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

Percentage Accurate: 88.7% → 99.0%

Time: 10.2s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{\frac{x}{t - z}}{y - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+234}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))) (t_2 (/ (/ x (- t z)) (- y z))))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 2e+234) (/ x t_1) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double t_2 = (x / (t - z)) / (y - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 2e+234) {
		tmp = x / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double t_2 = (x / (t - z)) / (y - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 2e+234) {
		tmp = x / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	t_2 = (x / (t - z)) / (y - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 2e+234:
		tmp = x / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	t_2 = Float64(Float64(x / Float64(t - z)) / Float64(y - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 2e+234)
		tmp = Float64(x / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	t_2 = (x / (t - z)) / (y - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 2e+234)
		tmp = x / t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 2e+234], N[(x / t$95$1), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0 or 2.00000000000000004e234 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 81.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 99.9

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

   4. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 2.00000000000000004e234

   1. Initial program 98.1%

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

Alternative 2: 97.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z - t}}{\frac{z - y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 -5e-310) t_1 (/ (/ 1.0 (- z t)) (/ (- z y) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -5e-310) {
		tmp = t_1;
	} else {
		tmp = (1.0 / (z - t)) / ((z - y) / 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (t - z))
    if (t_1 <= (-5d-310)) then
        tmp = t_1
    else
        tmp = (1.0d0 / (z - t)) / ((z - y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -5e-310) {
		tmp = t_1;
	} else {
		tmp = (1.0 / (z - t)) / ((z - y) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -5e-310:
		tmp = t_1
	else:
		tmp = (1.0 / (z - t)) / ((z - y) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -5e-310)
		tmp = t_1;
	else
		tmp = Float64(Float64(1.0 / Float64(z - t)) / Float64(Float64(z - y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -5e-310)
		tmp = t_1;
	else
		tmp = (1.0 / (z - t)) / ((z - y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-310], t$95$1, N[(N[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -4.999999999999985e-310

   1. Initial program 97.6%

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

   if -4.999999999999985e-310 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 88.2%

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

      1. associate-/r* 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 97.7

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

   4. Applied egg-rr 97.7%

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

      1. div-inv N/A

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

      2. clear-num N/A

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

      3. associate-*l/ N/A

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

      4. div-inv N/A

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

      5. frac-2neg N/A

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

      6. distribute-frac-neg2 N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. flip3-- N/A

          \[\leadsto \frac{\frac{1}{\color{blue}{\frac{{z}^{3} - {t}^{3}}{z \cdot z + \left(t \cdot t + z \cdot t\right)}}}}{\mathsf{neg}\left(\frac{y - z}{x}\right)} \]

      13. clear-num N/A

          \[\leadsto \frac{\color{blue}{\frac{z \cdot z + \left(t \cdot t + z \cdot t\right)}{{z}^{3} - {t}^{3}}}}{\mathsf{neg}\left(\frac{y - z}{x}\right)} \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{z \cdot z + \left(t \cdot t + z \cdot t\right)}{{z}^{3} - {t}^{3}}}{\mathsf{neg}\left(\frac{y - z}{x}\right)}} \]

   6. Applied egg-rr 97.4%

      \[\leadsto \color{blue}{\frac{\frac{1}{z - t}}{\frac{z - y}{x}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 97.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 -5e-310) t_1 (/ (/ x (- y z)) (- t z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -5e-310) {
		tmp = t_1;
	} else {
		tmp = (x / (y - 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 = x / ((y - z) * (t - z))
    if (t_1 <= (-5d-310)) then
        tmp = t_1
    else
        tmp = (x / (y - 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 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -5e-310) {
		tmp = t_1;
	} else {
		tmp = (x / (y - z)) / (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -5e-310:
		tmp = t_1
	else:
		tmp = (x / (y - z)) / (t - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -5e-310)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -5e-310)
		tmp = t_1;
	else
		tmp = (x / (y - z)) / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-310], t$95$1, N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -4.999999999999985e-310

   1. Initial program 97.6%

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

   if -4.999999999999985e-310 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 88.2%

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

      1. associate-/r* 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 97.7

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

   4. Applied egg-rr 97.7%

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

Alternative 4: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-177}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e-83)
   (/ x (* y (- t z)))
   (if (<= y 6.5e-177) (/ x (* z (- z t))) (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e-83) {
		tmp = x / (y * (t - z));
	} else if (y <= 6.5e-177) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.8d-83)) then
        tmp = x / (y * (t - z))
    else if (y <= 6.5d-177) then
        tmp = x / (z * (z - t))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e-83) {
		tmp = x / (y * (t - z));
	} else if (y <= 6.5e-177) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e-83:
		tmp = x / (y * (t - z))
	elif y <= 6.5e-177:
		tmp = x / (z * (z - t))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e-83)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 6.5e-177)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.8e-83)
		tmp = x / (y * (t - z));
	elseif (y <= 6.5e-177)
		tmp = x / (z * (z - t));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e-83], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-177], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.80000000000000006e-83

   1. Initial program 85.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 79.3

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

   5. Simplified 79.3%

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

   if -1.80000000000000006e-83 < y < 6.4999999999999998e-177

   1. Initial program 91.2%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   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 81.1

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

   5. Simplified 81.1%

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

   if 6.4999999999999998e-177 < y

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 54.0%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-177}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y (- t z)))))
   (if (<= y -1.45e-90) t_1 (if (<= y 1.5e-99) (/ x (* z (- z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (y * (t - z));
	double tmp;
	if (y <= -1.45e-90) {
		tmp = t_1;
	} else if (y <= 1.5e-99) {
		tmp = x / (z * (z - t));
	} 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 / (y * (t - z))
    if (y <= (-1.45d-90)) then
        tmp = t_1
    else if (y <= 1.5d-99) then
        tmp = x / (z * (z - t))
    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 / (y * (t - z));
	double tmp;
	if (y <= -1.45e-90) {
		tmp = t_1;
	} else if (y <= 1.5e-99) {
		tmp = x / (z * (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (y * (t - z))
	tmp = 0
	if y <= -1.45e-90:
		tmp = t_1
	elif y <= 1.5e-99:
		tmp = x / (z * (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * Float64(t - z)))
	tmp = 0.0
	if (y <= -1.45e-90)
		tmp = t_1;
	elseif (y <= 1.5e-99)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * (t - z));
	tmp = 0.0;
	if (y <= -1.45e-90)
		tmp = t_1;
	elseif (y <= 1.5e-99)
		tmp = x / (z * (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e-90], t$95$1, If[LessEqual[y, 1.5e-99], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999992e-90 or 1.50000000000000003e-99 < y

   1. Initial program 89.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 76.0

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

   5. Simplified 76.0%

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

   if -1.44999999999999992e-90 < y < 1.50000000000000003e-99

   1. Initial program 92.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 82.7

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

   5. Simplified 82.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-134}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.4e-90)
   (/ x (* z (- z y)))
   (if (<= z 1.55e-134) (/ x (* y t)) (/ x (* z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.4e-90) {
		tmp = x / (z * (z - y));
	} else if (z <= 1.55e-134) {
		tmp = x / (y * t);
	} 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) :: tmp
    if (z <= (-6.4d-90)) then
        tmp = x / (z * (z - y))
    else if (z <= 1.55d-134) then
        tmp = x / (y * t)
    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 tmp;
	if (z <= -6.4e-90) {
		tmp = x / (z * (z - y));
	} else if (z <= 1.55e-134) {
		tmp = x / (y * t);
	} else {
		tmp = x / (z * (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.4e-90:
		tmp = x / (z * (z - y))
	elif z <= 1.55e-134:
		tmp = x / (y * t)
	else:
		tmp = x / (z * (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.4e-90)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	elseif (z <= 1.55e-134)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = Float64(x / Float64(z * Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.4e-90)
		tmp = x / (z * (z - y));
	elseif (z <= 1.55e-134)
		tmp = x / (y * t);
	else
		tmp = x / (z * (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.4e-90], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-134], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.40000000000000014e-90

   1. Initial program 87.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. remove-double-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 74.0

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

   5. Simplified 74.0%

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

   if -6.40000000000000014e-90 < z < 1.55000000000000003e-134

   1. Initial program 96.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 73.9

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

   5. Simplified 73.9%

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

   if 1.55000000000000003e-134 < z

   1. Initial program 88.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 69.7

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

   5. Simplified 69.7%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-134}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-131}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z t)))))
   (if (<= z -3.2e-72) t_1 (if (<= z 6.4e-131) (/ x (* y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - t));
	double tmp;
	if (z <= -3.2e-72) {
		tmp = t_1;
	} else if (z <= 6.4e-131) {
		tmp = x / (y * t);
	} 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 <= (-3.2d-72)) then
        tmp = t_1
    else if (z <= 6.4d-131) then
        tmp = x / (y * t)
    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 <= -3.2e-72) {
		tmp = t_1;
	} else if (z <= 6.4e-131) {
		tmp = x / (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * (z - t))
	tmp = 0
	if z <= -3.2e-72:
		tmp = t_1
	elif z <= 6.4e-131:
		tmp = x / (y * t)
	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 <= -3.2e-72)
		tmp = t_1;
	elseif (z <= 6.4e-131)
		tmp = Float64(x / Float64(y * t));
	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 <= -3.2e-72)
		tmp = t_1;
	elseif (z <= 6.4e-131)
		tmp = x / (y * t);
	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, -3.2e-72], t$95$1, If[LessEqual[z, 6.4e-131], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999999e-72 or 6.3999999999999999e-131 < z

   1. Initial program 87.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 70.6

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

   5. Simplified 70.6%

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

   if -3.19999999999999999e-72 < z < 6.3999999999999999e-131

   1. Initial program 96.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 72.6

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

   5. Simplified 72.6%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-131}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+186}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.02e+186) (/ (/ x y) (- t z)) (/ x (* (- y z) (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e+186) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - 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) :: tmp
    if (y <= (-1.02d+186)) then
        tmp = (x / y) / (t - z)
    else
        tmp = x / ((y - z) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e+186) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.02e+186:
		tmp = (x / y) / (t - z)
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.02e+186)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.02e+186)
		tmp = (x / y) / (t - z);
	else
		tmp = x / ((y - z) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.02e+186], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.01999999999999999e186

   1. Initial program 68.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 68.0

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

   5. Simplified 68.0%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]
   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 92.9

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

   7. Applied egg-rr 92.9%

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

   if -1.01999999999999999e186 < y

   1. Initial program 93.1%

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

Alternative 9: 89.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.1 \cdot 10^{+221}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.1e+221) (/ x (* (- y z) (- t z))) (/ (/ x t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.1e+221) {
		tmp = x / ((y - 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 (t <= 3.1d+221) then
        tmp = x / ((y - 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 (t <= 3.1e+221) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 3.1e+221:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3.1e+221)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 3.1e+221)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 3.1e+221], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.10000000000000006e221

   1. Initial program 91.4%

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

   if 3.10000000000000006e221 < t

   1. Initial program 73.2%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 73.2

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

   4. Applied egg-rr 73.2%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 73.2%

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

      1. associate-*l/ N/A

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

      2. *-lft-identity N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. /-lowering-/.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. --lowering--.f64 100.0

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

   9. Applied egg-rr 100.0%

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

Alternative 10: 60.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z z))))
   (if (<= z -2.6e-68) t_1 (if (<= z 1.6e-5) (/ x (* y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -2.6e-68) {
		tmp = t_1;
	} else if (z <= 1.6e-5) {
		tmp = x / (y * t);
	} 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 <= (-2.6d-68)) then
        tmp = t_1
    else if (z <= 1.6d-5) then
        tmp = x / (y * t)
    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 <= -2.6e-68) {
		tmp = t_1;
	} else if (z <= 1.6e-5) {
		tmp = x / (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -2.6e-68:
		tmp = t_1
	elif z <= 1.6e-5:
		tmp = x / (y * t)
	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 <= -2.6e-68)
		tmp = t_1;
	elseif (z <= 1.6e-5)
		tmp = Float64(x / Float64(y * t));
	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 <= -2.6e-68)
		tmp = t_1;
	elseif (z <= 1.6e-5)
		tmp = x / (y * t);
	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, -2.6e-68], t$95$1, If[LessEqual[z, 1.6e-5], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5999999999999998e-68 or 1.59999999999999993e-5 < z

   1. Initial program 85.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 66.6

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

   5. Simplified 66.6%

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

   if -2.5999999999999998e-68 < z < 1.59999999999999993e-5

   1. Initial program 96.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 62.6

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

   5. Simplified 62.6%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.4%

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

Alternative 12: 39.4% accurate, 1.4× 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 90.4%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
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 37.0

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

5. Simplified 37.0%

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

6. Final simplification 37.0%

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

Developer Target 1: 87.6% 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 2024195 
(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))))