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

Percentage Accurate: 89.0% → 96.2%

Time: 10.7s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

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 = (-1.0d0) / ((y - z) * ((z - t) / x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.4%

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

   1. associate-/l/ 98.0%

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

   2. clear-num 97.7%

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

   3. inv-pow 97.7%

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

   4. div-inv 97.6%

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

   5. clear-num 97.7%

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

4. Applied egg-rr 97.7%

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

   1. unpow-1 97.7%

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

6. Simplified 97.7%

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

7. Final simplification 97.7%

   \[\leadsto \frac{-1}{\left(y - z\right) \cdot \frac{z - t}{x}} \]
8. Add Preprocessing

Alternative 2: 48.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot t}\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+160}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-65} \lor \neg \left(y \leq 490000000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y t))))
   (if (<= y -6.4e+160)
     (/ (/ x y) (- z))
     (if (<= y -5.1e+76)
       t_1
       (if (<= y -6.5e+18)
         (/ x (* y (- z)))
         (if (or (<= y -9.8e-65) (not (<= y 490000000.0)))
           t_1
           (/ x (* z (- t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (y * t);
	double tmp;
	if (y <= -6.4e+160) {
		tmp = (x / y) / -z;
	} else if (y <= -5.1e+76) {
		tmp = t_1;
	} else if (y <= -6.5e+18) {
		tmp = x / (y * -z);
	} else if ((y <= -9.8e-65) || !(y <= 490000000.0)) {
		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 = x / (y * t)
    if (y <= (-6.4d+160)) then
        tmp = (x / y) / -z
    else if (y <= (-5.1d+76)) then
        tmp = t_1
    else if (y <= (-6.5d+18)) then
        tmp = x / (y * -z)
    else if ((y <= (-9.8d-65)) .or. (.not. (y <= 490000000.0d0))) 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 = x / (y * t);
	double tmp;
	if (y <= -6.4e+160) {
		tmp = (x / y) / -z;
	} else if (y <= -5.1e+76) {
		tmp = t_1;
	} else if (y <= -6.5e+18) {
		tmp = x / (y * -z);
	} else if ((y <= -9.8e-65) || !(y <= 490000000.0)) {
		tmp = t_1;
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (y * t)
	tmp = 0
	if y <= -6.4e+160:
		tmp = (x / y) / -z
	elif y <= -5.1e+76:
		tmp = t_1
	elif y <= -6.5e+18:
		tmp = x / (y * -z)
	elif (y <= -9.8e-65) or not (y <= 490000000.0):
		tmp = t_1
	else:
		tmp = x / (z * -t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * t))
	tmp = 0.0
	if (y <= -6.4e+160)
		tmp = Float64(Float64(x / y) / Float64(-z));
	elseif (y <= -5.1e+76)
		tmp = t_1;
	elseif (y <= -6.5e+18)
		tmp = Float64(x / Float64(y * Float64(-z)));
	elseif ((y <= -9.8e-65) || !(y <= 490000000.0))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(z * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * t);
	tmp = 0.0;
	if (y <= -6.4e+160)
		tmp = (x / y) / -z;
	elseif (y <= -5.1e+76)
		tmp = t_1;
	elseif (y <= -6.5e+18)
		tmp = x / (y * -z);
	elseif ((y <= -9.8e-65) || ~((y <= 490000000.0)))
		tmp = t_1;
	else
		tmp = x / (z * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+160], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[y, -5.1e+76], t$95$1, If[LessEqual[y, -6.5e+18], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -9.8e-65], N[Not[LessEqual[y, 490000000.0]], $MachinePrecision]], t$95$1, N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.3999999999999995e160

   1. Initial program 85.2%

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

   3. Taylor expanded in t around 0 69.1%

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

      1. mul-1-neg 69.1%

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

      2. distribute-rgt-neg-in 69.1%

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

      3. neg-sub0 69.1%

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

      4. sub-neg 69.1%

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

      5. +-commutative 69.1%

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

      6. associate--r+ 69.1%

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

      7. neg-sub0 69.1%

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

      8. remove-double-neg 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in z around 0 69.1%

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

      1. associate-*r/ 69.1%

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

      2. neg-mul-1 69.1%

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

   8. Simplified 69.1%

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

   9. Taylor expanded in x around 0 69.1%

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

       1. mul-1-neg 69.1%

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

       2. associate-/r* 80.5%

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

       3. distribute-neg-frac2 80.5%

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

   11. Simplified 80.5%

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

   if -6.3999999999999995e160 < y < -5.1000000000000002e76 or -6.5e18 < y < -9.79999999999999929e-65 or 4.9e8 < y

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0 48.1%

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

   if -5.1000000000000002e76 < y < -6.5e18

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. distribute-rgt-neg-in 65.4%

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

      3. neg-sub0 65.4%

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

      4. sub-neg 65.4%

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

      5. +-commutative 65.4%

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

      6. associate--r+ 65.4%

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

      7. neg-sub0 65.4%

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

      8. remove-double-neg 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in z around 0 48.2%

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

      1. associate-*r/ 48.2%

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

      2. neg-mul-1 48.2%

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

   8. Simplified 48.2%

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

   if -9.79999999999999929e-65 < y < 4.9e8

   1. Initial program 88.1%

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

      1. associate-/l/ 98.1%

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

      2. clear-num 97.8%

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

      3. inv-pow 97.8%

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

      4. div-inv 97.7%

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

      5. clear-num 97.8%

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

   4. Applied egg-rr 97.8%

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

      1. unpow-1 97.8%

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

   6. Simplified 97.8%

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

   7. Taylor expanded in t around inf 51.9%

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

      1. associate-/l* 56.3%

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

   9. Simplified 56.3%

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

   10. Taylor expanded in y around 0 39.9%

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

       1. mul-1-neg 39.9%

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

       2. distribute-neg-frac2 39.9%

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

       3. mul-1-neg 39.9%

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

       4. associate-*r* 39.9%

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

       5. neg-mul-1 39.9%

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

   12. Simplified 39.9%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+160}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-65} \lor \neg \left(y \leq 490000000\right):\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-96} \lor \neg \left(t \leq 8.6 \cdot 10^{-45}\right) \land t \leq 4.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7.4e-116)
   (/ (/ x y) (- t z))
   (if (or (<= t 5e-96) (and (not (<= t 8.6e-45)) (<= t 4.5e+21)))
     (/ (/ x z) (- z y))
     (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.4e-116) {
		tmp = (x / y) / (t - z);
	} else if ((t <= 5e-96) || (!(t <= 8.6e-45) && (t <= 4.5e+21))) {
		tmp = (x / z) / (z - y);
	} 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 <= (-7.4d-116)) then
        tmp = (x / y) / (t - z)
    else if ((t <= 5d-96) .or. (.not. (t <= 8.6d-45)) .and. (t <= 4.5d+21)) then
        tmp = (x / z) / (z - y)
    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 <= -7.4e-116) {
		tmp = (x / y) / (t - z);
	} else if ((t <= 5e-96) || (!(t <= 8.6e-45) && (t <= 4.5e+21))) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7.4e-116:
		tmp = (x / y) / (t - z)
	elif (t <= 5e-96) or (not (t <= 8.6e-45) and (t <= 4.5e+21)):
		tmp = (x / z) / (z - y)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7.4e-116)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif ((t <= 5e-96) || (!(t <= 8.6e-45) && (t <= 4.5e+21)))
		tmp = Float64(Float64(x / z) / Float64(z - y));
	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 <= -7.4e-116)
		tmp = (x / y) / (t - z);
	elseif ((t <= 5e-96) || (~((t <= 8.6e-45)) && (t <= 4.5e+21)))
		tmp = (x / z) / (z - y);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7.4e-116], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 5e-96], And[N[Not[LessEqual[t, 8.6e-45]], $MachinePrecision], LessEqual[t, 4.5e+21]]], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.4000000000000005e-116

   1. Initial program 84.1%

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

   3. Taylor expanded in y around inf 58.2%

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

      1. associate-/r* 62.6%

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

   5. Simplified 62.6%

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

   if -7.4000000000000005e-116 < t < 4.99999999999999995e-96 or 8.5999999999999998e-45 < t < 4.5e21

   1. Initial program 91.7%

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

   3. Taylor expanded in t around 0 79.6%

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

      1. mul-1-neg 79.6%

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

      2. associate-/r* 86.8%

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

      3. distribute-neg-frac2 86.8%

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

      4. neg-sub0 86.8%

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

      5. sub-neg 86.8%

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

      6. +-commutative 86.8%

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

      7. associate--r+ 86.8%

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

      8. neg-sub0 86.8%

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

      9. remove-double-neg 86.8%

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

   5. Simplified 86.8%

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

   if 4.99999999999999995e-96 < t < 8.5999999999999998e-45 or 4.5e21 < t

   1. Initial program 88.4%

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

      1. associate-/l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around inf 81.8%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-96} \lor \neg \left(t \leq 8.6 \cdot 10^{-45}\right) \land t \leq 4.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y - z}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-44} \lor \neg \left(t \leq 4.8 \cdot 10^{+14}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) (- y z))))
   (if (<= t -3e+19)
     t_1
     (if (<= t 3e-96)
       (/ x (* z (- z y)))
       (if (or (<= t 1.45e-44) (not (<= t 4.8e+14)))
         t_1
         (/ x (* z (- z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / (y - z);
	double tmp;
	if (t <= -3e+19) {
		tmp = t_1;
	} else if (t <= 3e-96) {
		tmp = x / (z * (z - y));
	} else if ((t <= 1.45e-44) || !(t <= 4.8e+14)) {
		tmp = t_1;
	} else {
		tmp = x / (z * (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 = (x / t) / (y - z)
    if (t <= (-3d+19)) then
        tmp = t_1
    else if (t <= 3d-96) then
        tmp = x / (z * (z - y))
    else if ((t <= 1.45d-44) .or. (.not. (t <= 4.8d+14))) then
        tmp = t_1
    else
        tmp = x / (z * (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / (y - z);
	double tmp;
	if (t <= -3e+19) {
		tmp = t_1;
	} else if (t <= 3e-96) {
		tmp = x / (z * (z - y));
	} else if ((t <= 1.45e-44) || !(t <= 4.8e+14)) {
		tmp = t_1;
	} else {
		tmp = x / (z * (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / t) / (y - z)
	tmp = 0
	if t <= -3e+19:
		tmp = t_1
	elif t <= 3e-96:
		tmp = x / (z * (z - y))
	elif (t <= 1.45e-44) or not (t <= 4.8e+14):
		tmp = t_1
	else:
		tmp = x / (z * (z - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / Float64(y - z))
	tmp = 0.0
	if (t <= -3e+19)
		tmp = t_1;
	elseif (t <= 3e-96)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	elseif ((t <= 1.45e-44) || !(t <= 4.8e+14))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(z * Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / (y - z);
	tmp = 0.0;
	if (t <= -3e+19)
		tmp = t_1;
	elseif (t <= 3e-96)
		tmp = x / (z * (z - y));
	elseif ((t <= 1.45e-44) || ~((t <= 4.8e+14)))
		tmp = t_1;
	else
		tmp = x / (z * (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+19], t$95$1, If[LessEqual[t, 3e-96], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.45e-44], N[Not[LessEqual[t, 4.8e+14]], $MachinePrecision]], t$95$1, N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3e19 or 3e-96 < t < 1.4500000000000001e-44 or 4.8e14 < t

   1. Initial program 85.3%

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

      1. associate-/l/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around inf 81.3%

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

   if -3e19 < t < 3e-96

   1. Initial program 91.6%

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

   3. Taylor expanded in t around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. distribute-rgt-neg-in 75.1%

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

      3. neg-sub0 75.1%

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

      4. sub-neg 75.1%

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

      5. +-commutative 75.1%

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

      6. associate--r+ 75.1%

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

      7. neg-sub0 75.1%

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

      8. remove-double-neg 75.1%

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

   5. Simplified 75.1%

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

   if 1.4500000000000001e-44 < t < 4.8e14

   1. Initial program 91.6%

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

   3. Taylor expanded in y around 0 43.7%

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

      1. mul-1-neg 43.7%

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

      2. distribute-neg-frac2 43.7%

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

      3. distribute-rgt-neg-in 43.7%

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

      4. sub-neg 43.7%

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

      5. +-commutative 43.7%

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

      6. distribute-neg-in 43.7%

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

      7. remove-double-neg 43.7%

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

      8. unsub-neg 43.7%

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

   5. Simplified 43.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-44} \lor \neg \left(t \leq 4.8 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t\_1 \leq 10^{+306}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 1e+306) (/ x t_1) (/ (/ x (- z t)) z))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 1e+306) {
		tmp = x / t_1;
	} else {
		tmp = (x / (z - 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 = (y - z) * (t - z)
    if (t_1 <= 1d+306) then
        tmp = x / t_1
    else
        tmp = (x / (z - t)) / z
    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 (t_1 <= 1e+306) {
		tmp = x / t_1;
	} else {
		tmp = (x / (z - t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= 1e+306:
		tmp = x / t_1
	else:
		tmp = (x / (z - t)) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= 1e+306)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / Float64(z - t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= 1e+306)
		tmp = x / t_1;
	else
		tmp = (x / (z - t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+306], N[(x / t$95$1), $MachinePrecision], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 1.00000000000000002e306

   1. Initial program 96.5%

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

   if 1.00000000000000002e306 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 71.5%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 88.0%

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

      1. neg-mul-1 88.0%

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

   7. Simplified 88.0%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq 10^{+306}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -700000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 8800000000:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y - z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -700000000000.0)
   (/ (/ x y) (- t z))
   (if (<= y 8800000000.0) (/ (/ 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 <= -700000000000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= 8800000000.0) {
		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 <= (-700000000000.0d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= 8800000000.0d0) 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 <= -700000000000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= 8800000000.0) {
		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 <= -700000000000.0:
		tmp = (x / y) / (t - z)
	elif y <= 8800000000.0:
		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 <= -700000000000.0)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 8800000000.0)
		tmp = Float64(Float64(x / Float64(z - 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 <= -700000000000.0)
		tmp = (x / y) / (t - z);
	elseif (y <= 8800000000.0)
		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, -700000000000.0], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8800000000.0], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(1.0 / N[(t * N[(N[(y - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7e11

   1. Initial program 89.1%

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

   3. Taylor expanded in y around inf 85.8%

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

      1. associate-/r* 88.7%

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

   5. Simplified 88.7%

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

   if -7e11 < y < 8.8e9

   1. Initial program 89.0%

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

      1. associate-/l/ 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in y around 0 83.5%

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

      1. neg-mul-1 83.5%

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

   7. Simplified 83.5%

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

   if 8.8e9 < y

   1. Initial program 86.9%

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

      1. associate-/l/ 97.3%

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

      2. clear-num 97.0%

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

      3. inv-pow 97.0%

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

      4. div-inv 96.9%

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

      5. clear-num 96.9%

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

   4. Applied egg-rr 96.9%

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

      1. unpow-1 96.9%

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

   6. Simplified 96.9%

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

   7. Taylor expanded in t around inf 48.4%

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

      1. associate-/l* 62.5%

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

   9. Simplified 62.5%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -700000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 8800000000:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-14} \lor \neg \left(z \leq 8.6 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.6e-14) (not (<= z 8.6e-91)))
   (/ x (* z (- z t)))
   (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.6e-14) || !(z <= 8.6e-91)) {
		tmp = x / (z * (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 <= (-5.6d-14)) .or. (.not. (z <= 8.6d-91))) then
        tmp = x / (z * (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 <= -5.6e-14) || !(z <= 8.6e-91)) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.6e-14) or not (z <= 8.6e-91):
		tmp = x / (z * (z - t))
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.6e-14) || !(z <= 8.6e-91))
		tmp = Float64(x / Float64(z * 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 <= -5.6e-14) || ~((z <= 8.6e-91)))
		tmp = x / (z * (z - t));
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.6e-14], N[Not[LessEqual[z, 8.6e-91]], $MachinePrecision]], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.6000000000000001e-14 or 8.6e-91 < z

   1. Initial program 84.1%

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

   3. Taylor expanded in y around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. distribute-neg-frac2 65.7%

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

      3. distribute-rgt-neg-in 65.7%

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

      4. sub-neg 65.7%

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

      5. +-commutative 65.7%

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

      6. distribute-neg-in 65.7%

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

      7. remove-double-neg 65.7%

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

      8. unsub-neg 65.7%

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

   5. Simplified 65.7%

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

   if -5.6000000000000001e-14 < z < 8.6e-91

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 70.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-14} \lor \neg \left(z \leq 8.6 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4600:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2150000000:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4600.0)
   (/ (/ x y) (- t z))
   (if (<= y 2150000000.0) (/ (/ x (- z t)) z) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4600.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2150000000.0) {
		tmp = (x / (z - t)) / z;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4600.0d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= 2150000000.0d0) then
        tmp = (x / (z - t)) / z
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4600.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2150000000.0) {
		tmp = (x / (z - t)) / z;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4600.0:
		tmp = (x / y) / (t - z)
	elif y <= 2150000000.0:
		tmp = (x / (z - t)) / z
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4600.0)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 2150000000.0)
		tmp = Float64(Float64(x / Float64(z - t)) / z);
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4600.0)
		tmp = (x / y) / (t - z);
	elseif (y <= 2150000000.0)
		tmp = (x / (z - t)) / z;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4600.0], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2150000000.0], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4600

   1. Initial program 89.1%

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

   3. Taylor expanded in y around inf 85.8%

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

      1. associate-/r* 88.7%

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

   5. Simplified 88.7%

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

   if -4600 < y < 2.15e9

   1. Initial program 89.0%

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

      1. associate-/l/ 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in y around 0 83.5%

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

      1. neg-mul-1 83.5%

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

   7. Simplified 83.5%

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

   if 2.15e9 < y

   1. Initial program 86.9%

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

      1. associate-/l/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 50.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4600:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2150000000:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{z - y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.25e-116)
   (/ (/ x y) (- t z))
   (if (<= t 7.2e+21) (/ (/ x (- z y)) z) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.25e-116) {
		tmp = (x / y) / (t - z);
	} else if (t <= 7.2e+21) {
		tmp = (x / (z - y)) / z;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.25d-116)) then
        tmp = (x / y) / (t - z)
    else if (t <= 7.2d+21) then
        tmp = (x / (z - y)) / z
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.25e-116) {
		tmp = (x / y) / (t - z);
	} else if (t <= 7.2e+21) {
		tmp = (x / (z - y)) / z;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.25e-116:
		tmp = (x / y) / (t - z)
	elif t <= 7.2e+21:
		tmp = (x / (z - y)) / z
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.25e-116)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 7.2e+21)
		tmp = Float64(Float64(x / Float64(z - y)) / z);
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.25e-116)
		tmp = (x / y) / (t - z);
	elseif (t <= 7.2e+21)
		tmp = (x / (z - y)) / z;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.25e-116], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+21], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.25000000000000006e-116

   1. Initial program 84.1%

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

   3. Taylor expanded in y around inf 58.2%

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

      1. associate-/r* 62.6%

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

   5. Simplified 62.6%

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

   if -2.25000000000000006e-116 < t < 7.2e21

   1. Initial program 91.0%

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

   3. Taylor expanded in t around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. distribute-rgt-neg-in 76.6%

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

      3. neg-sub0 76.6%

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

      4. sub-neg 76.6%

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

      5. +-commutative 76.6%

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

      6. associate--r+ 76.6%

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

      7. neg-sub0 76.6%

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

      8. remove-double-neg 76.6%

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

   5. Simplified 76.6%

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

      1. div-inv 76.5%

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

      2. associate-/r* 77.7%

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

   7. Applied egg-rr 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-*l/ 84.4%

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

      3. associate-*r/ 83.7%

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

      4. associate-*l/ 83.7%

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

      5. *-lft-identity 83.7%

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

   9. Simplified 83.7%

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

   if 7.2e21 < t

   1. Initial program 89.0%

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

      1. associate-/l/ 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in t around inf 90.7%

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

Alternative 10: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.1e-28)
   (/ (/ x y) (- t z))
   (if (<= y 3.8e-73) (/ x (* z (- z t))) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-28) {
		tmp = (x / y) / (t - z);
	} else if (y <= 3.8e-73) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.1d-28)) then
        tmp = (x / y) / (t - z)
    else if (y <= 3.8d-73) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-28) {
		tmp = (x / y) / (t - z);
	} else if (y <= 3.8e-73) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.1e-28:
		tmp = (x / y) / (t - z)
	elif y <= 3.8e-73:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.1e-28)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 3.8e-73)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.1e-28)
		tmp = (x / y) / (t - z);
	elseif (y <= 3.8e-73)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.1e-28], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e-73], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1000000000000002e-28

   1. Initial program 89.6%

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

   3. Taylor expanded in y around inf 85.0%

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

      1. associate-/r* 87.8%

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

   5. Simplified 87.8%

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

   if -4.1000000000000002e-28 < y < 3.8000000000000003e-73

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. mul-1-neg 74.7%

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

      2. distribute-neg-frac2 74.7%

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

      3. distribute-rgt-neg-in 74.7%

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

      4. sub-neg 74.7%

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

      5. +-commutative 74.7%

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

      6. distribute-neg-in 74.7%

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

      7. remove-double-neg 74.7%

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

      8. unsub-neg 74.7%

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

   5. Simplified 74.7%

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

   if 3.8000000000000003e-73 < y

   1. Initial program 87.7%

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

      1. associate-/l/ 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t around inf 50.3%

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

Alternative 11: 47.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0028 \lor \neg \left(z \leq 1.05 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.0028) (not (<= z 1.05e-90)))
   (/ x (* z (- t)))
   (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.0028) || !(z <= 1.05e-90)) {
		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 <= (-0.0028d0)) .or. (.not. (z <= 1.05d-90))) 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 <= -0.0028) || !(z <= 1.05e-90)) {
		tmp = x / (z * -t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.0028) or not (z <= 1.05e-90):
		tmp = x / (z * -t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.0028) || !(z <= 1.05e-90))
		tmp = Float64(x / Float64(z * Float64(-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 <= -0.0028) || ~((z <= 1.05e-90)))
		tmp = x / (z * -t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.0028], N[Not[LessEqual[z, 1.05e-90]], $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 < -0.00279999999999999997 or 1.05e-90 < z

   1. Initial program 83.9%

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

      1. associate-/l/ 99.8%

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

      2. clear-num 99.5%

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

      3. inv-pow 99.5%

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

      4. div-inv 99.4%

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

      5. clear-num 99.5%

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

   4. Applied egg-rr 99.5%

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

      1. unpow-1 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in t around inf 37.9%

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

      1. associate-/l* 50.7%

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

   9. Simplified 50.7%

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

   10. Taylor expanded in y around 0 34.3%

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

       1. mul-1-neg 34.3%

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

       2. distribute-neg-frac2 34.3%

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

       3. mul-1-neg 34.3%

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

       4. associate-*r* 34.3%

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

       5. neg-mul-1 34.3%

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

   12. Simplified 34.3%

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

   if -0.00279999999999999997 < z < 1.05e-90

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 70.5%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0028 \lor \neg \left(z \leq 1.05 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+67} \lor \neg \left(z \leq 7.8 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.16e+67) (not (<= z 7.8e+84))) (/ (/ x z) y) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.16e+67) || !(z <= 7.8e+84)) {
		tmp = (x / z) / y;
	} 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 <= (-1.16d+67)) .or. (.not. (z <= 7.8d+84))) then
        tmp = (x / z) / y
    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 <= -1.16e+67) || !(z <= 7.8e+84)) {
		tmp = (x / z) / y;
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.16e+67) or not (z <= 7.8e+84):
		tmp = (x / z) / y
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.16e+67) || !(z <= 7.8e+84))
		tmp = Float64(Float64(x / z) / y);
	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 <= -1.16e+67) || ~((z <= 7.8e+84)))
		tmp = (x / z) / y;
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.16e+67], N[Not[LessEqual[z, 7.8e+84]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15999999999999994e67 or 7.80000000000000032e84 < z

   1. Initial program 79.3%

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

   3. Taylor expanded in t around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. distribute-rgt-neg-in 77.7%

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

      3. neg-sub0 77.7%

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

      4. sub-neg 77.7%

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

      5. +-commutative 77.7%

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

      6. associate--r+ 77.7%

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

      7. neg-sub0 77.7%

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

      8. remove-double-neg 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in z around 0 47.1%

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

      1. associate-*r/ 47.1%

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

      2. neg-mul-1 47.1%

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

   8. Simplified 47.1%

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

      1. div-inv 47.1%

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

      2. add-sqr-sqrt 23.2%

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

      3. sqrt-unprod 47.5%

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

      4. sqr-neg 47.5%

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

      5. sqrt-unprod 23.0%

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

      6. add-sqr-sqrt 45.1%

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

      7. associate-/r* 45.0%

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

   10. Applied egg-rr 45.0%

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

       1. *-commutative 45.0%

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

       2. associate-*l/ 40.5%

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

       3. associate-*r/ 46.2%

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

       4. associate-*l/ 46.2%

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

       5. *-lft-identity 46.2%

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

   12. Simplified 46.2%

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

   if -1.15999999999999994e67 < z < 7.80000000000000032e84

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 49.7%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+67} \lor \neg \left(z \leq 7.8 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+66} \lor \neg \left(z \leq 4.8 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.4e+66) (not (<= z 4.8e+76))) (/ x (* y z)) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.4e+66) || !(z <= 4.8e+76)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.4d+66)) .or. (.not. (z <= 4.8d+76))) then
        tmp = x / (y * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.4e+66) || !(z <= 4.8e+76)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.4e+66) or not (z <= 4.8e+76):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.4e+66) || !(z <= 4.8e+76))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.4e+66) || ~((z <= 4.8e+76)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.4e+66], N[Not[LessEqual[z, 4.8e+76]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.3999999999999999e66 or 4.8e76 < z

   1. Initial program 79.3%

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

   3. Taylor expanded in t around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. distribute-rgt-neg-in 77.7%

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

      3. neg-sub0 77.7%

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

      4. sub-neg 77.7%

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

      5. +-commutative 77.7%

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

      6. associate--r+ 77.7%

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

      7. neg-sub0 77.7%

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

      8. remove-double-neg 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in z around 0 47.1%

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

      1. associate-*r/ 47.1%

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

      2. neg-mul-1 47.1%

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

   8. Simplified 47.1%

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

      1. *-un-lft-identity 47.1%

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

      2. *-commutative 47.1%

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

      3. add-sqr-sqrt 23.2%

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

      4. sqrt-unprod 47.5%

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

      5. sqr-neg 47.5%

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

      6. sqrt-unprod 23.0%

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

      7. add-sqr-sqrt 45.1%

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

      8. associate-/r* 40.5%

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

   10. Applied egg-rr 40.5%

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

       1. *-rgt-identity 40.5%

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

       2. associate-/r* 45.1%

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

   12. Simplified 45.1%

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

   if -6.3999999999999999e66 < z < 4.8e76

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 49.7%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+66} \lor \neg \left(z \leq 4.8 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.4%

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

   1. associate-/l/ 98.0%

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

3. Simplified 98.0%

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

Alternative 15: 39.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.4%

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

3. Taylor expanded in z around 0 36.1%

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

4. Final simplification 36.1%

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

Developer target: 88.0% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

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

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