System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2

Percentage Accurate: 61.4% → 98.4%

Time: 13.7s

Alternatives: 7

Speedup: 30.1×

• could not determine a ground truth

  1. x = 2.1560692296959438e+98
  2. y = 4.690658034031168e+33
  3. z = 1.046539726280781e+265
  4. t = -1.7469676924252823e+205

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return x - (Math.log(((1.0 - y) + (y * Math.exp(z)))) / t);
}

Python

def code(x, y, z, t):
	return x - (math.log(((1.0 - y) + (y * math.exp(z)))) / t)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return x - (Math.log(((1.0 - y) + (y * Math.exp(z)))) / t);
}

Python

def code(x, y, z, t):
	return x - (math.log(((1.0 - y) + (y * math.exp(z)))) / t)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- x (/ (log1p (* y (expm1 z))) t)))

C

double code(double x, double y, double z, double t) {
	return x - (log1p((y * expm1(z))) / t);
}

Java

public static double code(double x, double y, double z, double t) {
	return x - (Math.log1p((y * Math.expm1(z))) / t);
}

Python

def code(x, y, z, t):
	return x - (math.log1p((y * math.expm1(z))) / t)

Julia

function code(x, y, z, t)
	return Float64(x - Float64(log1p(Float64(y * expm1(z))) / t))
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(N[Log[1 + N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 63.1%

   \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
2. Step-by-step derivation

   1. associate-+l- 74.5%

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

   2. sub-neg 74.5%

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

   3. log1p-def 82.0%

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

   4. neg-sub0 82.0%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{0 - \left(y - y \cdot e^{z}\right)}\right)}{t} \]

   5. associate-+l- 82.0%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(0 - y\right) + y \cdot e^{z}}\right)}{t} \]

   6. neg-sub0 82.0%

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

   7. neg-mul-1 82.0%

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

   8. *-commutative 82.0%

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

   9. distribute-rgt-out 82.0%

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

   10. +-commutative 82.0%

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

   11. metadata-eval 82.0%

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

   12. sub-neg 82.0%

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

   13. expm1-def 99.1%

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

3. Simplified 99.1%

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

4. Final simplification 99.1%

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

Alternative 2: 86.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-80}:\\ \;\;\;\;x - \mathsf{expm1}\left(z\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(0.5 \cdot \frac{y \cdot \left(z \cdot z\right)}{t} + y \cdot \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e-80)
   (- x (* (expm1 z) (/ y t)))
   (- x (+ (* 0.5 (/ (* y (* z z)) t)) (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e-80) {
		tmp = x - (expm1(z) * (y / t));
	} else {
		tmp = x - ((0.5 * ((y * (z * z)) / t)) + (y * (z / t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e-80) {
		tmp = x - (Math.expm1(z) * (y / t));
	} else {
		tmp = x - ((0.5 * ((y * (z * z)) / t)) + (y * (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1e-80:
		tmp = x - (math.expm1(z) * (y / t))
	else:
		tmp = x - ((0.5 * ((y * (z * z)) / t)) + (y * (z / t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e-80)
		tmp = Float64(x - Float64(expm1(z) * Float64(y / t)));
	else
		tmp = Float64(x - Float64(Float64(0.5 * Float64(Float64(y * Float64(z * z)) / t)) + Float64(y * Float64(z / t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e-80], N[(x - N[(N[(Exp[z] - 1), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(0.5 * N[(N[(y * N[(z * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999961e-81

   1. Initial program 76.5%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. associate-+l- 77.5%

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

      2. sub-neg 77.5%

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

      3. log1p-def 93.5%

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

      4. neg-sub0 93.5%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{0 - \left(y - y \cdot e^{z}\right)}\right)}{t} \]

      5. associate-+l- 93.5%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(0 - y\right) + y \cdot e^{z}}\right)}{t} \]

      6. neg-sub0 93.5%

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

      7. neg-mul-1 93.5%

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

      8. *-commutative 93.5%

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

      9. distribute-rgt-out 93.6%

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

      10. +-commutative 93.6%

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

      11. metadata-eval 93.6%

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

      12. sub-neg 93.6%

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

      13. expm1-def 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}}} \]

      2. associate-/r/ 99.7%

         \[\leadsto x - \color{blue}{\frac{1}{t} \cdot \mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)} \]

   5. Applied egg-rr 99.7%

      \[\leadsto x - \color{blue}{\frac{1}{t} \cdot \mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)} \]

   6. Taylor expanded in y around 0 71.9%

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

      1. expm1-def 76.3%

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

      2. associate-*r/ 76.3%

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

   8. Simplified 76.3%

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

   if -9.99999999999999961e-81 < z

   1. Initial program 52.7%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. associate-+l- 72.3%

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

      2. sub-neg 72.3%

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

      3. log1p-def 73.0%

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

      4. neg-sub0 73.0%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{0 - \left(y - y \cdot e^{z}\right)}\right)}{t} \]

      5. associate-+l- 73.0%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(0 - y\right) + y \cdot e^{z}}\right)}{t} \]

      6. neg-sub0 73.0%

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

      7. neg-mul-1 73.0%

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

      8. *-commutative 73.0%

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

      9. distribute-rgt-out 73.0%

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

      10. +-commutative 73.0%

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

      11. metadata-eval 73.0%

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

      12. sub-neg 73.0%

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

      13. expm1-def 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around 0 72.2%

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

   5. Taylor expanded in z around 0 89.9%

      \[\leadsto x - \color{blue}{\left(\frac{y \cdot z}{t} + 0.5 \cdot \frac{y \cdot {z}^{2}}{t}\right)} \]
   6. Step-by-step derivation

      1. +-commutative 89.9%

         \[\leadsto x - \color{blue}{\left(0.5 \cdot \frac{y \cdot {z}^{2}}{t} + \frac{y \cdot z}{t}\right)} \]

      2. unpow2 89.9%

         \[\leadsto x - \left(0.5 \cdot \frac{y \cdot \color{blue}{\left(z \cdot z\right)}}{t} + \frac{y \cdot z}{t}\right) \]

      3. *-commutative 89.9%

         \[\leadsto x - \left(0.5 \cdot \frac{y \cdot \left(z \cdot z\right)}{t} + \frac{\color{blue}{z \cdot y}}{t}\right) \]

      4. associate-/l* 85.5%

         \[\leadsto x - \left(0.5 \cdot \frac{y \cdot \left(z \cdot z\right)}{t} + \color{blue}{\frac{z}{\frac{t}{y}}}\right) \]

      5. associate-/r/ 90.4%

         \[\leadsto x - \left(0.5 \cdot \frac{y \cdot \left(z \cdot z\right)}{t} + \color{blue}{\frac{z}{t} \cdot y}\right) \]

   7. Simplified 90.4%

      \[\leadsto x - \color{blue}{\left(0.5 \cdot \frac{y \cdot \left(z \cdot z\right)}{t} + \frac{z}{t} \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-80}:\\ \;\;\;\;x - \mathsf{expm1}\left(z\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(0.5 \cdot \frac{y \cdot \left(z \cdot z\right)}{t} + y \cdot \frac{z}{t}\right)\\ \end{array} \]

Alternative 3: 87.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+213}:\\ \;\;\;\;x + \frac{-1}{z \cdot \left(y \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{\mathsf{expm1}\left(z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.4e+213)
   (+ x (/ -1.0 (* z (* y t))))
   (- x (* y (/ (expm1 z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e+213) {
		tmp = x + (-1.0 / (z * (y * t)));
	} else {
		tmp = x - (y * (expm1(z) / t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e+213) {
		tmp = x + (-1.0 / (z * (y * t)));
	} else {
		tmp = x - (y * (Math.expm1(z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.4e+213:
		tmp = x + (-1.0 / (z * (y * t)))
	else:
		tmp = x - (y * (math.expm1(z) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.4e+213)
		tmp = Float64(x + Float64(-1.0 / Float64(z * Float64(y * t))));
	else
		tmp = Float64(x - Float64(y * Float64(expm1(z) / t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.4e+213], N[(x + N[(-1.0 / N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999998e213

   1. Initial program 68.4%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. associate-+l- 77.8%

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

      2. sub-neg 77.8%

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

      3. log1p-def 77.8%

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

      4. neg-sub0 77.8%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{0 - \left(y - y \cdot e^{z}\right)}\right)}{t} \]

      5. associate-+l- 77.8%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(0 - y\right) + y \cdot e^{z}}\right)}{t} \]

      6. neg-sub0 77.8%

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

      7. neg-mul-1 77.8%

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

      8. *-commutative 77.8%

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

      9. distribute-rgt-out 77.8%

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

      10. +-commutative 77.8%

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

      11. metadata-eval 77.8%

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

      12. sub-neg 77.8%

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

      13. expm1-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 0.0%

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

      1. +-commutative 0.0%

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

      2. associate-+l+ 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-/r* 0.0%

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

      5. expm1-def 0.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\color{blue}{\mathsf{expm1}\left(z\right)}} + \left(-1 \cdot \log \left(\frac{1}{y}\right) + \log \left(e^{z} - 1\right)\right)}{t} \]

      6. mul-1-neg 0.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \left(\color{blue}{\left(-\log \left(\frac{1}{y}\right)\right)} + \log \left(e^{z} - 1\right)\right)}{t} \]

      7. log-rec 0.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \left(\left(-\color{blue}{\left(-\log y\right)}\right) + \log \left(e^{z} - 1\right)\right)}{t} \]

      8. remove-double-neg 0.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \left(\color{blue}{\log y} + \log \left(e^{z} - 1\right)\right)}{t} \]

      9. log-prod 68.4%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \color{blue}{\log \left(y \cdot \left(e^{z} - 1\right)\right)}}{t} \]

      10. expm1-def 90.7%

          \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

      11. expm1-def 68.4%

          \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \left(y \cdot \color{blue}{\left(e^{z} - 1\right)}\right)}{t} \]

      12. *-commutative 68.4%

          \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \color{blue}{\left(\left(e^{z} - 1\right) \cdot y\right)}}{t} \]

      13. expm1-def 90.7%

          \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \left(\color{blue}{\mathsf{expm1}\left(z\right)} \cdot y\right)}{t} \]

   6. Simplified 90.7%

      \[\leadsto x - \frac{\color{blue}{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \left(\mathsf{expm1}\left(z\right) \cdot y\right)}}{t} \]

   7. Taylor expanded in z around 0 39.3%

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

      1. associate-*r* 39.3%

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

   9. Simplified 39.3%

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

   if -4.3999999999999998e213 < y

   1. Initial program 62.6%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. associate-+l- 74.2%

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

      2. sub-neg 74.2%

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

      3. log1p-def 82.4%

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

      4. neg-sub0 82.4%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{0 - \left(y - y \cdot e^{z}\right)}\right)}{t} \]

      5. associate-+l- 82.4%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(0 - y\right) + y \cdot e^{z}}\right)}{t} \]

      6. neg-sub0 82.4%

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

      7. neg-mul-1 82.4%

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

      8. *-commutative 82.4%

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

      9. distribute-rgt-out 82.4%

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

      10. +-commutative 82.4%

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

      11. metadata-eval 82.4%

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

      12. sub-neg 82.4%

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

      13. expm1-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 77.6%

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

      1. associate-/l* 76.3%

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

      2. associate-/r/ 77.6%

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

      3. expm1-def 91.2%

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

   6. Simplified 91.2%

      \[\leadsto x - \color{blue}{\frac{\mathsf{expm1}\left(z\right)}{t} \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+213}:\\ \;\;\;\;x + \frac{-1}{z \cdot \left(y \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{\mathsf{expm1}\left(z\right)}{t}\\ \end{array} \]

Alternative 4: 78.7% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{-1}{z \cdot \left(y \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.36e+78) (+ x (/ -1.0 (* z (* y t)))) (- x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.36e+78) {
		tmp = x + (-1.0 / (z * (y * 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 (z <= (-1.36d+78)) then
        tmp = x + ((-1.0d0) / (z * (y * 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 (z <= -1.36e+78) {
		tmp = x + (-1.0 / (z * (y * t)));
	} else {
		tmp = x - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.36e+78:
		tmp = x + (-1.0 / (z * (y * t)))
	else:
		tmp = x - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.36e+78)
		tmp = Float64(x + Float64(-1.0 / Float64(z * Float64(y * t))));
	else
		tmp = Float64(x - Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.36e+78)
		tmp = x + (-1.0 / (z * (y * t)));
	else
		tmp = x - (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.36e+78], N[(x + N[(-1.0 / N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35999999999999999e78

   1. Initial program 77.3%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. associate-+l- 77.3%

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

      2. sub-neg 77.3%

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

      3. log1p-def 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{0 - \left(y - y \cdot e^{z}\right)}\right)}{t} \]

      5. associate-+l- 99.9%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(0 - y\right) + y \cdot e^{z}}\right)}{t} \]

      6. neg-sub0 99.9%

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

      7. neg-mul-1 99.9%

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

      8. *-commutative 99.9%

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

      9. distribute-rgt-out 99.9%

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

      10. +-commutative 99.9%

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

      11. metadata-eval 99.9%

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

      12. sub-neg 99.9%

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

      13. expm1-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 0.0%

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

      1. +-commutative 0.0%

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

      2. associate-+l+ 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-/r* 0.0%

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

      5. expm1-def 0.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\color{blue}{\mathsf{expm1}\left(z\right)}} + \left(-1 \cdot \log \left(\frac{1}{y}\right) + \log \left(e^{z} - 1\right)\right)}{t} \]

      6. mul-1-neg 0.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \left(\color{blue}{\left(-\log \left(\frac{1}{y}\right)\right)} + \log \left(e^{z} - 1\right)\right)}{t} \]

      7. log-rec 0.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \left(\left(-\color{blue}{\left(-\log y\right)}\right) + \log \left(e^{z} - 1\right)\right)}{t} \]

      8. remove-double-neg 0.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \left(\color{blue}{\log y} + \log \left(e^{z} - 1\right)\right)}{t} \]

      9. log-prod 48.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \color{blue}{\log \left(y \cdot \left(e^{z} - 1\right)\right)}}{t} \]

      10. expm1-def 48.0%

          \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

      11. expm1-def 48.0%

          \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \left(y \cdot \color{blue}{\left(e^{z} - 1\right)}\right)}{t} \]

      12. *-commutative 48.0%

          \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \color{blue}{\left(\left(e^{z} - 1\right) \cdot y\right)}}{t} \]

      13. expm1-def 48.0%

          \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \left(\color{blue}{\mathsf{expm1}\left(z\right)} \cdot y\right)}{t} \]

   6. Simplified 48.0%

      \[\leadsto x - \frac{\color{blue}{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \left(\mathsf{expm1}\left(z\right) \cdot y\right)}}{t} \]

   7. Taylor expanded in z around 0 56.4%

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

      1. associate-*r* 54.8%

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

   9. Simplified 54.8%

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

   if -1.35999999999999999e78 < z

   1. Initial program 58.5%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. associate-+l- 73.6%

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

      2. sub-neg 73.6%

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

      3. log1p-def 76.1%

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

      4. neg-sub0 76.1%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{0 - \left(y - y \cdot e^{z}\right)}\right)}{t} \]

      5. associate-+l- 76.1%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(0 - y\right) + y \cdot e^{z}}\right)}{t} \]

      6. neg-sub0 76.1%

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

      7. neg-mul-1 76.1%

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

      8. *-commutative 76.1%

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

      9. distribute-rgt-out 76.1%

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

      10. +-commutative 76.1%

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

      11. metadata-eval 76.1%

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

      12. sub-neg 76.1%

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

      13. expm1-def 98.9%

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

   3. Simplified 98.9%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. clear-num 98.8%

         \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}}} \]

      2. associate-/r/ 98.8%

         \[\leadsto x - \color{blue}{\frac{1}{t} \cdot \mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)} \]

   5. Applied egg-rr 98.8%

      \[\leadsto x - \color{blue}{\frac{1}{t} \cdot \mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)} \]

   6. Taylor expanded in z around 0 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-/l* 81.3%

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

      3. associate-/r/ 84.9%

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

   8. Simplified 84.9%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{-1}{z \cdot \left(y \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 79.4% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{\frac{-1}{y}}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e+77) (+ x (/ (/ -1.0 y) (* z t))) (- x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e+77) {
		tmp = x + ((-1.0 / y) / (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 (z <= (-3.7d+77)) then
        tmp = x + (((-1.0d0) / y) / (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 (z <= -3.7e+77) {
		tmp = x + ((-1.0 / y) / (z * t));
	} else {
		tmp = x - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.7e+77:
		tmp = x + ((-1.0 / y) / (z * t))
	else:
		tmp = x - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e+77)
		tmp = Float64(x + Float64(Float64(-1.0 / y) / Float64(z * t)));
	else
		tmp = Float64(x - Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.7e+77)
		tmp = x + ((-1.0 / y) / (z * t));
	else
		tmp = x - (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e+77], N[(x + N[(N[(-1.0 / y), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999995e77

   1. Initial program 77.3%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. associate-+l- 77.3%

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

      2. sub-neg 77.3%

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

      3. log1p-def 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{0 - \left(y - y \cdot e^{z}\right)}\right)}{t} \]

      5. associate-+l- 99.9%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(0 - y\right) + y \cdot e^{z}}\right)}{t} \]

      6. neg-sub0 99.9%

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

      7. neg-mul-1 99.9%

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

      8. *-commutative 99.9%

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

      9. distribute-rgt-out 99.9%

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

      10. +-commutative 99.9%

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

      11. metadata-eval 99.9%

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

      12. sub-neg 99.9%

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

      13. expm1-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 0.0%

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

      1. +-commutative 0.0%

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

      2. associate-+l+ 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-/r* 0.0%

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

      5. expm1-def 0.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\color{blue}{\mathsf{expm1}\left(z\right)}} + \left(-1 \cdot \log \left(\frac{1}{y}\right) + \log \left(e^{z} - 1\right)\right)}{t} \]

      6. mul-1-neg 0.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \left(\color{blue}{\left(-\log \left(\frac{1}{y}\right)\right)} + \log \left(e^{z} - 1\right)\right)}{t} \]

      7. log-rec 0.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \left(\left(-\color{blue}{\left(-\log y\right)}\right) + \log \left(e^{z} - 1\right)\right)}{t} \]

      8. remove-double-neg 0.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \left(\color{blue}{\log y} + \log \left(e^{z} - 1\right)\right)}{t} \]

      9. log-prod 48.0%

         \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \color{blue}{\log \left(y \cdot \left(e^{z} - 1\right)\right)}}{t} \]

      10. expm1-def 48.0%

          \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

      11. expm1-def 48.0%

          \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \left(y \cdot \color{blue}{\left(e^{z} - 1\right)}\right)}{t} \]

      12. *-commutative 48.0%

          \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \color{blue}{\left(\left(e^{z} - 1\right) \cdot y\right)}}{t} \]

      13. expm1-def 48.0%

          \[\leadsto x - \frac{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \left(\color{blue}{\mathsf{expm1}\left(z\right)} \cdot y\right)}{t} \]

   6. Simplified 48.0%

      \[\leadsto x - \frac{\color{blue}{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)} + \log \left(\mathsf{expm1}\left(z\right) \cdot y\right)}}{t} \]

   7. Taylor expanded in z around 0 56.4%

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

      1. associate-/r* 56.4%

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

      2. *-commutative 56.4%

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

   9. Simplified 56.4%

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

   if -3.69999999999999995e77 < z

   1. Initial program 58.5%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. associate-+l- 73.6%

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

      2. sub-neg 73.6%

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

      3. log1p-def 76.1%

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

      4. neg-sub0 76.1%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{0 - \left(y - y \cdot e^{z}\right)}\right)}{t} \]

      5. associate-+l- 76.1%

         \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(0 - y\right) + y \cdot e^{z}}\right)}{t} \]

      6. neg-sub0 76.1%

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

      7. neg-mul-1 76.1%

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

      8. *-commutative 76.1%

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

      9. distribute-rgt-out 76.1%

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

      10. +-commutative 76.1%

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

      11. metadata-eval 76.1%

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

      12. sub-neg 76.1%

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

      13. expm1-def 98.9%

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

   3. Simplified 98.9%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. clear-num 98.8%

         \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}}} \]

      2. associate-/r/ 98.8%

         \[\leadsto x - \color{blue}{\frac{1}{t} \cdot \mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)} \]

   5. Applied egg-rr 98.8%

      \[\leadsto x - \color{blue}{\frac{1}{t} \cdot \mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)} \]

   6. Taylor expanded in z around 0 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-/l* 81.3%

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

      3. associate-/r/ 84.9%

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

   8. Simplified 84.9%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{\frac{-1}{y}}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 72.9% accurate, 30.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.1%

   \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
2. Step-by-step derivation

   1. associate-+l- 74.5%

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

   2. sub-neg 74.5%

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

   3. log1p-def 82.0%

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

   4. neg-sub0 82.0%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{0 - \left(y - y \cdot e^{z}\right)}\right)}{t} \]

   5. associate-+l- 82.0%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(0 - y\right) + y \cdot e^{z}}\right)}{t} \]

   6. neg-sub0 82.0%

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

   7. neg-mul-1 82.0%

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

   8. *-commutative 82.0%

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

   9. distribute-rgt-out 82.0%

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

   10. +-commutative 82.0%

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

   11. metadata-eval 82.0%

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

   12. sub-neg 82.0%

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

   13. expm1-def 99.1%

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

3. Simplified 99.1%

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

4. Taylor expanded in z around 0 71.1%

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

   1. associate-/l* 71.7%

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

   2. associate-/r/ 69.5%

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

6. Simplified 69.5%

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

7. Final simplification 69.5%

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

Alternative 7: 75.1% accurate, 30.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.1%

   \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
2. Step-by-step derivation

   1. associate-+l- 74.5%

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

   2. sub-neg 74.5%

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

   3. log1p-def 82.0%

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

   4. neg-sub0 82.0%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{0 - \left(y - y \cdot e^{z}\right)}\right)}{t} \]

   5. associate-+l- 82.0%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(0 - y\right) + y \cdot e^{z}}\right)}{t} \]

   6. neg-sub0 82.0%

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

   7. neg-mul-1 82.0%

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

   8. *-commutative 82.0%

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

   9. distribute-rgt-out 82.0%

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

   10. +-commutative 82.0%

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

   11. metadata-eval 82.0%

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

   12. sub-neg 82.0%

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

   13. expm1-def 99.1%

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

3. Simplified 99.1%

   \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
4. Step-by-step derivation

   1. clear-num 99.1%

      \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}}} \]

   2. associate-/r/ 99.0%

      \[\leadsto x - \color{blue}{\frac{1}{t} \cdot \mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)} \]

5. Applied egg-rr 99.0%

   \[\leadsto x - \color{blue}{\frac{1}{t} \cdot \mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)} \]

6. Taylor expanded in z around 0 71.1%

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

   1. *-commutative 71.1%

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

   2. associate-/l* 70.1%

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

   3. associate-/r/ 71.7%

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

8. Simplified 71.7%

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

9. Final simplification 71.7%

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

Developer target: 74.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-0.5}{y \cdot t}\\ \mathbf{if}\;z < -2.8874623088207947 \cdot 10^{+119}:\\ \;\;\;\;\left(x - \frac{t_1}{z \cdot z}\right) - t_1 \cdot \frac{\frac{2}{z}}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(1 + z \cdot y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- 0.5) (* y t))))
   (if (< z -2.8874623088207947e+119)
     (- (- x (/ t_1 (* z z))) (* t_1 (/ (/ 2.0 z) (* z z))))
     (- x (/ (log (+ 1.0 (* z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.5 / (y * t);
	double tmp;
	if (z < -2.8874623088207947e+119) {
		tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)));
	} else {
		tmp = x - (log((1.0 + (z * y))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -0.5d0 / (y * t)
    if (z < (-2.8874623088207947d+119)) then
        tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0d0 / z) / (z * z)))
    else
        tmp = x - (log((1.0d0 + (z * y))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -0.5 / (y * t);
	double tmp;
	if (z < -2.8874623088207947e+119) {
		tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)));
	} else {
		tmp = x - (Math.log((1.0 + (z * y))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.5 / (y * t)
	tmp = 0
	if z < -2.8874623088207947e+119:
		tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)))
	else:
		tmp = x - (math.log((1.0 + (z * y))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-0.5) / Float64(y * t))
	tmp = 0.0
	if (z < -2.8874623088207947e+119)
		tmp = Float64(Float64(x - Float64(t_1 / Float64(z * z))) - Float64(t_1 * Float64(Float64(2.0 / z) / Float64(z * z))));
	else
		tmp = Float64(x - Float64(log(Float64(1.0 + Float64(z * y))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.5 / (y * t);
	tmp = 0.0;
	if (z < -2.8874623088207947e+119)
		tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)));
	else
		tmp = x - (log((1.0 + (z * y))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-0.5) / N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.8874623088207947e+119], N[(N[(x - N[(t$95$1 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(N[(2.0 / z), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z t)
  :name "System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2"
  :precision binary64

  :herbie-target
  (if (< z -2.8874623088207947e+119) (- (- x (/ (/ (- 0.5) (* y t)) (* z z))) (* (/ (- 0.5) (* y t)) (/ (/ 2.0 z) (* z z)))) (- x (/ (log (+ 1.0 (* z y))) t)))

  (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))