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

Percentage Accurate: 61.2% → 98.4%

Time: 19.7s

Alternatives: 9

Speedup: 211.0×

• could not determine a ground truth

  1. x = -2.62503250943653e+232
  2. y = 7.446307243858215e+260
  3. z = 5.146259491167161e+180
  4. t = 1.5571282827303193e+268

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: 61.2% 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 68.3%

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

   1. remove-double-neg 68.3%

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

   2. neg-mul-1 68.3%

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

   3. *-commutative 68.3%

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

   4. *-commutative 68.3%

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

   5. neg-mul-1 68.3%

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

   6. remove-double-neg 68.3%

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

   7. sub-neg 68.3%

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

   8. associate-+l+ 82.9%

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

   9. cancel-sign-sub 82.9%

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

   10. log1p-def 85.9%

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

   11. cancel-sign-sub 85.9%

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

   12. +-commutative 85.9%

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

   13. unsub-neg 85.9%

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

   14. *-rgt-identity 85.9%

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

   15. distribute-lft-out-- 85.9%

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

   16. expm1-def 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 2: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+157}:\\ \;\;\;\;\frac{-\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+156}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t}{y}}{\mathsf{expm1}\left(z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.5e+157)
   (/ (- (log1p (* y (expm1 z)))) t)
   (if (<= y 4.8e+156) (+ x (/ -1.0 (/ (/ t y) (expm1 z)))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+157) {
		tmp = -log1p((y * expm1(z))) / t;
	} else if (y <= 4.8e+156) {
		tmp = x + (-1.0 / ((t / y) / expm1(z)));
	} else {
		tmp = x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+157) {
		tmp = -Math.log1p((y * Math.expm1(z))) / t;
	} else if (y <= 4.8e+156) {
		tmp = x + (-1.0 / ((t / y) / Math.expm1(z)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.5e+157:
		tmp = -math.log1p((y * math.expm1(z))) / t
	elif y <= 4.8e+156:
		tmp = x + (-1.0 / ((t / y) / math.expm1(z)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.5e+157)
		tmp = Float64(Float64(-log1p(Float64(y * expm1(z)))) / t);
	elseif (y <= 4.8e+156)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(t / y) / expm1(z))));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.5e+157], N[((-N[Log[1 + N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / t), $MachinePrecision], If[LessEqual[y, 4.8e+156], N[(x + N[(-1.0 / N[(N[(t / y), $MachinePrecision] / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < -1.50000000000000005e157

   1. Initial program 61.8%

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

      1. remove-double-neg 61.8%

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

      2. neg-mul-1 61.8%

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

      3. *-commutative 61.8%

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

      4. *-commutative 61.8%

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

      5. neg-mul-1 61.8%

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

      6. remove-double-neg 61.8%

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

      7. sub-neg 61.8%

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

      8. associate-+l+ 74.7%

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

      9. cancel-sign-sub 74.7%

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

      10. log1p-def 74.7%

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

      11. cancel-sign-sub 74.7%

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

      12. +-commutative 74.7%

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

      13. unsub-neg 74.7%

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

      14. *-rgt-identity 74.7%

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

      15. distribute-lft-out-- 74.7%

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

      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 x around 0 33.9%

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

      1. associate-*r/ 33.9%

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

      2. log1p-def 33.9%

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

      3. expm1-def 56.6%

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

      4. neg-mul-1 56.6%

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

   7. Simplified 56.6%

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

   if -1.50000000000000005e157 < y < 4.8000000000000002e156

   1. Initial program 73.2%

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

      1. remove-double-neg 73.2%

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

      2. neg-mul-1 73.2%

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

      3. *-commutative 73.2%

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

      4. *-commutative 73.2%

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

      5. neg-mul-1 73.2%

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

      6. remove-double-neg 73.2%

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

      7. sub-neg 73.2%

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

      8. associate-+l+ 83.9%

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

      9. cancel-sign-sub 83.9%

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

      10. log1p-def 87.6%

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

      11. cancel-sign-sub 87.6%

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

      12. +-commutative 87.6%

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

      13. unsub-neg 87.6%

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

      14. *-rgt-identity 87.6%

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

      15. distribute-lft-out-- 87.6%

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

      16. expm1-def 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around 0 84.2%

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

      1. expm1-def 92.3%

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

   7. Simplified 92.3%

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

      1. clear-num 92.2%

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

      2. inv-pow 92.2%

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

   9. Applied egg-rr 92.2%

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

       1. unpow-1 92.2%

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

       2. associate-/r* 92.8%

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

   11. Simplified 92.8%

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

   if 4.8000000000000002e156 < y

   1. Initial program 9.2%

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

      1. remove-double-neg 9.2%

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

      2. neg-mul-1 9.2%

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

      3. *-commutative 9.2%

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

      4. *-commutative 9.2%

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

      5. neg-mul-1 9.2%

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

      6. remove-double-neg 9.2%

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

      7. sub-neg 9.2%

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

      8. associate-+l+ 85.9%

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

      9. cancel-sign-sub 85.9%

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

      10. log1p-def 85.9%

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

      11. cancel-sign-sub 85.9%

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

      12. +-commutative 85.9%

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

      13. unsub-neg 85.9%

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

      14. *-rgt-identity 85.9%

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

      15. distribute-lft-out-- 85.9%

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

      16. expm1-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 83.2%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+157}:\\ \;\;\;\;\frac{-\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+156}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t}{y}}{\mathsf{expm1}\left(z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{-1}{\mathsf{fma}\left(-0.5, \frac{t}{y}, \frac{t}{y \cdot z}\right) - z \cdot \left(\frac{t}{y} \cdot -0.08333333333333333\right)}\\ \mathbf{elif}\;y \leq 10^{+158}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t}{y}}{\mathsf{expm1}\left(z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e+38)
   (+
    x
    (/
     -1.0
     (-
      (fma -0.5 (/ t y) (/ t (* y z)))
      (* z (* (/ t y) -0.08333333333333333)))))
   (if (<= y 1e+158) (+ x (/ -1.0 (/ (/ t y) (expm1 z)))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e+38) {
		tmp = x + (-1.0 / (fma(-0.5, (t / y), (t / (y * z))) - (z * ((t / y) * -0.08333333333333333))));
	} else if (y <= 1e+158) {
		tmp = x + (-1.0 / ((t / y) / expm1(z)));
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e+38)
		tmp = Float64(x + Float64(-1.0 / Float64(fma(-0.5, Float64(t / y), Float64(t / Float64(y * z))) - Float64(z * Float64(Float64(t / y) * -0.08333333333333333)))));
	elseif (y <= 1e+158)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(t / y) / expm1(z))));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e+38], N[(x + N[(-1.0 / N[(N[(-0.5 * N[(t / y), $MachinePrecision] + N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(t / y), $MachinePrecision] * -0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+158], N[(x + N[(-1.0 / N[(N[(t / y), $MachinePrecision] / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000003e38

   1. Initial program 53.4%

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

      1. remove-double-neg 53.4%

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

      2. neg-mul-1 53.4%

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

      3. *-commutative 53.4%

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

      4. *-commutative 53.4%

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

      5. neg-mul-1 53.4%

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

      6. remove-double-neg 53.4%

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

      7. sub-neg 53.4%

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

      8. associate-+l+ 78.6%

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

      9. cancel-sign-sub 78.6%

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

      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 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 45.0%

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

      1. expm1-def 51.9%

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

   7. Simplified 51.9%

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

      1. clear-num 51.9%

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

      2. inv-pow 51.9%

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

   9. Applied egg-rr 51.9%

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

       1. unpow-1 51.9%

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

       2. associate-/r* 47.6%

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

   11. Simplified 47.6%

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

   12. Taylor expanded in z around 0 56.7%

       \[\leadsto x - \frac{1}{\color{blue}{-1 \cdot \left(z \cdot \left(-0.25 \cdot \frac{t}{y} + 0.16666666666666666 \cdot \frac{t}{y}\right)\right) + \left(-0.5 \cdot \frac{t}{y} + \frac{t}{y \cdot z}\right)}} \]
   13. Step-by-step derivation

       1. +-commutative 56.7%

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

       2. mul-1-neg 56.7%

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

       3. unsub-neg 56.7%

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

       4. fma-def 56.7%

          \[\leadsto x - \frac{1}{\color{blue}{\mathsf{fma}\left(-0.5, \frac{t}{y}, \frac{t}{y \cdot z}\right)} - z \cdot \left(-0.25 \cdot \frac{t}{y} + 0.16666666666666666 \cdot \frac{t}{y}\right)} \]

       5. distribute-rgt-out 59.3%

          \[\leadsto x - \frac{1}{\mathsf{fma}\left(-0.5, \frac{t}{y}, \frac{t}{y \cdot z}\right) - z \cdot \color{blue}{\left(\frac{t}{y} \cdot \left(-0.25 + 0.16666666666666666\right)\right)}} \]

       6. metadata-eval 59.3%

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

   14. Simplified 59.3%

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

   if -5.5000000000000003e38 < y < 9.99999999999999953e157

   1. Initial program 77.1%

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

      1. remove-double-neg 77.1%

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

      2. neg-mul-1 77.1%

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

      3. *-commutative 77.1%

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

      4. *-commutative 77.1%

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

      5. neg-mul-1 77.1%

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

      6. remove-double-neg 77.1%

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

      7. sub-neg 77.1%

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

      8. associate-+l+ 83.9%

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

      9. cancel-sign-sub 83.9%

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

      10. log1p-def 88.1%

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

      11. cancel-sign-sub 88.1%

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

      12. +-commutative 88.1%

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

      13. unsub-neg 88.1%

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

      14. *-rgt-identity 88.1%

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

      15. distribute-lft-out-- 88.1%

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

      16. expm1-def 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in y around 0 86.5%

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

      1. expm1-def 95.0%

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

   7. Simplified 95.0%

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

      1. clear-num 94.9%

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

      2. inv-pow 94.9%

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

   9. Applied egg-rr 94.9%

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

       1. unpow-1 94.9%

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

       2. associate-/r* 95.5%

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

   11. Simplified 95.5%

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

   if 9.99999999999999953e157 < y

   1. Initial program 9.2%

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

      1. remove-double-neg 9.2%

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

      2. neg-mul-1 9.2%

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

      3. *-commutative 9.2%

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

      4. *-commutative 9.2%

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

      5. neg-mul-1 9.2%

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

      6. remove-double-neg 9.2%

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

      7. sub-neg 9.2%

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

      8. associate-+l+ 85.9%

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

      9. cancel-sign-sub 85.9%

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

      10. log1p-def 85.9%

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

      11. cancel-sign-sub 85.9%

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

      12. +-commutative 85.9%

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

      13. unsub-neg 85.9%

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

      14. *-rgt-identity 85.9%

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

      15. distribute-lft-out-- 85.9%

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

      16. expm1-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 83.2%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{-1}{\mathsf{fma}\left(-0.5, \frac{t}{y}, \frac{t}{y \cdot z}\right) - z \cdot \left(\frac{t}{y} \cdot -0.08333333333333333\right)}\\ \mathbf{elif}\;y \leq 10^{+158}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t}{y}}{\mathsf{expm1}\left(z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{-1}{t \cdot \left(\frac{1}{y \cdot z} + \left(0.5 \cdot \frac{-1}{y} - -0.08333333333333333 \cdot \frac{z}{y}\right)\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+157}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t}{y}}{\mathsf{expm1}\left(z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e+55)
   (+
    x
    (/
     -1.0
     (*
      t
      (+
       (/ 1.0 (* y z))
       (- (* 0.5 (/ -1.0 y)) (* -0.08333333333333333 (/ z y)))))))
   (if (<= y 3.5e+157) (+ x (/ -1.0 (/ (/ t y) (expm1 z)))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e+55) {
		tmp = x + (-1.0 / (t * ((1.0 / (y * z)) + ((0.5 * (-1.0 / y)) - (-0.08333333333333333 * (z / y))))));
	} else if (y <= 3.5e+157) {
		tmp = x + (-1.0 / ((t / y) / expm1(z)));
	} else {
		tmp = x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e+55) {
		tmp = x + (-1.0 / (t * ((1.0 / (y * z)) + ((0.5 * (-1.0 / y)) - (-0.08333333333333333 * (z / y))))));
	} else if (y <= 3.5e+157) {
		tmp = x + (-1.0 / ((t / y) / Math.expm1(z)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e+55:
		tmp = x + (-1.0 / (t * ((1.0 / (y * z)) + ((0.5 * (-1.0 / y)) - (-0.08333333333333333 * (z / y))))))
	elif y <= 3.5e+157:
		tmp = x + (-1.0 / ((t / y) / math.expm1(z)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e+55)
		tmp = Float64(x + Float64(-1.0 / Float64(t * Float64(Float64(1.0 / Float64(y * z)) + Float64(Float64(0.5 * Float64(-1.0 / y)) - Float64(-0.08333333333333333 * Float64(z / y)))))));
	elseif (y <= 3.5e+157)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(t / y) / expm1(z))));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e+55], N[(x + N[(-1.0 / N[(t * N[(N[(1.0 / N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(0.5 * N[(-1.0 / y), $MachinePrecision]), $MachinePrecision] - N[(-0.08333333333333333 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+157], N[(x + N[(-1.0 / N[(N[(t / y), $MachinePrecision] / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4499999999999999e55

   1. Initial program 56.6%

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

      1. remove-double-neg 56.6%

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

      2. neg-mul-1 56.6%

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

      3. *-commutative 56.6%

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

      4. *-commutative 56.6%

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

      5. neg-mul-1 56.6%

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

      6. remove-double-neg 56.6%

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

      7. sub-neg 56.6%

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

      8. associate-+l+ 80.4%

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

      9. cancel-sign-sub 80.4%

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

      10. log1p-def 80.4%

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

      11. cancel-sign-sub 80.4%

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

      12. +-commutative 80.4%

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

      13. unsub-neg 80.4%

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

      14. *-rgt-identity 80.4%

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

      15. distribute-lft-out-- 80.4%

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

      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 45.1%

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

      1. expm1-def 50.7%

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

   7. Simplified 50.7%

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

      1. clear-num 50.7%

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

      2. inv-pow 50.7%

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

   9. Applied egg-rr 50.7%

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

       1. unpow-1 50.7%

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

       2. associate-/r* 46.0%

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

   11. Simplified 46.0%

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

   12. Taylor expanded in z around 0 56.2%

       \[\leadsto x - \frac{1}{\color{blue}{-1 \cdot \left(z \cdot \left(-0.25 \cdot \frac{t}{y} + 0.16666666666666666 \cdot \frac{t}{y}\right)\right) + \left(-0.5 \cdot \frac{t}{y} + \frac{t}{y \cdot z}\right)}} \]
   13. Step-by-step derivation

       1. +-commutative 56.2%

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

       2. mul-1-neg 56.2%

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

       3. unsub-neg 56.2%

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

       4. fma-def 56.2%

          \[\leadsto x - \frac{1}{\color{blue}{\mathsf{fma}\left(-0.5, \frac{t}{y}, \frac{t}{y \cdot z}\right)} - z \cdot \left(-0.25 \cdot \frac{t}{y} + 0.16666666666666666 \cdot \frac{t}{y}\right)} \]

       5. distribute-rgt-out 58.8%

          \[\leadsto x - \frac{1}{\mathsf{fma}\left(-0.5, \frac{t}{y}, \frac{t}{y \cdot z}\right) - z \cdot \color{blue}{\left(\frac{t}{y} \cdot \left(-0.25 + 0.16666666666666666\right)\right)}} \]

       6. metadata-eval 58.8%

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

   14. Simplified 58.8%

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

   15. Taylor expanded in t around 0 58.8%

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

   if -1.4499999999999999e55 < y < 3.50000000000000002e157

   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+ 83.3%

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

      9. cancel-sign-sub 83.3%

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

      10. log1p-def 87.4%

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

      11. cancel-sign-sub 87.4%

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

      12. +-commutative 87.4%

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

      13. unsub-neg 87.4%

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

      14. *-rgt-identity 87.4%

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

      15. distribute-lft-out-- 87.4%

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

      16. expm1-def 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around 0 85.3%

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

      1. expm1-def 94.2%

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

   7. Simplified 94.2%

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

      1. clear-num 94.1%

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

      2. inv-pow 94.1%

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

   9. Applied egg-rr 94.1%

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

       1. unpow-1 94.1%

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

       2. associate-/r* 94.7%

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

   11. Simplified 94.7%

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

   if 3.50000000000000002e157 < y

   1. Initial program 9.2%

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

      1. remove-double-neg 9.2%

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

      2. neg-mul-1 9.2%

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

      3. *-commutative 9.2%

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

      4. *-commutative 9.2%

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

      5. neg-mul-1 9.2%

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

      6. remove-double-neg 9.2%

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

      7. sub-neg 9.2%

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

      8. associate-+l+ 85.9%

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

      9. cancel-sign-sub 85.9%

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

      10. log1p-def 85.9%

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

      11. cancel-sign-sub 85.9%

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

      12. +-commutative 85.9%

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

      13. unsub-neg 85.9%

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

      14. *-rgt-identity 85.9%

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

      15. distribute-lft-out-- 85.9%

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

      16. expm1-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 83.2%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{-1}{t \cdot \left(\frac{1}{y \cdot z} + \left(0.5 \cdot \frac{-1}{y} - -0.08333333333333333 \cdot \frac{z}{y}\right)\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+157}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{t}{y}}{\mathsf{expm1}\left(z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{-1}{t \cdot \left(\frac{1}{y \cdot z} + \left(0.5 \cdot \frac{-1}{y} - -0.08333333333333333 \cdot \frac{z}{y}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \mathsf{expm1}\left(z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e+55)
   (+
    x
    (/
     -1.0
     (*
      t
      (+
       (/ 1.0 (* y z))
       (- (* 0.5 (/ -1.0 y)) (* -0.08333333333333333 (/ z y)))))))
   (- x (/ (* y (expm1 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+55) {
		tmp = x + (-1.0 / (t * ((1.0 / (y * z)) + ((0.5 * (-1.0 / y)) - (-0.08333333333333333 * (z / y))))));
	} else {
		tmp = x - ((y * expm1(z)) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+55) {
		tmp = x + (-1.0 / (t * ((1.0 / (y * z)) + ((0.5 * (-1.0 / y)) - (-0.08333333333333333 * (z / y))))));
	} else {
		tmp = x - ((y * Math.expm1(z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e+55:
		tmp = x + (-1.0 / (t * ((1.0 / (y * z)) + ((0.5 * (-1.0 / y)) - (-0.08333333333333333 * (z / y))))))
	else:
		tmp = x - ((y * math.expm1(z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e+55)
		tmp = Float64(x + Float64(-1.0 / Float64(t * Float64(Float64(1.0 / Float64(y * z)) + Float64(Float64(0.5 * Float64(-1.0 / y)) - Float64(-0.08333333333333333 * Float64(z / y)))))));
	else
		tmp = Float64(x - Float64(Float64(y * expm1(z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e+55], N[(x + N[(-1.0 / N[(t * N[(N[(1.0 / N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(0.5 * N[(-1.0 / y), $MachinePrecision]), $MachinePrecision] - N[(-0.08333333333333333 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8000000000000001e55

   1. Initial program 56.6%

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

      1. remove-double-neg 56.6%

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

      2. neg-mul-1 56.6%

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

      3. *-commutative 56.6%

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

      4. *-commutative 56.6%

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

      5. neg-mul-1 56.6%

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

      6. remove-double-neg 56.6%

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

      7. sub-neg 56.6%

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

      8. associate-+l+ 80.4%

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

      9. cancel-sign-sub 80.4%

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

      10. log1p-def 80.4%

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

      11. cancel-sign-sub 80.4%

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

      12. +-commutative 80.4%

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

      13. unsub-neg 80.4%

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

      14. *-rgt-identity 80.4%

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

      15. distribute-lft-out-- 80.4%

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

      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 45.1%

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

      1. expm1-def 50.7%

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

   7. Simplified 50.7%

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

      1. clear-num 50.7%

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

      2. inv-pow 50.7%

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

   9. Applied egg-rr 50.7%

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

       1. unpow-1 50.7%

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

       2. associate-/r* 46.0%

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

   11. Simplified 46.0%

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

   12. Taylor expanded in z around 0 56.2%

       \[\leadsto x - \frac{1}{\color{blue}{-1 \cdot \left(z \cdot \left(-0.25 \cdot \frac{t}{y} + 0.16666666666666666 \cdot \frac{t}{y}\right)\right) + \left(-0.5 \cdot \frac{t}{y} + \frac{t}{y \cdot z}\right)}} \]
   13. Step-by-step derivation

       1. +-commutative 56.2%

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

       2. mul-1-neg 56.2%

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

       3. unsub-neg 56.2%

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

       4. fma-def 56.2%

          \[\leadsto x - \frac{1}{\color{blue}{\mathsf{fma}\left(-0.5, \frac{t}{y}, \frac{t}{y \cdot z}\right)} - z \cdot \left(-0.25 \cdot \frac{t}{y} + 0.16666666666666666 \cdot \frac{t}{y}\right)} \]

       5. distribute-rgt-out 58.8%

          \[\leadsto x - \frac{1}{\mathsf{fma}\left(-0.5, \frac{t}{y}, \frac{t}{y \cdot z}\right) - z \cdot \color{blue}{\left(\frac{t}{y} \cdot \left(-0.25 + 0.16666666666666666\right)\right)}} \]

       6. metadata-eval 58.8%

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

   14. Simplified 58.8%

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

   15. Taylor expanded in t around 0 58.8%

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

   if -2.8000000000000001e55 < y

   1. Initial program 71.2%

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

      1. remove-double-neg 71.2%

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

      2. neg-mul-1 71.2%

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

      3. *-commutative 71.2%

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

      4. *-commutative 71.2%

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

      5. neg-mul-1 71.2%

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

      6. remove-double-neg 71.2%

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

      7. sub-neg 71.2%

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

      8. associate-+l+ 83.5%

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

      9. cancel-sign-sub 83.5%

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

      10. log1p-def 87.3%

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

      11. cancel-sign-sub 87.3%

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

      12. +-commutative 87.3%

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

      13. unsub-neg 87.3%

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

      14. *-rgt-identity 87.3%

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

      15. distribute-lft-out-- 87.3%

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

      16. expm1-def 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around 0 84.9%

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

      1. expm1-def 91.8%

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

   7. Simplified 91.8%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{-1}{t \cdot \left(\frac{1}{y \cdot z} + \left(0.5 \cdot \frac{-1}{y} - -0.08333333333333333 \cdot \frac{z}{y}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \mathsf{expm1}\left(z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.5% accurate, 12.4× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.3%

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

   1. remove-double-neg 68.3%

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

   2. neg-mul-1 68.3%

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

   3. *-commutative 68.3%

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

   4. *-commutative 68.3%

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

   5. neg-mul-1 68.3%

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

   6. remove-double-neg 68.3%

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

   7. sub-neg 68.3%

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

   8. associate-+l+ 82.9%

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

   9. cancel-sign-sub 82.9%

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

   10. log1p-def 85.9%

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

   11. cancel-sign-sub 85.9%

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

   12. +-commutative 85.9%

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

   13. unsub-neg 85.9%

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

   14. *-rgt-identity 85.9%

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

   15. distribute-lft-out-- 85.9%

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

   16. expm1-def 98.0%

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

3. Simplified 98.0%

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

5. Taylor expanded in y around 0 77.1%

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

   1. expm1-def 83.8%

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

7. Simplified 83.8%

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

   1. clear-num 83.7%

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

   2. inv-pow 83.7%

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

9. Applied egg-rr 83.7%

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

    1. unpow-1 83.7%

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

    2. associate-/r* 82.5%

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

11. Simplified 82.5%

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

12. Taylor expanded in z around 0 66.4%

    \[\leadsto x - \frac{1}{\color{blue}{-1 \cdot \left(z \cdot \left(-0.25 \cdot \frac{t}{y} + 0.16666666666666666 \cdot \frac{t}{y}\right)\right) + \left(-0.5 \cdot \frac{t}{y} + \frac{t}{y \cdot z}\right)}} \]
13. Step-by-step derivation

    1. +-commutative 66.4%

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

    2. mul-1-neg 66.4%

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

    3. unsub-neg 66.4%

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

    4. fma-def 66.4%

       \[\leadsto x - \frac{1}{\color{blue}{\mathsf{fma}\left(-0.5, \frac{t}{y}, \frac{t}{y \cdot z}\right)} - z \cdot \left(-0.25 \cdot \frac{t}{y} + 0.16666666666666666 \cdot \frac{t}{y}\right)} \]

    5. distribute-rgt-out 76.3%

       \[\leadsto x - \frac{1}{\mathsf{fma}\left(-0.5, \frac{t}{y}, \frac{t}{y \cdot z}\right) - z \cdot \color{blue}{\left(\frac{t}{y} \cdot \left(-0.25 + 0.16666666666666666\right)\right)}} \]

    6. metadata-eval 76.3%

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

14. Simplified 76.3%

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

15. Taylor expanded in z around 0 82.2%

    \[\leadsto x - \frac{1}{\color{blue}{\frac{t}{y \cdot z}} - z \cdot \left(\frac{t}{y} \cdot -0.08333333333333333\right)} \]
16. Step-by-step derivation

    1. *-commutative 82.2%

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

    2. associate-/r* 83.4%

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

17. Simplified 83.4%

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

18. Final simplification 83.4%

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

Alternative 7: 78.8% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.95e-25) x (- x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.95e-25) {
		tmp = x;
	} else {
		tmp = x - (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) :: tmp
    if (z <= (-1.95d-25)) then
        tmp = x
    else
        tmp = x - (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.95e-25) {
		tmp = x;
	} else {
		tmp = x - (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.95e-25:
		tmp = x
	else:
		tmp = x - (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.95e-25)
		tmp = x;
	else
		tmp = Float64(x - Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.95e-25)
		tmp = x;
	else
		tmp = x - (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.95e-25], x, N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e-25

   1. Initial program 90.0%

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

      1. remove-double-neg 90.0%

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

      2. neg-mul-1 90.0%

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

      3. *-commutative 90.0%

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

      4. *-commutative 90.0%

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

      5. neg-mul-1 90.0%

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

      6. remove-double-neg 90.0%

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

      7. sub-neg 90.0%

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

      8. associate-+l+ 91.2%

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

      9. cancel-sign-sub 91.2%

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

      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 x around inf 73.2%

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

   if -1.95e-25 < z

   1. Initial program 56.7%

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

      1. remove-double-neg 56.7%

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

      2. neg-mul-1 56.7%

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

      3. *-commutative 56.7%

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

      4. *-commutative 56.7%

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

      5. neg-mul-1 56.7%

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

      6. remove-double-neg 56.7%

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

      7. sub-neg 56.7%

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

      8. associate-+l+ 78.4%

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

      9. cancel-sign-sub 78.4%

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

      10. log1p-def 78.4%

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

      11. cancel-sign-sub 78.4%

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

      12. +-commutative 78.4%

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

      13. unsub-neg 78.4%

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

      14. *-rgt-identity 78.4%

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

      15. distribute-lft-out-- 78.5%

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

      16. expm1-def 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around 0 88.3%

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

      1. associate-/l* 90.1%

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

      2. associate-/r/ 86.4%

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

   7. Simplified 86.4%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.0% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= z -7e-27) x (- x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7e-27) {
		tmp = x;
	} 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 <= (-7d-27)) then
        tmp = x
    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 <= -7e-27) {
		tmp = x;
	} else {
		tmp = x - (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7e-27:
		tmp = x
	else:
		tmp = x - (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7e-27)
		tmp = x;
	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 <= -7e-27)
		tmp = x;
	else
		tmp = x - (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7e-27], x, N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.0000000000000003e-27

   1. Initial program 90.0%

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

      1. remove-double-neg 90.0%

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

      2. neg-mul-1 90.0%

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

      3. *-commutative 90.0%

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

      4. *-commutative 90.0%

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

      5. neg-mul-1 90.0%

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

      6. remove-double-neg 90.0%

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

      7. sub-neg 90.0%

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

      8. associate-+l+ 91.2%

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

      9. cancel-sign-sub 91.2%

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

      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 x around inf 73.2%

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

   if -7.0000000000000003e-27 < z

   1. Initial program 56.7%

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

      1. remove-double-neg 56.7%

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

      2. neg-mul-1 56.7%

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

      3. *-commutative 56.7%

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

      4. *-commutative 56.7%

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

      5. neg-mul-1 56.7%

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

      6. remove-double-neg 56.7%

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

      7. sub-neg 56.7%

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

      8. associate-+l+ 78.4%

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

      9. cancel-sign-sub 78.4%

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

      10. log1p-def 78.4%

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

      11. cancel-sign-sub 78.4%

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

      12. +-commutative 78.4%

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

      13. unsub-neg 78.4%

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

      14. *-rgt-identity 78.4%

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

      15. distribute-lft-out-- 78.5%

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

      16. expm1-def 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around 0 88.3%

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

      1. associate-/l* 90.1%

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

   7. Simplified 90.1%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.0% 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 68.3%

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

   1. remove-double-neg 68.3%

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

   2. neg-mul-1 68.3%

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

   3. *-commutative 68.3%

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

   4. *-commutative 68.3%

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

   5. neg-mul-1 68.3%

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

   6. remove-double-neg 68.3%

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

   7. sub-neg 68.3%

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

   8. associate-+l+ 82.9%

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

   9. cancel-sign-sub 82.9%

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

   10. log1p-def 85.9%

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

   11. cancel-sign-sub 85.9%

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

   12. +-commutative 85.9%

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

   13. unsub-neg 85.9%

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

   14. *-rgt-identity 85.9%

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

   15. distribute-lft-out-- 85.9%

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

   16. expm1-def 98.0%

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

3. Simplified 98.0%

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

5. Taylor expanded in x around inf 76.3%

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

6. Final simplification 76.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 73.7% 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 2024029 
(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)))