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

Percentage Accurate: 61.5% → 98.4%

Time: 16.9s

Alternatives: 8

Speedup: 211.0×

• could not determine a ground truth

  1. x = 7.565823935937541e-289
  2. y = 4.4628568279484244e+185
  3. z = 9.749081873845947e+32
  4. t = 4.4785372168415185e+223

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: 61.5% 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 62.1%

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

   1. remove-double-neg 62.1%

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

   2. neg-mul-1 62.1%

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

   3. *-commutative 62.1%

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

   4. *-commutative 62.1%

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

   5. neg-mul-1 62.1%

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

   6. remove-double-neg 62.1%

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

   7. sub-neg 62.1%

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

   8. associate-+l+ 76.4%

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

   9. cancel-sign-sub 76.4%

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

   10. log1p-def 82.6%

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

   11. cancel-sign-sub 82.6%

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

   12. +-commutative 82.6%

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

   13. unsub-neg 82.6%

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

   14. *-rgt-identity 82.6%

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

   15. distribute-lft-out-- 82.7%

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

   16. expm1-def 98.5%

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

3. Simplified 98.5%

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

5. Final simplification 98.5%

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

Alternative 2: 85.8% 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 62.1%

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

   1. remove-double-neg 62.1%

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

   2. neg-mul-1 62.1%

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

   3. *-commutative 62.1%

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

   4. *-commutative 62.1%

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

   5. neg-mul-1 62.1%

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

   6. remove-double-neg 62.1%

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

   7. sub-neg 62.1%

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

   8. associate-+l+ 76.4%

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

   9. cancel-sign-sub 76.4%

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

   10. log1p-def 82.6%

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

   11. cancel-sign-sub 82.6%

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

   12. +-commutative 82.6%

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

   13. unsub-neg 82.6%

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

   14. *-rgt-identity 82.6%

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

   15. distribute-lft-out-- 82.7%

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

   16. expm1-def 98.5%

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

3. Simplified 98.5%

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

5. Taylor expanded in y around 0 73.5%

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

   1. associate-/l* 73.5%

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

   2. expm1-def 85.9%

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

7. Simplified 85.9%

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

   1. clear-num 85.9%

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

   2. associate-/r/ 85.9%

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

   3. clear-num 85.9%

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

9. Applied egg-rr 85.9%

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

10. Final simplification 85.9%

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

Alternative 3: 85.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Initial program 62.1%

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

   1. remove-double-neg 62.1%

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

   2. neg-mul-1 62.1%

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

   3. *-commutative 62.1%

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

   4. *-commutative 62.1%

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

   5. neg-mul-1 62.1%

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

   6. remove-double-neg 62.1%

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

   7. sub-neg 62.1%

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

   8. associate-+l+ 76.4%

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

   9. cancel-sign-sub 76.4%

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

   10. log1p-def 82.6%

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

   11. cancel-sign-sub 82.6%

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

   12. +-commutative 82.6%

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

   13. unsub-neg 82.6%

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

   14. *-rgt-identity 82.6%

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

   15. distribute-lft-out-- 82.7%

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

   16. expm1-def 98.5%

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

3. Simplified 98.5%

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

5. Taylor expanded in y around 0 73.5%

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

   1. associate-/l* 73.5%

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

   2. expm1-def 85.9%

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

7. Simplified 85.9%

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

8. Final simplification 85.9%

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

Alternative 4: 82.2% accurate, 14.1× speedup

Math

\[\begin{array}{l} \\ x - \frac{y}{t \cdot \left(\left(z \cdot 0.08333333333333333 + \frac{1}{z}\right) - 0.5\right)} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- x (/ y (* t (- (+ (* z 0.08333333333333333) (/ 1.0 z)) 0.5)))))

C

double code(double x, double y, double z, double t) {
	return x - (y / (t * (((z * 0.08333333333333333) + (1.0 / z)) - 0.5)));
}

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 * 0.08333333333333333d0) + (1.0d0 / z)) - 0.5d0)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x - (y / (t * (((z * 0.08333333333333333) + (1.0 / z)) - 0.5)));
}

Python

def code(x, y, z, t):
	return x - (y / (t * (((z * 0.08333333333333333) + (1.0 / z)) - 0.5)))

Julia

function code(x, y, z, t)
	return Float64(x - Float64(y / Float64(t * Float64(Float64(Float64(z * 0.08333333333333333) + Float64(1.0 / z)) - 0.5))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - (y / (t * (((z * 0.08333333333333333) + (1.0 / z)) - 0.5)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(y / N[(t * N[(N[(N[(z * 0.08333333333333333), $MachinePrecision] + N[(1.0 / z), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 62.1%

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

   1. remove-double-neg 62.1%

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

   2. neg-mul-1 62.1%

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

   3. *-commutative 62.1%

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

   4. *-commutative 62.1%

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

   5. neg-mul-1 62.1%

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

   6. remove-double-neg 62.1%

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

   7. sub-neg 62.1%

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

   8. associate-+l+ 76.4%

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

   9. cancel-sign-sub 76.4%

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

   10. log1p-def 82.6%

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

   11. cancel-sign-sub 82.6%

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

   12. +-commutative 82.6%

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

   13. unsub-neg 82.6%

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

   14. *-rgt-identity 82.6%

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

   15. distribute-lft-out-- 82.7%

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

   16. expm1-def 98.5%

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

3. Simplified 98.5%

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

5. Taylor expanded in y around 0 73.5%

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

   1. associate-/l* 73.5%

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

   2. expm1-def 85.9%

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

7. Simplified 85.9%

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

8. Taylor expanded in z around 0 79.3%

   \[\leadsto x - \frac{y}{\color{blue}{-1 \cdot \left(z \cdot \left(-0.25 \cdot t + 0.16666666666666666 \cdot t\right)\right) + \left(-1 \cdot \left({z}^{2} \cdot \left(-0.5 \cdot \left(-0.25 \cdot t + 0.16666666666666666 \cdot t\right) + \left(-0.08333333333333333 \cdot t + 0.041666666666666664 \cdot t\right)\right)\right) + \left(-0.5 \cdot t + \frac{t}{z}\right)\right)}} \]

9. Taylor expanded in t around 0 82.1%

   \[\leadsto x - \frac{y}{\color{blue}{t \cdot \left(\left(0.08333333333333333 \cdot z + \frac{1}{z}\right) - 0.5\right)}} \]

10. Final simplification 82.1%

    \[\leadsto x - \frac{y}{t \cdot \left(\left(z \cdot 0.08333333333333333 + \frac{1}{z}\right) - 0.5\right)} \]
11. Add Preprocessing

Alternative 5: 81.5% accurate, 19.2× speedup

Math

\[\begin{array}{l} \\ x - \frac{y}{t \cdot -0.5 + \frac{t}{z}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- x (/ y (+ (* t -0.5) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	return x - (y / ((t * -0.5) + (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 * (-0.5d0)) + (t / z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x - (y / ((t * -0.5) + (t / z)));
}

Python

def code(x, y, z, t):
	return x - (y / ((t * -0.5) + (t / z)))

Julia

function code(x, y, z, t)
	return Float64(x - Float64(y / Float64(Float64(t * -0.5) + Float64(t / z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - (y / ((t * -0.5) + (t / z)));
end

Wolfram

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

Derivation

1. Initial program 62.1%

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

   1. remove-double-neg 62.1%

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

   2. neg-mul-1 62.1%

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

   3. *-commutative 62.1%

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

   4. *-commutative 62.1%

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

   5. neg-mul-1 62.1%

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

   6. remove-double-neg 62.1%

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

   7. sub-neg 62.1%

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

   8. associate-+l+ 76.4%

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

   9. cancel-sign-sub 76.4%

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

   10. log1p-def 82.6%

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

   11. cancel-sign-sub 82.6%

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

   12. +-commutative 82.6%

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

   13. unsub-neg 82.6%

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

   14. *-rgt-identity 82.6%

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

   15. distribute-lft-out-- 82.7%

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

   16. expm1-def 98.5%

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

3. Simplified 98.5%

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

5. Taylor expanded in y around 0 73.5%

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

   1. associate-/l* 73.5%

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

   2. expm1-def 85.9%

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

7. Simplified 85.9%

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

8. Taylor expanded in z around 0 80.7%

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

9. Final simplification 80.7%

   \[\leadsto x - \frac{y}{t \cdot -0.5 + \frac{t}{z}} \]
10. Add Preprocessing

Alternative 6: 73.2% 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 62.1%

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

   1. remove-double-neg 62.1%

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

   2. neg-mul-1 62.1%

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

   3. *-commutative 62.1%

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

   4. *-commutative 62.1%

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

   5. neg-mul-1 62.1%

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

   6. remove-double-neg 62.1%

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

   7. sub-neg 62.1%

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

   8. associate-+l+ 76.4%

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

   9. cancel-sign-sub 76.4%

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

   10. log1p-def 82.6%

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

   11. cancel-sign-sub 82.6%

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

   12. +-commutative 82.6%

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

   13. unsub-neg 82.6%

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

   14. *-rgt-identity 82.6%

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

   15. distribute-lft-out-- 82.7%

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

   16. expm1-def 98.5%

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

3. Simplified 98.5%

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

5. Taylor expanded in z around 0 74.3%

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

   1. associate-/l* 75.2%

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

   2. associate-/r/ 72.7%

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

7. Simplified 72.7%

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

8. Final simplification 72.7%

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

Alternative 7: 74.8% 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 62.1%

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

   1. remove-double-neg 62.1%

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

   2. neg-mul-1 62.1%

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

   3. *-commutative 62.1%

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

   4. *-commutative 62.1%

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

   5. neg-mul-1 62.1%

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

   6. remove-double-neg 62.1%

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

   7. sub-neg 62.1%

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

   8. associate-+l+ 76.4%

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

   9. cancel-sign-sub 76.4%

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

   10. log1p-def 82.6%

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

   11. cancel-sign-sub 82.6%

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

   12. +-commutative 82.6%

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

   13. unsub-neg 82.6%

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

   14. *-rgt-identity 82.6%

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

   15. distribute-lft-out-- 82.7%

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

   16. expm1-def 98.5%

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

3. Simplified 98.5%

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

5. Taylor expanded in z around 0 74.3%

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

   1. associate-/l* 75.2%

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

7. Simplified 75.2%

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

8. Final simplification 75.2%

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

Alternative 8: 71.8% accurate, 211.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 62.1%

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

   1. remove-double-neg 62.1%

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

   2. neg-mul-1 62.1%

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

   3. *-commutative 62.1%

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

   4. *-commutative 62.1%

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

   5. neg-mul-1 62.1%

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

   6. remove-double-neg 62.1%

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

   7. sub-neg 62.1%

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

   8. associate-+l+ 76.4%

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

   9. cancel-sign-sub 76.4%

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

   10. log1p-def 82.6%

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

   11. cancel-sign-sub 82.6%

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

   12. +-commutative 82.6%

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

   13. unsub-neg 82.6%

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

   14. *-rgt-identity 82.6%

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

   15. distribute-lft-out-- 82.7%

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

   16. expm1-def 98.5%

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

3. Simplified 98.5%

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

5. Taylor expanded in x around inf 69.3%

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

6. Final simplification 69.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 75.0% 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 2024033 
(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)))