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

Percentage Accurate: 61.4% → 98.5%

Time: 17.0s

Alternatives: 11

Speedup: 30.1×

• could not determine a ground truth

  1. x = 4.5544957150925114e+136
  2. y = 3.399418450264746e+206
  3. z = 5.615964138947263e+90
  4. t = 9.275544397594602e+110

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: 98.5% 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 63.0%

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

   1. remove-double-neg 63.0%

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

   2. neg-mul-1 63.0%

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

   3. *-commutative 63.0%

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

   4. *-commutative 63.0%

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

   5. neg-mul-1 63.0%

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

   6. remove-double-neg 63.0%

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

   7. sub-neg 63.0%

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

   8. associate-+l+ 77.4%

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

   9. cancel-sign-sub 77.4%

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

   10. log1p-def 84.8%

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

   11. cancel-sign-sub 84.8%

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

   12. +-commutative 84.8%

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

   13. unsub-neg 84.8%

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

   14. *-rgt-identity 84.8%

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

   15. distribute-lft-out-- 84.8%

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

   16. expm1-def 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 2: 93.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x + \frac{-1}{t \cdot 0.5 + \frac{t}{y \cdot \left(e^{z} + -1\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(y \cdot z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (exp z) 0.0)
   (+ x (/ -1.0 (+ (* t 0.5) (/ t (* y (+ (exp z) -1.0))))))
   (- x (/ (log1p (* y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (exp(z) <= 0.0) {
		tmp = x + (-1.0 / ((t * 0.5) + (t / (y * (exp(z) + -1.0)))));
	} else {
		tmp = x - (log1p((y * z)) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (Math.exp(z) <= 0.0) {
		tmp = x + (-1.0 / ((t * 0.5) + (t / (y * (Math.exp(z) + -1.0)))));
	} else {
		tmp = x - (Math.log1p((y * z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if math.exp(z) <= 0.0:
		tmp = x + (-1.0 / ((t * 0.5) + (t / (y * (math.exp(z) + -1.0)))))
	else:
		tmp = x - (math.log1p((y * z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (exp(z) <= 0.0)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(t * 0.5) + Float64(t / Float64(y * Float64(exp(z) + -1.0))))));
	else
		tmp = Float64(x - Float64(log1p(Float64(y * z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[Exp[z], $MachinePrecision], 0.0], N[(x + N[(-1.0 / N[(N[(t * 0.5), $MachinePrecision] + N[(t / N[(y * N[(N[Exp[z], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[1 + N[(y * z), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (exp.f64 z) < 0.0

   1. Initial program 75.7%

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

      1. remove-double-neg 75.7%

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

      2. neg-mul-1 75.7%

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

      3. *-commutative 75.7%

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

      4. *-commutative 75.7%

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

      5. neg-mul-1 75.7%

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

      6. remove-double-neg 75.7%

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

      7. sub-neg 75.7%

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

      8. associate-+l+ 75.7%

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

      9. cancel-sign-sub 75.7%

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

      10. log1p-def 99.9%

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

      11. cancel-sign-sub 99.9%

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

      12. +-commutative 99.9%

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

      13. unsub-neg 99.9%

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

      14. *-rgt-identity 99.9%

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

      15. distribute-lft-out-- 99.9%

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

      16. 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. Add Preprocessing
   5. 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/ 99.8%

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

   6. Applied egg-rr 99.8%

      \[\leadsto x - \color{blue}{\frac{1}{t} \cdot \mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in y around 0 85.7%

      \[\leadsto x - \frac{1}{\color{blue}{0.5 \cdot t + \frac{t}{y \cdot \left(e^{z} - 1\right)}}} \]

   if 0.0 < (exp.f64 z)

   1. Initial program 57.4%

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

      1. remove-double-neg 57.4%

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

      2. neg-mul-1 57.4%

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

      3. *-commutative 57.4%

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

      4. *-commutative 57.4%

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

      5. neg-mul-1 57.4%

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

      6. remove-double-neg 57.4%

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

      7. sub-neg 57.4%

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

      8. associate-+l+ 78.1%

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

      9. cancel-sign-sub 78.1%

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

      10. log1p-def 78.1%

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

      11. cancel-sign-sub 78.1%

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

      12. +-commutative 78.1%

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

      13. unsub-neg 78.1%

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

      14. *-rgt-identity 78.1%

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

      15. distribute-lft-out-- 78.1%

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

      16. expm1-def 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around 0 98.2%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot z}\right)}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x + \frac{-1}{t \cdot 0.5 + \frac{t}{y \cdot \left(e^{z} + -1\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(y \cdot z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -25:\\ \;\;\;\;x + \frac{\frac{-1}{t}}{0.5 + \frac{1}{y \cdot \mathsf{expm1}\left(z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(y \cdot z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -25.0)
   (+ x (/ (/ -1.0 t) (+ 0.5 (/ 1.0 (* y (expm1 z))))))
   (- x (/ (log1p (* y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -25.0) {
		tmp = x + ((-1.0 / t) / (0.5 + (1.0 / (y * expm1(z)))));
	} else {
		tmp = x - (log1p((y * z)) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -25.0) {
		tmp = x + ((-1.0 / t) / (0.5 + (1.0 / (y * Math.expm1(z)))));
	} else {
		tmp = x - (Math.log1p((y * z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -25.0:
		tmp = x + ((-1.0 / t) / (0.5 + (1.0 / (y * math.expm1(z)))))
	else:
		tmp = x - (math.log1p((y * z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -25.0)
		tmp = Float64(x + Float64(Float64(-1.0 / t) / Float64(0.5 + Float64(1.0 / Float64(y * expm1(z))))));
	else
		tmp = Float64(x - Float64(log1p(Float64(y * z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -25.0], N[(x + N[(N[(-1.0 / t), $MachinePrecision] / N[(0.5 + N[(1.0 / N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[1 + N[(y * z), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -25

   1. Initial program 75.7%

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

      1. remove-double-neg 75.7%

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

      2. neg-mul-1 75.7%

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

      3. *-commutative 75.7%

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

      4. *-commutative 75.7%

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

      5. neg-mul-1 75.7%

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

      6. remove-double-neg 75.7%

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

      7. sub-neg 75.7%

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

      8. associate-+l+ 75.7%

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

      9. cancel-sign-sub 75.7%

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

      10. log1p-def 99.9%

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

      11. cancel-sign-sub 99.9%

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

      12. +-commutative 99.9%

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

      13. unsub-neg 99.9%

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

      14. *-rgt-identity 99.9%

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

      15. distribute-lft-out-- 99.9%

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

      16. 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. Add Preprocessing
   5. 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/ 99.8%

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

   6. Applied egg-rr 99.8%

      \[\leadsto x - \color{blue}{\frac{1}{t} \cdot \mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-/r/ 99.8%

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

      2. div-inv 99.7%

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

      3. associate-/r* 99.6%

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

   8. Applied egg-rr 99.6%

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

   9. Taylor expanded in y around 0 85.6%

      \[\leadsto x - \frac{\frac{1}{t}}{\color{blue}{0.5 + \frac{1}{y \cdot \left(e^{z} - 1\right)}}} \]
   10. Step-by-step derivation

       1. expm1-def 85.6%

          \[\leadsto x - \frac{\frac{1}{t}}{0.5 + \frac{1}{y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}}} \]

   11. Simplified 85.6%

       \[\leadsto x - \frac{\frac{1}{t}}{\color{blue}{0.5 + \frac{1}{y \cdot \mathsf{expm1}\left(z\right)}}} \]

   if -25 < z

   1. Initial program 57.4%

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

      1. remove-double-neg 57.4%

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

      2. neg-mul-1 57.4%

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

      3. *-commutative 57.4%

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

      4. *-commutative 57.4%

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

      5. neg-mul-1 57.4%

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

      6. remove-double-neg 57.4%

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

      7. sub-neg 57.4%

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

      8. associate-+l+ 78.1%

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

      9. cancel-sign-sub 78.1%

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

      10. log1p-def 78.1%

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

      11. cancel-sign-sub 78.1%

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

      12. +-commutative 78.1%

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

      13. unsub-neg 78.1%

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

      14. *-rgt-identity 78.1%

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

      15. distribute-lft-out-- 78.1%

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

      16. expm1-def 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around 0 98.2%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot z}\right)}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -25:\\ \;\;\;\;x + \frac{\frac{-1}{t}}{0.5 + \frac{1}{y \cdot \mathsf{expm1}\left(z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(y \cdot z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-207}:\\ \;\;\;\;x - \mathsf{expm1}\left(z\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.75e-207) (- x (* (expm1 z) (/ y t))) (- x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e-207) {
		tmp = x - (expm1(z) * (y / t));
	} else {
		tmp = x - (y * (z / t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e-207) {
		tmp = x - (Math.expm1(z) * (y / t));
	} else {
		tmp = x - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.75e-207:
		tmp = x - (math.expm1(z) * (y / t))
	else:
		tmp = x - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.75e-207)
		tmp = Float64(x - Float64(expm1(z) * Float64(y / t)));
	else
		tmp = Float64(x - Float64(y * Float64(z / t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.75e-207], N[(x - N[(N[(Exp[z] - 1), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7500000000000001e-207

   1. Initial program 65.5%

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

      1. remove-double-neg 65.5%

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

      2. neg-mul-1 65.5%

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

      3. *-commutative 65.5%

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

      4. *-commutative 65.5%

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

      5. neg-mul-1 65.5%

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

      6. remove-double-neg 65.5%

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

      7. sub-neg 65.5%

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

      8. associate-+l+ 75.5%

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

      9. cancel-sign-sub 75.5%

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

      10. log1p-def 90.0%

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

      11. cancel-sign-sub 90.0%

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

      12. +-commutative 90.0%

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

      13. unsub-neg 90.0%

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

      14. *-rgt-identity 90.0%

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

      15. distribute-lft-out-- 90.0%

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

      16. 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. Add Preprocessing

   5. Taylor expanded in y around 0 77.0%

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

      1. associate-/l* 77.0%

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

      2. associate-/r/ 76.9%

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

      3. expm1-def 84.5%

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

   7. Simplified 84.5%

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

   if -1.7500000000000001e-207 < z

   1. Initial program 60.4%

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

      1. remove-double-neg 60.4%

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

      2. neg-mul-1 60.4%

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

      3. *-commutative 60.4%

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

      4. *-commutative 60.4%

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

      5. neg-mul-1 60.4%

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

      6. remove-double-neg 60.4%

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

      7. sub-neg 60.4%

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

      8. associate-+l+ 79.4%

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

      9. cancel-sign-sub 79.4%

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

      10. log1p-def 79.4%

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

      11. cancel-sign-sub 79.4%

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

      12. +-commutative 79.4%

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

      13. unsub-neg 79.4%

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

      14. *-rgt-identity 79.4%

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

      15. distribute-lft-out-- 79.4%

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

      16. expm1-def 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around 0 93.8%

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

      1. associate-/l* 94.6%

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

   7. Simplified 94.6%

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

      1. clear-num 94.5%

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

      2. associate-/r/ 94.5%

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

      3. clear-num 94.6%

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

   9. Applied egg-rr 94.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-207}:\\ \;\;\;\;x - \mathsf{expm1}\left(z\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+23}:\\ \;\;\;\;x - \mathsf{expm1}\left(z\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(y \cdot z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.25e+23) (- x (* (expm1 z) (/ y t))) (- x (/ (log1p (* y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.25e+23) {
		tmp = x - (expm1(z) * (y / t));
	} else {
		tmp = x - (log1p((y * z)) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.25e+23) {
		tmp = x - (Math.expm1(z) * (y / t));
	} else {
		tmp = x - (Math.log1p((y * z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.25e+23:
		tmp = x - (math.expm1(z) * (y / t))
	else:
		tmp = x - (math.log1p((y * z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.25e+23)
		tmp = Float64(x - Float64(expm1(z) * Float64(y / t)));
	else
		tmp = Float64(x - Float64(log1p(Float64(y * z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.25e+23], N[(x - N[(N[(Exp[z] - 1), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[1 + N[(y * z), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2499999999999999e23

   1. Initial program 75.8%

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

      1. remove-double-neg 75.8%

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

      2. neg-mul-1 75.8%

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

      3. *-commutative 75.8%

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

      4. *-commutative 75.8%

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

      5. neg-mul-1 75.8%

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

      6. remove-double-neg 75.8%

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

      7. sub-neg 75.8%

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

      8. associate-+l+ 75.8%

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

      9. cancel-sign-sub 75.8%

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

      10. log1p-def 99.9%

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

      11. cancel-sign-sub 99.9%

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

      12. +-commutative 99.9%

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

      13. unsub-neg 99.9%

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

      14. *-rgt-identity 99.9%

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

      15. distribute-lft-out-- 99.9%

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

      16. 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. Add Preprocessing

   5. Taylor expanded in y around 0 81.7%

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

      1. associate-/l* 81.7%

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

      2. associate-/r/ 81.7%

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

      3. expm1-def 81.7%

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

   7. Simplified 81.7%

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

   if -2.2499999999999999e23 < z

   1. Initial program 57.8%

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

      1. remove-double-neg 57.8%

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

      2. neg-mul-1 57.8%

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

      3. *-commutative 57.8%

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

      4. *-commutative 57.8%

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

      5. neg-mul-1 57.8%

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

      6. remove-double-neg 57.8%

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

      7. sub-neg 57.8%

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

      8. associate-+l+ 78.0%

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

      9. cancel-sign-sub 78.0%

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

      10. log1p-def 78.6%

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

      11. cancel-sign-sub 78.6%

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

      12. +-commutative 78.6%

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

      13. unsub-neg 78.6%

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

      14. *-rgt-identity 78.6%

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

      15. distribute-lft-out-- 78.6%

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

      16. expm1-def 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around 0 97.3%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot z}\right)}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+23}:\\ \;\;\;\;x - \mathsf{expm1}\left(z\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(y \cdot z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.0% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Initial program 63.0%

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

   1. remove-double-neg 63.0%

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

   2. neg-mul-1 63.0%

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

   3. *-commutative 63.0%

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

   4. *-commutative 63.0%

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

   5. neg-mul-1 63.0%

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

   6. remove-double-neg 63.0%

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

   7. sub-neg 63.0%

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

   8. associate-+l+ 77.4%

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

   9. cancel-sign-sub 77.4%

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

   10. log1p-def 84.8%

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

   11. cancel-sign-sub 84.8%

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

   12. +-commutative 84.8%

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

   13. unsub-neg 84.8%

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

   14. *-rgt-identity 84.8%

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

   15. distribute-lft-out-- 84.8%

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

   16. expm1-def 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in y around 0 77.8%

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

   1. associate-/l* 77.8%

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

   2. associate-/r/ 77.3%

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

   3. expm1-def 86.2%

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

7. Simplified 86.2%

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

   1. *-commutative 86.2%

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

   2. clear-num 86.2%

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

   3. un-div-inv 87.0%

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

9. Applied egg-rr 87.0%

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

    1. associate-/r/ 89.4%

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

11. Applied egg-rr 89.4%

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

12. Final simplification 89.4%

    \[\leadsto x - y \cdot \frac{\mathsf{expm1}\left(z\right)}{t} \]
13. Add Preprocessing

Alternative 7: 76.6% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+71}:\\ \;\;\;\;x + \frac{1}{t} \cdot \left(-1 + \left(1 - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e+71)
   (+ x (* (/ 1.0 t) (+ -1.0 (- 1.0 (* y z)))))
   (- x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+71) {
		tmp = x + ((1.0 / t) * (-1.0 + (1.0 - (y * z))));
	} else {
		tmp = x - (y / (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 (z <= (-1.8d+71)) then
        tmp = x + ((1.0d0 / t) * ((-1.0d0) + (1.0d0 - (y * z))))
    else
        tmp = x - (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+71) {
		tmp = x + ((1.0 / t) * (-1.0 + (1.0 - (y * z))));
	} else {
		tmp = x - (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e+71:
		tmp = x + ((1.0 / t) * (-1.0 + (1.0 - (y * z))))
	else:
		tmp = x - (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e+71)
		tmp = Float64(x + Float64(Float64(1.0 / t) * Float64(-1.0 + Float64(1.0 - Float64(y * z)))));
	else
		tmp = Float64(x - Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e+71)
		tmp = x + ((1.0 / t) * (-1.0 + (1.0 - (y * z))));
	else
		tmp = x - (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e+71], N[(x + N[(N[(1.0 / t), $MachinePrecision] * N[(-1.0 + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e71

   1. Initial program 77.7%

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

      1. remove-double-neg 77.7%

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

      2. neg-mul-1 77.7%

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

      3. *-commutative 77.7%

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

      4. *-commutative 77.7%

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

      5. neg-mul-1 77.7%

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

      6. remove-double-neg 77.7%

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

      7. sub-neg 77.7%

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

      8. associate-+l+ 77.7%

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

      9. cancel-sign-sub 77.7%

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

      10. log1p-def 99.9%

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

      11. cancel-sign-sub 99.9%

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

      12. +-commutative 99.9%

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

      13. unsub-neg 99.9%

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

      14. *-rgt-identity 99.9%

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

      15. distribute-lft-out-- 99.9%

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

      16. 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. Add Preprocessing

   5. Taylor expanded in z around 0 30.7%

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

      1. associate-/l* 25.9%

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

   7. Simplified 25.9%

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

      1. *-un-lft-identity 25.9%

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

      2. div-inv 25.9%

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

      3. times-frac 30.7%

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

   9. Applied egg-rr 30.7%

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

       1. associate-/r/ 30.7%

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

       2. /-rgt-identity 30.7%

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

       3. expm1-log1p-u 24.4%

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

       4. expm1-udef 31.9%

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

       5. log1p-udef 31.9%

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

       6. rem-exp-log 38.2%

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

   11. Applied egg-rr 38.2%

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

       1. associate--l+ 38.2%

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

   13. Simplified 38.2%

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

   if -1.8e71 < z

   1. Initial program 58.2%

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

      1. remove-double-neg 58.2%

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

      2. neg-mul-1 58.2%

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

      3. *-commutative 58.2%

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

      4. *-commutative 58.2%

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

      5. neg-mul-1 58.2%

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

      6. remove-double-neg 58.2%

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

      7. sub-neg 58.2%

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

      8. associate-+l+ 77.3%

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

      9. cancel-sign-sub 77.3%

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

      10. log1p-def 79.8%

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

      11. cancel-sign-sub 79.8%

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

      12. +-commutative 79.8%

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

      13. unsub-neg 79.8%

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

      14. *-rgt-identity 79.8%

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

      15. distribute-lft-out-- 79.8%

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

      16. 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. Add Preprocessing

   5. Taylor expanded in z around 0 88.1%

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

      1. associate-/l* 88.6%

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

   7. Simplified 88.6%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+71}:\\ \;\;\;\;x + \frac{1}{t} \cdot \left(-1 + \left(1 - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.8% 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 63.0%

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

   1. remove-double-neg 63.0%

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

   2. neg-mul-1 63.0%

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

   3. *-commutative 63.0%

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

   4. *-commutative 63.0%

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

   5. neg-mul-1 63.0%

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

   6. remove-double-neg 63.0%

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

   7. sub-neg 63.0%

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

   8. associate-+l+ 77.4%

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

   9. cancel-sign-sub 77.4%

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

   10. log1p-def 84.8%

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

   11. cancel-sign-sub 84.8%

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

   12. +-commutative 84.8%

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

   13. unsub-neg 84.8%

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

   14. *-rgt-identity 84.8%

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

   15. distribute-lft-out-- 84.8%

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

   16. expm1-def 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in z around 0 74.0%

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

   1. associate-/l* 73.2%

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

7. Simplified 73.2%

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

   1. associate-/r/ 71.5%

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

9. Applied egg-rr 71.5%

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

10. Final simplification 71.5%

    \[\leadsto x - z \cdot \frac{y}{t} \]
11. Add Preprocessing

Alternative 9: 75.5% 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 63.0%

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

   1. remove-double-neg 63.0%

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

   2. neg-mul-1 63.0%

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

   3. *-commutative 63.0%

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

   4. *-commutative 63.0%

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

   5. neg-mul-1 63.0%

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

   6. remove-double-neg 63.0%

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

   7. sub-neg 63.0%

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

   8. associate-+l+ 77.4%

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

   9. cancel-sign-sub 77.4%

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

   10. log1p-def 84.8%

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

   11. cancel-sign-sub 84.8%

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

   12. +-commutative 84.8%

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

   13. unsub-neg 84.8%

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

   14. *-rgt-identity 84.8%

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

   15. distribute-lft-out-- 84.8%

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

   16. expm1-def 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in z around 0 74.0%

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

   1. associate-/l* 73.2%

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

7. Simplified 73.2%

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

   1. clear-num 73.2%

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

   2. associate-/r/ 72.8%

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

   3. clear-num 72.8%

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

9. Applied egg-rr 72.8%

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

10. Final simplification 72.8%

    \[\leadsto x - y \cdot \frac{z}{t} \]
11. Add Preprocessing

Alternative 10: 75.6% accurate, 30.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.0%

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

   1. remove-double-neg 63.0%

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

   2. neg-mul-1 63.0%

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

   3. *-commutative 63.0%

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

   4. *-commutative 63.0%

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

   5. neg-mul-1 63.0%

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

   6. remove-double-neg 63.0%

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

   7. sub-neg 63.0%

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

   8. associate-+l+ 77.4%

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

   9. cancel-sign-sub 77.4%

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

   10. log1p-def 84.8%

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

   11. cancel-sign-sub 84.8%

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

   12. +-commutative 84.8%

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

   13. unsub-neg 84.8%

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

   14. *-rgt-identity 84.8%

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

   15. distribute-lft-out-- 84.8%

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

   16. expm1-def 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in z around 0 74.0%

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

   1. associate-/l* 73.2%

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

7. Simplified 73.2%

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

8. Final simplification 73.2%

   \[\leadsto x - \frac{y}{\frac{t}{z}} \]
9. Add Preprocessing

Alternative 11: 75.1% accurate, 30.1× speedup

Math

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

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

Derivation

1. Initial program 63.0%

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

   1. remove-double-neg 63.0%

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

   2. neg-mul-1 63.0%

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

   3. *-commutative 63.0%

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

   4. *-commutative 63.0%

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

   5. neg-mul-1 63.0%

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

   6. remove-double-neg 63.0%

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

   7. sub-neg 63.0%

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

   8. associate-+l+ 77.4%

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

   9. cancel-sign-sub 77.4%

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

   10. log1p-def 84.8%

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

   11. cancel-sign-sub 84.8%

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

   12. +-commutative 84.8%

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

   13. unsub-neg 84.8%

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

   14. *-rgt-identity 84.8%

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

   15. distribute-lft-out-- 84.8%

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

   16. expm1-def 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in z around 0 74.0%

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

6. Final simplification 74.0%

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

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 2024027 
(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)))