8e-124) || !(t <= 2.5e-220))
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(-x) / Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.8e-124) || ~((t <= 2.5e-220)))
		tmp = x / ((y - z) * t);
	else
		tmp = -x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.8e-124], N[Not[LessEqual[t, 2.5e-220]], $MachinePrecision]], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.80000000000000012e-124 or 2.5000000000000001e-220 < t

   1. Initial program 94.0%

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

   2. Taylor expanded in t around inf 74.2%

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

   if -3.80000000000000012e-124 < t < 2.5000000000000001e-220

   1. Initial program 83.7%

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

   2. Taylor expanded in y around inf 59.5%

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

      1. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in t around 0 55.6%

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

      1. associate-*r/ 55.6%

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

      2. neg-mul-1 55.6%

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

      3. *-commutative 55.6%

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

   7. Simplified 55.6%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-124} \lor \neg \left(t \leq 2.5 \cdot 10^{-220}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \end{array} \]

Alternative 10: 67.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+86} \lor \neg \left(z \leq 1.7 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.5e+86) (not (<= z 1.7e+80)))
   (/ x (* z (- y z)))
   (/ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e+86) || !(z <= 1.7e+80)) {
		tmp = x / (z * (y - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8.5d+86)) .or. (.not. (z <= 1.7d+80))) then
        tmp = x / (z * (y - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e+86) || !(z <= 1.7e+80)) {
		tmp = x / (z * (y - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.5e+86) or not (z <= 1.7e+80):
		tmp = x / (z * (y - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.5e+86) || !(z <= 1.7e+80))
		tmp = Float64(x / Float64(z * Float64(y - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.5e+86) || ~((z <= 1.7e+80)))
		tmp = x / (z * (y - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.5e+86], N[Not[LessEqual[z, 1.7e+80]], $MachinePrecision]], N[(x / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000005e86 or 1.69999999999999996e80 < z

   1. Initial program 86.3%

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

   2. Taylor expanded in t around 0 85.2%

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

      1. associate-*r/ 85.2%

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

      2. neg-mul-1 85.2%

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

   4. Simplified 85.2%

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

      1. expm1-log1p-u 83.1%

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

      2. expm1-udef 75.3%

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

      3. add-sqr-sqrt 36.2%

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

      4. sqrt-unprod 69.8%

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

      5. sqr-neg 69.8%

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

      6. sqrt-unprod 39.2%

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

      7. add-sqr-sqrt 75.4%

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

   6. Applied egg-rr 75.4%

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

      1. expm1-def 75.3%

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

      2. expm1-log1p 75.3%

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

   8. Simplified 75.3%

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

   if -8.5000000000000005e86 < z < 1.69999999999999996e80

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 68.4%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+86} \lor \neg \left(z \leq 1.7 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 11: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.8 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+219}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.8e-39)
   (/ x (* y (- t z)))
   (if (<= t 1.8e+219) (/ x (* (- y z) t)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.8e-39) {
		tmp = x / (y * (t - z));
	} else if (t <= 1.8e+219) {
		tmp = x / ((y - 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 (t <= 2.8d-39) then
        tmp = x / (y * (t - z))
    else if (t <= 1.8d+219) then
        tmp = x / ((y - 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 (t <= 2.8e-39) {
		tmp = x / (y * (t - z));
	} else if (t <= 1.8e+219) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 2.8e-39:
		tmp = x / (y * (t - z))
	elif t <= 1.8e+219:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.8e-39)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 1.8e+219)
		tmp = Float64(x / Float64(Float64(y - 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 (t <= 2.8e-39)
		tmp = x / (y * (t - z));
	elseif (t <= 1.8e+219)
		tmp = x / ((y - z) * t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.8e-39], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+219], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 2.8000000000000001e-39

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

   4. Simplified 66.9%

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

   if 2.8000000000000001e-39 < t < 1.80000000000000003e219

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 84.3%

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

   if 1.80000000000000003e219 < t

   1. Initial program 74.1%

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

      1. associate-/r* 94.3%

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

      2. div-inv 94.4%

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

   3. Applied egg-rr 94.4%

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

   4. Taylor expanded in t around inf 74.1%

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

      1. associate-/r* 92.1%

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

   6. Simplified 92.1%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.8 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+219}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 12: 65.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.4 \cdot 10^{-80}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+219}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 4.4e-80)
   (/ (/ x y) (- t z))
   (if (<= t 5.2e+219) (/ x (* (- y z) t)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.4e-80) {
		tmp = (x / y) / (t - z);
	} else if (t <= 5.2e+219) {
		tmp = x / ((y - 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 (t <= 4.4d-80) then
        tmp = (x / y) / (t - z)
    else if (t <= 5.2d+219) then
        tmp = x / ((y - 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 (t <= 4.4e-80) {
		tmp = (x / y) / (t - z);
	} else if (t <= 5.2e+219) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 4.4e-80:
		tmp = (x / y) / (t - z)
	elif t <= 5.2e+219:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 4.4e-80)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 5.2e+219)
		tmp = Float64(x / Float64(Float64(y - 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 (t <= 4.4e-80)
		tmp = (x / y) / (t - z);
	elseif (t <= 5.2e+219)
		tmp = x / ((y - z) * t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 4.4e-80], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+219], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 4.4000000000000002e-80

   1. Initial program 92.4%

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

      1. associate-/r* 97.5%

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

      2. div-inv 97.5%

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

   3. Applied egg-rr 97.5%

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

      1. un-div-inv 97.5%

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

   5. Applied egg-rr 97.5%

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

   6. Taylor expanded in y around inf 67.3%

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

      1. associate-/r* 68.3%

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

   8. Simplified 68.3%

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

   if 4.4000000000000002e-80 < t < 5.1999999999999999e219

   1. Initial program 93.9%

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

   2. Taylor expanded in t around inf 80.6%

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

   if 5.1999999999999999e219 < t

   1. Initial program 74.1%

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

      1. associate-/r* 94.3%

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

      2. div-inv 94.4%

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

   3. Applied egg-rr 94.4%

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

   4. Taylor expanded in t around inf 74.1%

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

      1. associate-/r* 92.1%

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

   6. Simplified 92.1%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.4 \cdot 10^{-80}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+219}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 13: 69.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+221}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 3e-78)
   (/ (/ x (- t z)) y)
   (if (<= t 6.4e+221) (/ x (* (- y z) t)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3e-78) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 6.4e+221) {
		tmp = x / ((y - 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 (t <= 3d-78) then
        tmp = (x / (t - z)) / y
    else if (t <= 6.4d+221) then
        tmp = x / ((y - 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 (t <= 3e-78) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 6.4e+221) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 3e-78:
		tmp = (x / (t - z)) / y
	elif t <= 6.4e+221:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3e-78)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 6.4e+221)
		tmp = Float64(x / Float64(Float64(y - 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 (t <= 3e-78)
		tmp = (x / (t - z)) / y;
	elseif (t <= 6.4e+221)
		tmp = x / ((y - z) * t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 3e-78], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 6.4e+221], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 2.99999999999999988e-78

   1. Initial program 92.5%

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

   2. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. associate-/r* 73.5%

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

   4. Simplified 73.5%

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

   if 2.99999999999999988e-78 < t < 6.4e221

   1. Initial program 93.8%

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

   2. Taylor expanded in t around inf 81.7%

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

   if 6.4e221 < t

   1. Initial program 74.1%

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

      1. associate-/r* 94.3%

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

      2. div-inv 94.4%

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

   3. Applied egg-rr 94.4%

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

   4. Taylor expanded in t around inf 74.1%

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

      1. associate-/r* 92.1%

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

   6. Simplified 92.1%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+221}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 14: 50.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{-69} \lor \neg \left(z \leq 10500000000000\right):\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.55e-69) (not (<= z 10500000000000.0)))
   (- (/ x (* z t)))
   (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.55e-69) || !(z <= 10500000000000.0)) {
		tmp = -(x / (z * t));
	} 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 <= (-3.55d-69)) .or. (.not. (z <= 10500000000000.0d0))) then
        tmp = -(x / (z * t))
    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 <= -3.55e-69) || !(z <= 10500000000000.0)) {
		tmp = -(x / (z * t));
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.55e-69) or not (z <= 10500000000000.0):
		tmp = -(x / (z * t))
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.55e-69) || !(z <= 10500000000000.0))
		tmp = Float64(-Float64(x / Float64(z * t)));
	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 <= -3.55e-69) || ~((z <= 10500000000000.0)))
		tmp = -(x / (z * t));
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.55e-69], N[Not[LessEqual[z, 10500000000000.0]], $MachinePrecision]], (-N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5499999999999999e-69 or 1.05e13 < z

   1. Initial program 89.7%

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

      1. associate-/r* 99.8%

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

      2. div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in t around inf 44.5%

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

      1. associate-/r* 44.2%

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

   6. Simplified 44.2%

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

   7. Taylor expanded in y around 0 41.6%

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

      1. associate-*r/ 41.6%

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

      2. neg-mul-1 41.6%

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

   9. Simplified 41.6%

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

   if -3.5499999999999999e-69 < z < 1.05e13

   1. Initial program 94.0%

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

      1. associate-/r* 94.8%

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

      2. div-inv 94.7%

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

   3. Applied egg-rr 94.7%

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

      1. clear-num 93.1%

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

      2. frac-times 93.2%

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

      3. metadata-eval 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in z around 0 69.1%

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

      1. associate-/r* 69.5%

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

   8. Simplified 69.5%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{-69} \lor \neg \left(z \leq 10500000000000\right):\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 15: 46.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+59} \lor \neg \left(z \leq 1.65 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.55e+59) (not (<= z 1.65e+48))) (/ x (* z t)) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55e+59) || !(z <= 1.65e+48)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.55d+59)) .or. (.not. (z <= 1.65d+48))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55e+59) || !(z <= 1.65e+48)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.55e+59) or not (z <= 1.65e+48):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.55e+59) || !(z <= 1.65e+48))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.55e+59) || ~((z <= 1.65e+48)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.55e+59], N[Not[LessEqual[z, 1.65e+48]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55000000000000007e59 or 1.65000000000000011e48 < z

   1. Initial program 87.9%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in t around inf 43.4%

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

      1. associate-/r* 42.6%

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

   6. Simplified 42.6%

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

   7. Taylor expanded in y around 0 40.8%

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

      1. associate-*r/ 40.8%

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

      2. neg-mul-1 40.8%

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

   9. Simplified 40.8%

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

       1. expm1-log1p-u 40.3%

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

       2. expm1-udef 60.2%

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

       3. add-sqr-sqrt 28.7%

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

       4. sqrt-unprod 57.6%

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

       5. sqr-neg 57.6%

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

       6. sqrt-unprod 31.7%

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

       7. add-sqr-sqrt 60.4%

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

       8. *-commutative 60.4%

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

   11. Applied egg-rr 60.4%

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

       1. expm1-def 38.0%

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

       2. expm1-log1p 38.2%

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

   13. Simplified 38.2%

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

   if -1.55000000000000007e59 < z < 1.65000000000000011e48

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 59.2%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+59} \lor \neg \left(z \leq 1.65 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 16: 49.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+82} \lor \neg \left(z \leq 9 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.15e+82) (not (<= z 9e+51))) (/ x (* z t)) (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.15e+82) || !(z <= 9e+51)) {
		tmp = x / (z * t);
	} 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 <= (-2.15d+82)) .or. (.not. (z <= 9d+51))) then
        tmp = x / (z * t)
    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 <= -2.15e+82) || !(z <= 9e+51)) {
		tmp = x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.15e+82) or not (z <= 9e+51):
		tmp = x / (z * t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.15e+82) || !(z <= 9e+51))
		tmp = Float64(x / Float64(z * t));
	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 <= -2.15e+82) || ~((z <= 9e+51)))
		tmp = x / (z * t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.15e+82], N[Not[LessEqual[z, 9e+51]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15000000000000007e82 or 8.9999999999999999e51 < z

   1. Initial program 88.1%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in t around inf 45.2%

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

      1. associate-/r* 43.5%

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

   6. Simplified 43.5%

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

   7. Taylor expanded in y around 0 42.4%

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

      1. associate-*r/ 42.4%

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

      2. neg-mul-1 42.4%

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

   9. Simplified 42.4%

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

       1. expm1-log1p-u 42.0%

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

       2. expm1-udef 62.8%

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

       3. add-sqr-sqrt 29.9%

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

       4. sqrt-unprod 60.1%

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

       5. sqr-neg 60.1%

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

       6. sqrt-unprod 33.2%

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

       7. add-sqr-sqrt 63.0%

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

       8. *-commutative 63.0%

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

   11. Applied egg-rr 63.0%

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

       1. expm1-def 39.6%

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

       2. expm1-log1p 39.7%

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

   13. Simplified 39.7%

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

   if -2.15000000000000007e82 < z < 8.9999999999999999e51

   1. Initial program 94.1%

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

      1. associate-/r* 95.9%

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

      2. div-inv 95.9%

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

   3. Applied egg-rr 95.9%

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

      1. clear-num 94.6%

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

      2. frac-times 94.7%

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

      3. metadata-eval 94.7%

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

   5. Applied egg-rr 94.7%

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

   6. Taylor expanded in z around 0 57.2%

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

      1. associate-/r* 59.4%

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

   8. Simplified 59.4%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+82} \lor \neg \left(z \leq 9 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 17: 64.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.65 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.65e-37) (/ x (* y (- t z))) (/ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.65e-37) {
		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 (t <= 2.65d-37) 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 (t <= 2.65e-37) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 2.65e-37:
		tmp = x / (y * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.65e-37)
		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 (t <= 2.65e-37)
		tmp = x / (y * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.65e-37], 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 < 2.64999999999999998e-37

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

   4. Simplified 66.9%

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

   if 2.64999999999999998e-37 < t

   1. Initial program 89.6%

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

   2. Taylor expanded in t around inf 81.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.65 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 18: 39.6% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.5%

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

2. Taylor expanded in z around 0 40.7%

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

3. Final simplification 40.7%

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

Developer target: 87.5% 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 2023318 
(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))))