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

Percentage Accurate: 89.1% → 96.6%

Time: 11.3s

Alternatives: 13

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: 89.1% 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: 96.6% accurate, 0.8× 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 89.7%

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

   1. associate-/l/ N/A

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

   2. /-lowering-/.f64 N/A

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

   3. /-lowering-/.f64 N/A

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

   4. --lowering--.f64 N/A

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

   5. --lowering--.f64 98.5

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

4. Applied egg-rr 98.5%

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

Alternative 2: 93.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot \left(y - z\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+282}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t z) (- y z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x (- y z)) t)
     (if (<= t_1 1e+282) (/ x t_1) (/ (/ x (- z t)) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x / (y - z)) / t;
	} else if (t_1 <= 1e+282) {
		tmp = x / t_1;
	} else {
		tmp = (x / (z - t)) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / (y - z)) / t;
	} else if (t_1 <= 1e+282) {
		tmp = x / t_1;
	} else {
		tmp = (x / (z - t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t - z) * (y - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x / (y - z)) / t
	elif t_1 <= 1e+282:
		tmp = x / t_1
	else:
		tmp = (x / (z - t)) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - z) * Float64(y - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	elseif (t_1 <= 1e+282)
		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 = (t - z) * (y - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x / (y - z)) / t;
	elseif (t_1 <= 1e+282)
		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[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 1e+282], N[(x / t$95$1), $MachinePrecision], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 79.7%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. --lowering--.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 91.0%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 1.00000000000000003e282

   1. Initial program 98.4%

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

   if 1.00000000000000003e282 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 78.6%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 72.6

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

   5. Simplified 72.6%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. sub-neg N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. +-commutative N/A

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

      7. sub-neg N/A

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

      8. distribute-neg-frac2 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. distribute-neg-frac2 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. sub-neg N/A

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

      17. --lowering--.f64 86.2

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

   7. Applied egg-rr 86.2%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;\left(t - z\right) \cdot \left(y - z\right) \leq 10^{+282}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ t_2 := -\frac{x}{z \cdot y}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-152}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z z))) (t_2 (- (/ x (* z y)))))
   (if (<= z -3.2e+45)
     t_1
     (if (<= z -1.65e-152)
       t_2
       (if (<= z 3e-55) (/ x (* t y)) (if (<= z 1.95e+34) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double t_2 = -(x / (z * y));
	double tmp;
	if (z <= -3.2e+45) {
		tmp = t_1;
	} else if (z <= -1.65e-152) {
		tmp = t_2;
	} else if (z <= 3e-55) {
		tmp = x / (t * y);
	} else if (z <= 1.95e+34) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = x / (z * z)
    t_2 = -(x / (z * y))
    if (z <= (-3.2d+45)) then
        tmp = t_1
    else if (z <= (-1.65d-152)) then
        tmp = t_2
    else if (z <= 3d-55) then
        tmp = x / (t * y)
    else if (z <= 1.95d+34) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double t_2 = -(x / (z * y));
	double tmp;
	if (z <= -3.2e+45) {
		tmp = t_1;
	} else if (z <= -1.65e-152) {
		tmp = t_2;
	} else if (z <= 3e-55) {
		tmp = x / (t * y);
	} else if (z <= 1.95e+34) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * z)
	t_2 = -(x / (z * y))
	tmp = 0
	if z <= -3.2e+45:
		tmp = t_1
	elif z <= -1.65e-152:
		tmp = t_2
	elif z <= 3e-55:
		tmp = x / (t * y)
	elif z <= 1.95e+34:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	t_2 = Float64(-Float64(x / Float64(z * y)))
	tmp = 0.0
	if (z <= -3.2e+45)
		tmp = t_1;
	elseif (z <= -1.65e-152)
		tmp = t_2;
	elseif (z <= 3e-55)
		tmp = Float64(x / Float64(t * y));
	elseif (z <= 1.95e+34)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	t_2 = -(x / (z * y));
	tmp = 0.0;
	if (z <= -3.2e+45)
		tmp = t_1;
	elseif (z <= -1.65e-152)
		tmp = t_2;
	elseif (z <= 3e-55)
		tmp = x / (t * y);
	elseif (z <= 1.95e+34)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = (-N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[z, -3.2e+45], t$95$1, If[LessEqual[z, -1.65e-152], t$95$2, If[LessEqual[z, 3e-55], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+34], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2000000000000003e45 or 1.9500000000000001e34 < z

   1. Initial program 84.0%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]

      2. unpow2 N/A

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

      3. *-lowering-*.f64 71.3

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

   5. Simplified 71.3%

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

   if -3.2000000000000003e45 < z < -1.64999999999999999e-152 or 3.00000000000000016e-55 < z < 1.9500000000000001e34

   1. Initial program 93.8%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 43.3

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

   5. Simplified 43.3%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 29.0

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

   8. Simplified 29.0%

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

   if -1.64999999999999999e-152 < z < 3.00000000000000016e-55

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 77.5

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

   5. Simplified 77.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-152}:\\ \;\;\;\;-\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;-\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z y)))))
   (if (<= z -5.2e-33)
     (/ x (* z (- z t)))
     (if (<= z -1.65e-152) t_1 (if (<= z 8e-55) (/ x (* t y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - y));
	double tmp;
	if (z <= -5.2e-33) {
		tmp = x / (z * (z - t));
	} else if (z <= -1.65e-152) {
		tmp = t_1;
	} else if (z <= 8e-55) {
		tmp = x / (t * y);
	} else {
		tmp = 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 = x / (z * (z - y))
    if (z <= (-5.2d-33)) then
        tmp = x / (z * (z - t))
    else if (z <= (-1.65d-152)) then
        tmp = t_1
    else if (z <= 8d-55) then
        tmp = x / (t * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - y));
	double tmp;
	if (z <= -5.2e-33) {
		tmp = x / (z * (z - t));
	} else if (z <= -1.65e-152) {
		tmp = t_1;
	} else if (z <= 8e-55) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * (z - y))
	tmp = 0
	if z <= -5.2e-33:
		tmp = x / (z * (z - t))
	elif z <= -1.65e-152:
		tmp = t_1
	elif z <= 8e-55:
		tmp = x / (t * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - y)))
	tmp = 0.0
	if (z <= -5.2e-33)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	elseif (z <= -1.65e-152)
		tmp = t_1;
	elseif (z <= 8e-55)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (z - y));
	tmp = 0.0;
	if (z <= -5.2e-33)
		tmp = x / (z * (z - t));
	elseif (z <= -1.65e-152)
		tmp = t_1;
	elseif (z <= 8e-55)
		tmp = x / (t * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-33], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e-152], t$95$1, If[LessEqual[z, 8e-55], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.19999999999999988e-33

   1. Initial program 83.3%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 70.3

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

   5. Simplified 70.3%

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

   if -5.19999999999999988e-33 < z < -1.64999999999999999e-152 or 7.99999999999999996e-55 < z

   1. Initial program 89.2%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

      15. --lowering--.f64 63.5

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

   5. Simplified 63.5%

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

   if -1.64999999999999999e-152 < z < 7.99999999999999996e-55

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 77.5

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

   5. Simplified 77.5%

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

Alternative 5: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-152}:\\ \;\;\;\;-\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z t)))))
   (if (<= z -1.22e-39)
     t_1
     (if (<= z -1.65e-152)
       (- (/ x (* z y)))
       (if (<= z 9.6e-33) (/ x (* t y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - t));
	double tmp;
	if (z <= -1.22e-39) {
		tmp = t_1;
	} else if (z <= -1.65e-152) {
		tmp = -(x / (z * y));
	} else if (z <= 9.6e-33) {
		tmp = x / (t * y);
	} else {
		tmp = 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 = x / (z * (z - t))
    if (z <= (-1.22d-39)) then
        tmp = t_1
    else if (z <= (-1.65d-152)) then
        tmp = -(x / (z * y))
    else if (z <= 9.6d-33) then
        tmp = x / (t * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - t));
	double tmp;
	if (z <= -1.22e-39) {
		tmp = t_1;
	} else if (z <= -1.65e-152) {
		tmp = -(x / (z * y));
	} else if (z <= 9.6e-33) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * (z - t))
	tmp = 0
	if z <= -1.22e-39:
		tmp = t_1
	elif z <= -1.65e-152:
		tmp = -(x / (z * y))
	elif z <= 9.6e-33:
		tmp = x / (t * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - t)))
	tmp = 0.0
	if (z <= -1.22e-39)
		tmp = t_1;
	elseif (z <= -1.65e-152)
		tmp = Float64(-Float64(x / Float64(z * y)));
	elseif (z <= 9.6e-33)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (z - t));
	tmp = 0.0;
	if (z <= -1.22e-39)
		tmp = t_1;
	elseif (z <= -1.65e-152)
		tmp = -(x / (z * y));
	elseif (z <= 9.6e-33)
		tmp = x / (t * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.22e-39], t$95$1, If[LessEqual[z, -1.65e-152], (-N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), If[LessEqual[z, 9.6e-33], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2200000000000001e-39 or 9.6e-33 < z

   1. Initial program 85.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 74.6

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

   5. Simplified 74.6%

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

   if -1.2200000000000001e-39 < z < -1.64999999999999999e-152

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 47.3

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

   5. Simplified 47.3%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 26.8

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

   8. Simplified 26.8%

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

   if -1.64999999999999999e-152 < z < 9.6e-33

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 75.7

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

   5. Simplified 75.7%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-152}:\\ \;\;\;\;-\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z z))))
   (if (<= z -7.5e-59)
     t_1
     (if (<= z 3.2e-30)
       (/ x (* t y))
       (if (<= z 2.25e+79) (/ x (* t (- z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -7.5e-59) {
		tmp = t_1;
	} else if (z <= 3.2e-30) {
		tmp = x / (t * y);
	} else if (z <= 2.25e+79) {
		tmp = x / (t * -z);
	} else {
		tmp = 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 = x / (z * z)
    if (z <= (-7.5d-59)) then
        tmp = t_1
    else if (z <= 3.2d-30) then
        tmp = x / (t * y)
    else if (z <= 2.25d+79) then
        tmp = x / (t * -z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -7.5e-59) {
		tmp = t_1;
	} else if (z <= 3.2e-30) {
		tmp = x / (t * y);
	} else if (z <= 2.25e+79) {
		tmp = x / (t * -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -7.5e-59:
		tmp = t_1
	elif z <= 3.2e-30:
		tmp = x / (t * y)
	elif z <= 2.25e+79:
		tmp = x / (t * -z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -7.5e-59)
		tmp = t_1;
	elseif (z <= 3.2e-30)
		tmp = Float64(x / Float64(t * y));
	elseif (z <= 2.25e+79)
		tmp = Float64(x / Float64(t * Float64(-z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	tmp = 0.0;
	if (z <= -7.5e-59)
		tmp = t_1;
	elseif (z <= 3.2e-30)
		tmp = x / (t * y);
	elseif (z <= 2.25e+79)
		tmp = x / (t * -z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e-59], t$95$1, If[LessEqual[z, 3.2e-30], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e+79], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000019e-59 or 2.24999999999999997e79 < z

   1. Initial program 83.9%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]

      2. unpow2 N/A

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

      3. *-lowering-*.f64 69.1

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

   5. Simplified 69.1%

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

   if -7.50000000000000019e-59 < z < 3.2e-30

   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

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 70.4

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

   5. Simplified 70.4%

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

   if 3.2e-30 < z < 2.24999999999999997e79

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 72.1

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

   5. Simplified 72.1%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 50.7

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

   8. Simplified 50.7%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z t)))))
   (if (<= z -1.32e-28) t_1 (if (<= z 1.25e-31) (/ x (* (- t z) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - t));
	double tmp;
	if (z <= -1.32e-28) {
		tmp = t_1;
	} else if (z <= 1.25e-31) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = 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 = x / (z * (z - t))
    if (z <= (-1.32d-28)) then
        tmp = t_1
    else if (z <= 1.25d-31) then
        tmp = x / ((t - z) * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - t));
	double tmp;
	if (z <= -1.32e-28) {
		tmp = t_1;
	} else if (z <= 1.25e-31) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * (z - t))
	tmp = 0
	if z <= -1.32e-28:
		tmp = t_1
	elif z <= 1.25e-31:
		tmp = x / ((t - z) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - t)))
	tmp = 0.0
	if (z <= -1.32e-28)
		tmp = t_1;
	elseif (z <= 1.25e-31)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (z - t));
	tmp = 0.0;
	if (z <= -1.32e-28)
		tmp = t_1;
	elseif (z <= 1.25e-31)
		tmp = x / ((t - z) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.32e-28], t$95$1, If[LessEqual[z, 1.25e-31], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32000000000000011e-28 or 1.25e-31 < z

   1. Initial program 85.7%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 74.5

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

   5. Simplified 74.5%

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

   if -1.32000000000000011e-28 < z < 1.25e-31

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 78.4

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

   5. Simplified 78.4%

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

Alternative 8: 90.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+186}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7e+186) (/ (/ x (- t z)) y) (/ x (* (- t z) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e+186) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = x / ((t - z) * (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 <= (-7d+186)) then
        tmp = (x / (t - z)) / y
    else
        tmp = x / ((t - z) * (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 <= -7e+186) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = x / ((t - z) * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7e+186:
		tmp = (x / (t - z)) / y
	else:
		tmp = x / ((t - z) * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7e+186)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7e+186)
		tmp = (x / (t - z)) / y;
	else
		tmp = x / ((t - z) * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7e+186], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999974e186

   1. Initial program 75.7%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 75.7

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

   5. Simplified 75.7%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. --lowering--.f64 99.7

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

   7. Applied egg-rr 99.7%

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

   if -6.99999999999999974e186 < y

   1. Initial program 91.1%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+186}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+186}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.8e+186) (/ (/ x y) (- t z)) (/ x (* (- t z) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.8e+186) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((t - z) * (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 <= (-7.8d+186)) then
        tmp = (x / y) / (t - z)
    else
        tmp = x / ((t - z) * (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 <= -7.8e+186) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((t - z) * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.8e+186:
		tmp = (x / y) / (t - z)
	else:
		tmp = x / ((t - z) * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.8e+186)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.8e+186)
		tmp = (x / y) / (t - z);
	else
		tmp = x / ((t - z) * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.8e+186], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.8000000000000002e186

   1. Initial program 75.7%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 75.7

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

   5. Simplified 75.7%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 95.7

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

   7. Applied egg-rr 95.7%

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

   if -7.8000000000000002e186 < y

   1. Initial program 91.1%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+186}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z z))))
   (if (<= z -2.8e-58) t_1 (if (<= z 1.22e+19) (/ x (* t y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -2.8e-58) {
		tmp = t_1;
	} else if (z <= 1.22e+19) {
		tmp = x / (t * y);
	} else {
		tmp = 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 = x / (z * z)
    if (z <= (-2.8d-58)) then
        tmp = t_1
    else if (z <= 1.22d+19) then
        tmp = x / (t * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -2.8e-58) {
		tmp = t_1;
	} else if (z <= 1.22e+19) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -2.8e-58:
		tmp = t_1
	elif z <= 1.22e+19:
		tmp = x / (t * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -2.8e-58)
		tmp = t_1;
	elseif (z <= 1.22e+19)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	tmp = 0.0;
	if (z <= -2.8e-58)
		tmp = t_1;
	elseif (z <= 1.22e+19)
		tmp = x / (t * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-58], t$95$1, If[LessEqual[z, 1.22e+19], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000001e-58 or 1.22e19 < z

   1. Initial program 84.9%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]

      2. unpow2 N/A

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

      3. *-lowering-*.f64 64.4

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

   5. Simplified 64.4%

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

   if -2.8000000000000001e-58 < z < 1.22e19

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 66.4

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

   5. Simplified 66.4%

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

Alternative 11: 90.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+193}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.5e+193) (/ (/ x z) z) (/ x (* (- t z) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+193) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((t - z) * (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 (z <= (-1.5d+193)) then
        tmp = (x / z) / z
    else
        tmp = x / ((t - z) * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+193) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((t - z) * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.5e+193:
		tmp = (x / z) / z
	else:
		tmp = x / ((t - z) * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.5e+193)
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.5e+193)
		tmp = (x / z) / z;
	else
		tmp = x / ((t - z) * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.5e+193], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e193

   1. Initial program 73.0%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]

      2. unpow2 N/A

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

      3. *-lowering-*.f64 73.0

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

   5. Simplified 73.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 89.9

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

   7. Applied egg-rr 89.9%

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

   if -1.5e193 < z

   1. Initial program 91.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+193}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.1% accurate, 1.0× speedup

Math

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

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(x / Float64(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[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.7%

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

3. Final simplification 89.7%

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

Alternative 13: 39.1% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

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 * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.7%

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

3. Taylor expanded in z around 0

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

   1. /-lowering-/.f64 N/A

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

   2. *-lowering-*.f64 43.8

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

5. Simplified 43.8%

   \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
6. Add Preprocessing

Developer Target 1: 87.9% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024204 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ x (* (- y z) (- t z))) 0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z))))))

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