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

Percentage Accurate: 62.0% → 98.6%

Time: 19.4s

Alternatives: 13

Speedup: 211.0×

• could not determine a ground truth

  1. x = -7.923074946784477e-99
  2. y = 1.0866893135714117e+129
  3. z = 7.416447651496803e+163
  4. t = 3.3029426087985153e-12

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: 62.0% 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: 98.6% 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 65.8%

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

   1. associate-+l- 79.0%

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

   2. sub-neg 79.0%

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

   3. log1p-define 83.7%

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

   4. neg-sub0 83.7%

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

   5. associate-+l- 83.7%

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

   6. neg-sub0 83.7%

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

   7. +-commutative 83.7%

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

   8. unsub-neg 83.7%

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

   9. *-rgt-identity 83.7%

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

   10. distribute-lft-out-- 83.7%

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

   11. expm1-define 98.2%

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

3. Simplified 98.2%

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

Alternative 2: 91.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{z} \leq 0.0002:\\ \;\;\;\;x - \frac{y}{\frac{t}{\mathsf{expm1}\left(z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(y \cdot \left(z \cdot \left(1 + z \cdot \left(0.5 + z \cdot \left(0.16666666666666666 + z \cdot 0.041666666666666664\right)\right)\right)\right)\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (exp z) 0.0002)
   (- x (/ y (/ t (expm1 z))))
   (-
    x
    (/
     (log1p
      (*
       y
       (*
        z
        (+
         1.0
         (*
          z
          (+ 0.5 (* z (+ 0.16666666666666666 (* z 0.041666666666666664)))))))))
     t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (exp(z) <= 0.0002) {
		tmp = x - (y / (t / expm1(z)));
	} else {
		tmp = x - (log1p((y * (z * (1.0 + (z * (0.5 + (z * (0.16666666666666666 + (z * 0.041666666666666664))))))))) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (Math.exp(z) <= 0.0002) {
		tmp = x - (y / (t / Math.expm1(z)));
	} else {
		tmp = x - (Math.log1p((y * (z * (1.0 + (z * (0.5 + (z * (0.16666666666666666 + (z * 0.041666666666666664))))))))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if math.exp(z) <= 0.0002:
		tmp = x - (y / (t / math.expm1(z)))
	else:
		tmp = x - (math.log1p((y * (z * (1.0 + (z * (0.5 + (z * (0.16666666666666666 + (z * 0.041666666666666664))))))))) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (exp(z) <= 0.0002)
		tmp = Float64(x - Float64(y / Float64(t / expm1(z))));
	else
		tmp = Float64(x - Float64(log1p(Float64(y * Float64(z * Float64(1.0 + Float64(z * Float64(0.5 + Float64(z * Float64(0.16666666666666666 + Float64(z * 0.041666666666666664))))))))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[Exp[z], $MachinePrecision], 0.0002], N[(x - N[(y / N[(t / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[1 + N[(y * N[(z * N[(1.0 + N[(z * N[(0.5 + N[(z * N[(0.16666666666666666 + N[(z * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (exp.f64 z) < 2.0000000000000001e-4

   1. Initial program 87.6%

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

      1. associate-+l- 87.6%

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

      2. sub-neg 87.6%

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

      3. log1p-define 99.9%

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

      4. neg-sub0 99.9%

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

      5. associate-+l- 99.9%

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

      6. neg-sub0 99.9%

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

      7. +-commutative 99.9%

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

      8. unsub-neg 99.9%

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

      9. *-rgt-identity 99.9%

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

      10. distribute-lft-out-- 99.9%

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

      11. expm1-define 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 78.3%

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

      1. expm1-define 78.3%

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

      2. associate-/l* 78.2%

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

   7. Simplified 78.2%

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

      1. clear-num 78.2%

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

      2. inv-pow 78.2%

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

   9. Applied egg-rr 78.2%

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

       1. unpow-1 78.2%

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

   11. Simplified 78.2%

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

       1. un-div-inv 78.3%

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

   13. Applied egg-rr 78.3%

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

   if 2.0000000000000001e-4 < (exp.f64 z)

   1. Initial program 55.3%

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

      1. associate-+l- 74.9%

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

      2. sub-neg 74.9%

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

      3. log1p-define 75.9%

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

      4. neg-sub0 75.9%

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

      5. associate-+l- 75.9%

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

      6. neg-sub0 75.9%

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

      7. +-commutative 75.9%

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

      8. unsub-neg 75.9%

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

      9. *-rgt-identity 75.9%

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

      10. distribute-lft-out-- 75.9%

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

      11. expm1-define 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 z around 0 96.9%

      \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\left(z \cdot \left(1 + z \cdot \left(0.5 + z \cdot \left(0.16666666666666666 + 0.041666666666666664 \cdot z\right)\right)\right)\right)}\right)}{t} \]
   6. Step-by-step derivation

      1. *-commutative 96.9%

         \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \left(z \cdot \left(1 + z \cdot \left(0.5 + z \cdot \left(0.16666666666666666 + \color{blue}{z \cdot 0.041666666666666664}\right)\right)\right)\right)\right)}{t} \]

   7. Simplified 96.9%

      \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\left(z \cdot \left(1 + z \cdot \left(0.5 + z \cdot \left(0.16666666666666666 + z \cdot 0.041666666666666664\right)\right)\right)\right)}\right)}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 91.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{z} \leq 0.0002:\\ \;\;\;\;x - \frac{y}{\frac{t}{\mathsf{expm1}\left(z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(z \cdot \left(y + 0.5 \cdot \left(y \cdot z\right)\right)\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (exp z) 0.0002)
   (- x (/ y (/ t (expm1 z))))
   (- x (/ (log1p (* z (+ y (* 0.5 (* y z))))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (exp(z) <= 0.0002) {
		tmp = x - (y / (t / expm1(z)));
	} else {
		tmp = x - (log1p((z * (y + (0.5 * (y * z))))) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (Math.exp(z) <= 0.0002) {
		tmp = x - (y / (t / Math.expm1(z)));
	} else {
		tmp = x - (Math.log1p((z * (y + (0.5 * (y * z))))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if math.exp(z) <= 0.0002:
		tmp = x - (y / (t / math.expm1(z)))
	else:
		tmp = x - (math.log1p((z * (y + (0.5 * (y * z))))) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (exp(z) <= 0.0002)
		tmp = Float64(x - Float64(y / Float64(t / expm1(z))));
	else
		tmp = Float64(x - Float64(log1p(Float64(z * Float64(y + Float64(0.5 * Float64(y * z))))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[Exp[z], $MachinePrecision], 0.0002], N[(x - N[(y / N[(t / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[1 + N[(z * N[(y + N[(0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (exp.f64 z) < 2.0000000000000001e-4

   1. Initial program 87.6%

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

      1. associate-+l- 87.6%

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

      2. sub-neg 87.6%

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

      3. log1p-define 99.9%

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

      4. neg-sub0 99.9%

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

      5. associate-+l- 99.9%

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

      6. neg-sub0 99.9%

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

      7. +-commutative 99.9%

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

      8. unsub-neg 99.9%

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

      9. *-rgt-identity 99.9%

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

      10. distribute-lft-out-- 99.9%

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

      11. expm1-define 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 78.3%

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

      1. expm1-define 78.3%

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

      2. associate-/l* 78.2%

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

   7. Simplified 78.2%

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

      1. clear-num 78.2%

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

      2. inv-pow 78.2%

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

   9. Applied egg-rr 78.2%

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

       1. unpow-1 78.2%

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

   11. Simplified 78.2%

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

       1. un-div-inv 78.3%

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

   13. Applied egg-rr 78.3%

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

   if 2.0000000000000001e-4 < (exp.f64 z)

   1. Initial program 55.3%

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

      1. associate-+l- 74.9%

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

      2. sub-neg 74.9%

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

      3. log1p-define 75.9%

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

      4. neg-sub0 75.9%

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

      5. associate-+l- 75.9%

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

      6. neg-sub0 75.9%

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

      7. +-commutative 75.9%

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

      8. unsub-neg 75.9%

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

      9. *-rgt-identity 75.9%

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

      10. distribute-lft-out-- 75.9%

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

      11. expm1-define 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 z around 0 96.6%

      \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{z \cdot \left(y + 0.5 \cdot \left(y \cdot z\right)\right)}\right)}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 91.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;x - \frac{y}{\frac{t}{\mathsf{expm1}\left(z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(y \cdot \left(z \cdot \left(1 + z \cdot \left(0.5 + z \cdot 0.16666666666666666\right)\right)\right)\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.3e+19)
   (- x (/ y (/ t (expm1 z))))
   (-
    x
    (/
     (log1p (* y (* z (+ 1.0 (* z (+ 0.5 (* z 0.16666666666666666)))))))
     t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e+19) {
		tmp = x - (y / (t / expm1(z)));
	} else {
		tmp = x - (log1p((y * (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666))))))) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e+19) {
		tmp = x - (y / (t / Math.expm1(z)));
	} else {
		tmp = x - (Math.log1p((y * (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666))))))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.3e+19:
		tmp = x - (y / (t / math.expm1(z)))
	else:
		tmp = x - (math.log1p((y * (z * (1.0 + (z * (0.5 + (z * 0.16666666666666666))))))) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.3e+19)
		tmp = Float64(x - Float64(y / Float64(t / expm1(z))));
	else
		tmp = Float64(x - Float64(log1p(Float64(y * Float64(z * Float64(1.0 + Float64(z * Float64(0.5 + Float64(z * 0.16666666666666666))))))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.3e+19], N[(x - N[(y / N[(t / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[1 + N[(y * N[(z * N[(1.0 + N[(z * N[(0.5 + N[(z * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e19

   1. Initial program 86.4%

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

      1. associate-+l- 86.4%

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

      2. sub-neg 86.4%

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

      3. log1p-define 99.9%

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

      4. neg-sub0 99.9%

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

      5. associate-+l- 99.9%

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

      6. neg-sub0 99.9%

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

      7. +-commutative 99.9%

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

      8. unsub-neg 99.9%

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

      9. *-rgt-identity 99.9%

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

      10. distribute-lft-out-- 99.9%

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

      11. expm1-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 77.5%

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

      1. expm1-define 77.5%

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

      2. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

      1. clear-num 77.4%

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

      2. inv-pow 77.4%

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

   9. Applied egg-rr 77.4%

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

       1. unpow-1 77.4%

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

   11. Simplified 77.4%

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

       1. un-div-inv 77.5%

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

   13. Applied egg-rr 77.5%

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

   if -1.3e19 < z

   1. Initial program 57.0%

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

      1. associate-+l- 75.8%

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

      2. sub-neg 75.8%

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

      3. log1p-define 76.8%

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

      4. neg-sub0 76.8%

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

      5. associate-+l- 76.8%

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

      6. neg-sub0 76.8%

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

      7. +-commutative 76.8%

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

      8. unsub-neg 76.8%

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

      9. *-rgt-identity 76.8%

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

      10. distribute-lft-out-- 76.8%

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

      11. expm1-define 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 z around 0 96.4%

      \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\left(z \cdot \left(1 + z \cdot \left(0.5 + 0.16666666666666666 \cdot z\right)\right)\right)}\right)}{t} \]
   6. Step-by-step derivation

      1. *-commutative 96.4%

         \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \left(z \cdot \left(1 + z \cdot \left(0.5 + \color{blue}{z \cdot 0.16666666666666666}\right)\right)\right)\right)}{t} \]

   7. Simplified 96.4%

      \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\left(z \cdot \left(1 + z \cdot \left(0.5 + z \cdot 0.16666666666666666\right)\right)\right)}\right)}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 91.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;x - \frac{y}{\frac{t}{\mathsf{expm1}\left(z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{log1p}\left(y \cdot z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.3e+19) (- x (/ y (/ t (expm1 z)))) (- x (/ (log1p (* y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e+19) {
		tmp = x - (y / (t / expm1(z)));
	} else {
		tmp = x - (log1p((y * z)) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e+19) {
		tmp = x - (y / (t / Math.expm1(z)));
	} else {
		tmp = x - (Math.log1p((y * z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.3e+19:
		tmp = x - (y / (t / math.expm1(z)))
	else:
		tmp = x - (math.log1p((y * z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.3e+19)
		tmp = Float64(x - Float64(y / Float64(t / expm1(z))));
	else
		tmp = Float64(x - Float64(log1p(Float64(y * z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.3e+19], N[(x - N[(y / N[(t / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[1 + N[(y * z), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e19

   1. Initial program 86.4%

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

      1. associate-+l- 86.4%

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

      2. sub-neg 86.4%

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

      3. log1p-define 99.9%

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

      4. neg-sub0 99.9%

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

      5. associate-+l- 99.9%

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

      6. neg-sub0 99.9%

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

      7. +-commutative 99.9%

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

      8. unsub-neg 99.9%

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

      9. *-rgt-identity 99.9%

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

      10. distribute-lft-out-- 99.9%

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

      11. expm1-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 77.5%

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

      1. expm1-define 77.5%

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

      2. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

      1. clear-num 77.4%

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

      2. inv-pow 77.4%

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

   9. Applied egg-rr 77.4%

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

       1. unpow-1 77.4%

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

   11. Simplified 77.4%

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

       1. un-div-inv 77.5%

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

   13. Applied egg-rr 77.5%

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

   if -1.3e19 < z

   1. Initial program 57.0%

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

      1. associate-+l- 75.8%

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

      2. sub-neg 75.8%

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

      3. log1p-define 76.8%

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

      4. neg-sub0 76.8%

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

      5. associate-+l- 76.8%

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

      6. neg-sub0 76.8%

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

      7. +-commutative 76.8%

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

      8. unsub-neg 76.8%

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

      9. *-rgt-identity 76.8%

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

      10. distribute-lft-out-- 76.8%

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

      11. expm1-define 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 z around 0 96.2%

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

Alternative 6: 87.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot -0.25 + t \cdot 0.16666666666666666\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+112}:\\ \;\;\;\;x - y \cdot \frac{1}{\frac{t - z \cdot \left(t \cdot 0.5 + z \cdot \left(t\_1 + z \cdot \left(-0.5 \cdot t\_1 + \left(t \cdot 0.041666666666666664 + t \cdot -0.08333333333333333\right)\right)\right)\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{\mathsf{expm1}\left(z\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* t -0.25) (* t 0.16666666666666666))))
   (if (<= y -2.3e+112)
     (-
      x
      (*
       y
       (/
        1.0
        (/
         (-
          t
          (*
           z
           (+
            (* t 0.5)
            (*
             z
             (+
              t_1
              (*
               z
               (+
                (* -0.5 t_1)
                (+
                 (* t 0.041666666666666664)
                 (* t -0.08333333333333333)))))))))
         z))))
     (- x (/ y (/ t (expm1 z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * -0.25) + (t * 0.16666666666666666);
	double tmp;
	if (y <= -2.3e+112) {
		tmp = x - (y * (1.0 / ((t - (z * ((t * 0.5) + (z * (t_1 + (z * ((-0.5 * t_1) + ((t * 0.041666666666666664) + (t * -0.08333333333333333))))))))) / z)));
	} else {
		tmp = x - (y / (t / expm1(z)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * -0.25) + (t * 0.16666666666666666);
	double tmp;
	if (y <= -2.3e+112) {
		tmp = x - (y * (1.0 / ((t - (z * ((t * 0.5) + (z * (t_1 + (z * ((-0.5 * t_1) + ((t * 0.041666666666666664) + (t * -0.08333333333333333))))))))) / z)));
	} else {
		tmp = x - (y / (t / Math.expm1(z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * -0.25) + (t * 0.16666666666666666)
	tmp = 0
	if y <= -2.3e+112:
		tmp = x - (y * (1.0 / ((t - (z * ((t * 0.5) + (z * (t_1 + (z * ((-0.5 * t_1) + ((t * 0.041666666666666664) + (t * -0.08333333333333333))))))))) / z)))
	else:
		tmp = x - (y / (t / math.expm1(z)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * -0.25) + Float64(t * 0.16666666666666666))
	tmp = 0.0
	if (y <= -2.3e+112)
		tmp = Float64(x - Float64(y * Float64(1.0 / Float64(Float64(t - Float64(z * Float64(Float64(t * 0.5) + Float64(z * Float64(t_1 + Float64(z * Float64(Float64(-0.5 * t_1) + Float64(Float64(t * 0.041666666666666664) + Float64(t * -0.08333333333333333))))))))) / z))));
	else
		tmp = Float64(x - Float64(y / Float64(t / expm1(z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * -0.25), $MachinePrecision] + N[(t * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+112], N[(x - N[(y * N[(1.0 / N[(N[(t - N[(z * N[(N[(t * 0.5), $MachinePrecision] + N[(z * N[(t$95$1 + N[(z * N[(N[(-0.5 * t$95$1), $MachinePrecision] + N[(N[(t * 0.041666666666666664), $MachinePrecision] + N[(t * -0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e112

   1. Initial program 52.2%

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

      1. associate-+l- 80.8%

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

      2. sub-neg 80.8%

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

      3. log1p-define 80.8%

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

      4. neg-sub0 80.8%

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

      5. associate-+l- 80.8%

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

      6. neg-sub0 80.8%

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

      7. +-commutative 80.8%

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

      8. unsub-neg 80.8%

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

      9. *-rgt-identity 80.8%

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

      10. distribute-lft-out-- 80.7%

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

      11. expm1-define 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 42.2%

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

      1. expm1-define 49.8%

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

      2. associate-/l* 47.4%

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

   7. Simplified 47.4%

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

      1. clear-num 47.4%

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

      2. inv-pow 47.4%

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

   9. Applied egg-rr 47.4%

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

       1. unpow-1 47.4%

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

   11. Simplified 47.4%

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

   12. Taylor expanded in z around 0 58.2%

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

   if -2.3e112 < y

   1. Initial program 68.1%

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

      1. associate-+l- 78.7%

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

      2. sub-neg 78.7%

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

      3. log1p-define 84.2%

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

      4. neg-sub0 84.2%

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

      5. associate-+l- 84.2%

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

      6. neg-sub0 84.2%

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

      7. +-commutative 84.2%

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

      8. unsub-neg 84.2%

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

      9. *-rgt-identity 84.2%

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

      10. distribute-lft-out-- 84.2%

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

      11. expm1-define 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in y around 0 82.1%

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

      1. expm1-define 92.5%

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

      2. associate-/l* 93.8%

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

   7. Simplified 93.8%

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

      1. clear-num 93.8%

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

      2. inv-pow 93.8%

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

   9. Applied egg-rr 93.8%

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

       1. unpow-1 93.8%

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

   11. Simplified 93.8%

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

       1. un-div-inv 93.8%

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

   13. Applied egg-rr 93.8%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+112}:\\ \;\;\;\;x - y \cdot \frac{1}{\frac{t - z \cdot \left(t \cdot 0.5 + z \cdot \left(\left(t \cdot -0.25 + t \cdot 0.16666666666666666\right) + z \cdot \left(-0.5 \cdot \left(t \cdot -0.25 + t \cdot 0.16666666666666666\right) + \left(t \cdot 0.041666666666666664 + t \cdot -0.08333333333333333\right)\right)\right)\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{\mathsf{expm1}\left(z\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot -0.25 + t \cdot 0.16666666666666666\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+112}:\\ \;\;\;\;x - y \cdot \frac{1}{\frac{t - z \cdot \left(t \cdot 0.5 + z \cdot \left(t\_1 + z \cdot \left(-0.5 \cdot t\_1 + \left(t \cdot 0.041666666666666664 + t \cdot -0.08333333333333333\right)\right)\right)\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{\mathsf{expm1}\left(z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* t -0.25) (* t 0.16666666666666666))))
   (if (<= y -3.1e+112)
     (-
      x
      (*
       y
       (/
        1.0
        (/
         (-
          t
          (*
           z
           (+
            (* t 0.5)
            (*
             z
             (+
              t_1
              (*
               z
               (+
                (* -0.5 t_1)
                (+
                 (* t 0.041666666666666664)
                 (* t -0.08333333333333333)))))))))
         z))))
     (- x (* y (/ (expm1 z) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * -0.25) + (t * 0.16666666666666666);
	double tmp;
	if (y <= -3.1e+112) {
		tmp = x - (y * (1.0 / ((t - (z * ((t * 0.5) + (z * (t_1 + (z * ((-0.5 * t_1) + ((t * 0.041666666666666664) + (t * -0.08333333333333333))))))))) / z)));
	} else {
		tmp = x - (y * (expm1(z) / t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * -0.25) + (t * 0.16666666666666666);
	double tmp;
	if (y <= -3.1e+112) {
		tmp = x - (y * (1.0 / ((t - (z * ((t * 0.5) + (z * (t_1 + (z * ((-0.5 * t_1) + ((t * 0.041666666666666664) + (t * -0.08333333333333333))))))))) / z)));
	} else {
		tmp = x - (y * (Math.expm1(z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * -0.25) + (t * 0.16666666666666666)
	tmp = 0
	if y <= -3.1e+112:
		tmp = x - (y * (1.0 / ((t - (z * ((t * 0.5) + (z * (t_1 + (z * ((-0.5 * t_1) + ((t * 0.041666666666666664) + (t * -0.08333333333333333))))))))) / z)))
	else:
		tmp = x - (y * (math.expm1(z) / t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * -0.25) + Float64(t * 0.16666666666666666))
	tmp = 0.0
	if (y <= -3.1e+112)
		tmp = Float64(x - Float64(y * Float64(1.0 / Float64(Float64(t - Float64(z * Float64(Float64(t * 0.5) + Float64(z * Float64(t_1 + Float64(z * Float64(Float64(-0.5 * t_1) + Float64(Float64(t * 0.041666666666666664) + Float64(t * -0.08333333333333333))))))))) / z))));
	else
		tmp = Float64(x - Float64(y * Float64(expm1(z) / t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * -0.25), $MachinePrecision] + N[(t * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+112], N[(x - N[(y * N[(1.0 / N[(N[(t - N[(z * N[(N[(t * 0.5), $MachinePrecision] + N[(z * N[(t$95$1 + N[(z * N[(N[(-0.5 * t$95$1), $MachinePrecision] + N[(N[(t * 0.041666666666666664), $MachinePrecision] + N[(t * -0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.09999999999999983e112

   1. Initial program 52.2%

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

      1. associate-+l- 80.8%

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

      2. sub-neg 80.8%

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

      3. log1p-define 80.8%

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

      4. neg-sub0 80.8%

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

      5. associate-+l- 80.8%

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

      6. neg-sub0 80.8%

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

      7. +-commutative 80.8%

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

      8. unsub-neg 80.8%

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

      9. *-rgt-identity 80.8%

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

      10. distribute-lft-out-- 80.7%

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

      11. expm1-define 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 42.2%

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

      1. expm1-define 49.8%

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

      2. associate-/l* 47.4%

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

   7. Simplified 47.4%

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

      1. clear-num 47.4%

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

      2. inv-pow 47.4%

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

   9. Applied egg-rr 47.4%

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

       1. unpow-1 47.4%

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

   11. Simplified 47.4%

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

   12. Taylor expanded in z around 0 58.2%

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

   if -3.09999999999999983e112 < y

   1. Initial program 68.1%

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

      1. associate-+l- 78.7%

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

      2. sub-neg 78.7%

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

      3. log1p-define 84.2%

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

      4. neg-sub0 84.2%

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

      5. associate-+l- 84.2%

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

      6. neg-sub0 84.2%

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

      7. +-commutative 84.2%

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

      8. unsub-neg 84.2%

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

      9. *-rgt-identity 84.2%

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

      10. distribute-lft-out-- 84.2%

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

      11. expm1-define 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in y around 0 82.1%

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

      1. expm1-define 92.5%

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

      2. associate-/l* 93.8%

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

   7. Simplified 93.8%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+112}:\\ \;\;\;\;x - y \cdot \frac{1}{\frac{t - z \cdot \left(t \cdot 0.5 + z \cdot \left(\left(t \cdot -0.25 + t \cdot 0.16666666666666666\right) + z \cdot \left(-0.5 \cdot \left(t \cdot -0.25 + t \cdot 0.16666666666666666\right) + \left(t \cdot 0.041666666666666664 + t \cdot -0.08333333333333333\right)\right)\right)\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{\mathsf{expm1}\left(z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.3% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot -0.25 + t \cdot 0.16666666666666666\\ x - y \cdot \frac{1}{\frac{t - z \cdot \left(t \cdot 0.5 + z \cdot \left(t\_1 + z \cdot \left(-0.5 \cdot t\_1 + \left(t \cdot 0.041666666666666664 + t \cdot -0.08333333333333333\right)\right)\right)\right)}{z}} \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* t -0.25) (* t 0.16666666666666666))))
   (-
    x
    (*
     y
     (/
      1.0
      (/
       (-
        t
        (*
         z
         (+
          (* t 0.5)
          (*
           z
           (+
            t_1
            (*
             z
             (+
              (* -0.5 t_1)
              (+ (* t 0.041666666666666664) (* t -0.08333333333333333)))))))))
       z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * -0.25) + (t * 0.16666666666666666);
	return x - (y * (1.0 / ((t - (z * ((t * 0.5) + (z * (t_1 + (z * ((-0.5 * t_1) + ((t * 0.041666666666666664) + (t * -0.08333333333333333))))))))) / 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
    real(8) :: t_1
    t_1 = (t * (-0.25d0)) + (t * 0.16666666666666666d0)
    code = x - (y * (1.0d0 / ((t - (z * ((t * 0.5d0) + (z * (t_1 + (z * (((-0.5d0) * t_1) + ((t * 0.041666666666666664d0) + (t * (-0.08333333333333333d0)))))))))) / z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * -0.25) + (t * 0.16666666666666666);
	return x - (y * (1.0 / ((t - (z * ((t * 0.5) + (z * (t_1 + (z * ((-0.5 * t_1) + ((t * 0.041666666666666664) + (t * -0.08333333333333333))))))))) / z)));
}

Python

def code(x, y, z, t):
	t_1 = (t * -0.25) + (t * 0.16666666666666666)
	return x - (y * (1.0 / ((t - (z * ((t * 0.5) + (z * (t_1 + (z * ((-0.5 * t_1) + ((t * 0.041666666666666664) + (t * -0.08333333333333333))))))))) / z)))

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * -0.25) + Float64(t * 0.16666666666666666))
	return Float64(x - Float64(y * Float64(1.0 / Float64(Float64(t - Float64(z * Float64(Float64(t * 0.5) + Float64(z * Float64(t_1 + Float64(z * Float64(Float64(-0.5 * t_1) + Float64(Float64(t * 0.041666666666666664) + Float64(t * -0.08333333333333333))))))))) / z))))
end

MATLAB

function tmp = code(x, y, z, t)
	t_1 = (t * -0.25) + (t * 0.16666666666666666);
	tmp = x - (y * (1.0 / ((t - (z * ((t * 0.5) + (z * (t_1 + (z * ((-0.5 * t_1) + ((t * 0.041666666666666664) + (t * -0.08333333333333333))))))))) / z)));
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * -0.25), $MachinePrecision] + N[(t * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]}, N[(x - N[(y * N[(1.0 / N[(N[(t - N[(z * N[(N[(t * 0.5), $MachinePrecision] + N[(z * N[(t$95$1 + N[(z * N[(N[(-0.5 * t$95$1), $MachinePrecision] + N[(N[(t * 0.041666666666666664), $MachinePrecision] + N[(t * -0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 65.8%

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

   1. associate-+l- 79.0%

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

   2. sub-neg 79.0%

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

   3. log1p-define 83.7%

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

   4. neg-sub0 83.7%

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

   5. associate-+l- 83.7%

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

   6. neg-sub0 83.7%

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

   7. +-commutative 83.7%

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

   8. unsub-neg 83.7%

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

   9. *-rgt-identity 83.7%

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

   10. distribute-lft-out-- 83.7%

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

   11. expm1-define 98.2%

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

3. Simplified 98.2%

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

5. Taylor expanded in y around 0 76.2%

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

   1. expm1-define 86.2%

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

   2. associate-/l* 86.9%

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

7. Simplified 86.9%

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

   1. clear-num 86.9%

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

   2. inv-pow 86.9%

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

9. Applied egg-rr 86.9%

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

    1. unpow-1 86.9%

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

11. Simplified 86.9%

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

12. Taylor expanded in z around 0 84.1%

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

13. Final simplification 84.1%

    \[\leadsto x - y \cdot \frac{1}{\frac{t - z \cdot \left(t \cdot 0.5 + z \cdot \left(\left(t \cdot -0.25 + t \cdot 0.16666666666666666\right) + z \cdot \left(-0.5 \cdot \left(t \cdot -0.25 + t \cdot 0.16666666666666666\right) + \left(t \cdot 0.041666666666666664 + t \cdot -0.08333333333333333\right)\right)\right)\right)}{z}} \]
14. Add Preprocessing

Alternative 9: 82.2% accurate, 10.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + (y * (-1.0 / ((t + (z * ((t * -0.5) - (z * (t * -0.08333333333333333))))) / 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 * ((-1.0d0) / ((t + (z * ((t * (-0.5d0)) - (z * (t * (-0.08333333333333333d0)))))) / z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.8%

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

   1. associate-+l- 79.0%

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

   2. sub-neg 79.0%

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

   3. log1p-define 83.7%

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

   4. neg-sub0 83.7%

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

   5. associate-+l- 83.7%

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

   6. neg-sub0 83.7%

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

   7. +-commutative 83.7%

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

   8. unsub-neg 83.7%

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

   9. *-rgt-identity 83.7%

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

   10. distribute-lft-out-- 83.7%

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

   11. expm1-define 98.2%

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

3. Simplified 98.2%

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

5. Taylor expanded in y around 0 76.2%

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

   1. expm1-define 86.2%

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

   2. associate-/l* 86.9%

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

7. Simplified 86.9%

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

   1. clear-num 86.9%

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

   2. inv-pow 86.9%

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

9. Applied egg-rr 86.9%

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

    1. unpow-1 86.9%

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

11. Simplified 86.9%

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

12. Taylor expanded in z around 0 83.7%

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

    1. cancel-sign-sub-inv 83.7%

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

    2. mul-1-neg 83.7%

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

    3. distribute-rgt-out 83.7%

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

    4. metadata-eval 83.7%

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

    5. metadata-eval 83.7%

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

14. Simplified 83.7%

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

15. Final simplification 83.7%

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

Alternative 10: 82.4% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z \cdot \left(1 + z \cdot 0.5\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2) x (- x (* y (/ (* z (+ 1.0 (* z 0.5))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2) {
		tmp = x;
	} else {
		tmp = x - (y * ((z * (1.0 + (z * 0.5))) / 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 <= (-2.2d0)) then
        tmp = x
    else
        tmp = x - (y * ((z * (1.0d0 + (z * 0.5d0))) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2) {
		tmp = x;
	} else {
		tmp = x - (y * ((z * (1.0 + (z * 0.5))) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.2:
		tmp = x
	else:
		tmp = x - (y * ((z * (1.0 + (z * 0.5))) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2)
		tmp = x;
	else
		tmp = Float64(x - Float64(y * Float64(Float64(z * Float64(1.0 + Float64(z * 0.5))) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.2)
		tmp = x;
	else
		tmp = x - (y * ((z * (1.0 + (z * 0.5))) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.2], x, N[(x - N[(y * N[(N[(z * N[(1.0 + N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000002

   1. Initial program 87.6%

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

      1. associate-+l- 87.6%

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

      2. sub-neg 87.6%

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

      3. log1p-define 99.9%

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

      4. neg-sub0 99.9%

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

      5. associate-+l- 99.9%

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

      6. neg-sub0 99.9%

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

      7. +-commutative 99.9%

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

      8. unsub-neg 99.9%

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

      9. *-rgt-identity 99.9%

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

      10. distribute-lft-out-- 99.9%

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

      11. expm1-define 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 71.5%

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

   if -2.2000000000000002 < z

   1. Initial program 55.3%

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

      1. associate-+l- 74.9%

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

      2. sub-neg 74.9%

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

      3. log1p-define 75.9%

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

      4. neg-sub0 75.9%

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

      5. associate-+l- 75.9%

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

      6. neg-sub0 75.9%

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

      7. +-commutative 75.9%

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

      8. unsub-neg 75.9%

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

      9. *-rgt-identity 75.9%

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

      10. distribute-lft-out-- 75.9%

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

      11. expm1-define 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 75.1%

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

      1. expm1-define 90.0%

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

      2. associate-/l* 91.1%

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

   7. Simplified 91.1%

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

   8. Taylor expanded in z around 0 90.5%

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

      1. *-commutative 90.5%

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

   10. Simplified 90.5%

       \[\leadsto x - y \cdot \frac{\color{blue}{z \cdot \left(1 + z \cdot 0.5\right)}}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 82.0% accurate, 14.1× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (y * ((-1.0d0) / ((t + ((-0.5d0) * (z * t))) / z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.8%

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

   1. associate-+l- 79.0%

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

   2. sub-neg 79.0%

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

   3. log1p-define 83.7%

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

   4. neg-sub0 83.7%

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

   5. associate-+l- 83.7%

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

   6. neg-sub0 83.7%

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

   7. +-commutative 83.7%

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

   8. unsub-neg 83.7%

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

   9. *-rgt-identity 83.7%

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

   10. distribute-lft-out-- 83.7%

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

   11. expm1-define 98.2%

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

3. Simplified 98.2%

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

5. Taylor expanded in y around 0 76.2%

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

   1. expm1-define 86.2%

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

   2. associate-/l* 86.9%

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

7. Simplified 86.9%

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

   1. clear-num 86.9%

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

   2. inv-pow 86.9%

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

9. Applied egg-rr 86.9%

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

    1. unpow-1 86.9%

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

11. Simplified 86.9%

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

12. Taylor expanded in z around 0 83.6%

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

    1. *-commutative 83.6%

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

14. Simplified 83.6%

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

15. Final simplification 83.6%

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

Alternative 12: 81.6% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.5e+63) x (- x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e+63) {
		tmp = x;
	} else {
		tmp = x - (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-9.5d+63)) then
        tmp = x
    else
        tmp = x - (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e+63) {
		tmp = x;
	} else {
		tmp = x - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.5e+63:
		tmp = x
	else:
		tmp = x - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.5e+63)
		tmp = x;
	else
		tmp = Float64(x - Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.5e+63)
		tmp = x;
	else
		tmp = x - (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.5e+63], x, N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000003e63

   1. Initial program 89.2%

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

      1. associate-+l- 89.2%

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

      2. sub-neg 89.2%

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

      3. log1p-define 99.9%

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

      4. neg-sub0 99.9%

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

      5. associate-+l- 99.9%

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

      6. neg-sub0 99.9%

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

      7. +-commutative 99.9%

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

      8. unsub-neg 99.9%

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

      9. *-rgt-identity 99.9%

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

      10. distribute-lft-out-- 99.9%

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

      11. expm1-define 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 71.3%

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

   if -9.5000000000000003e63 < z

   1. Initial program 57.1%

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

      1. associate-+l- 75.2%

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

      2. sub-neg 75.2%

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

      3. log1p-define 77.7%

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

      4. neg-sub0 77.7%

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

      5. associate-+l- 77.7%

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

      6. neg-sub0 77.7%

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

      7. +-commutative 77.7%

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

      8. unsub-neg 77.7%

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

      9. *-rgt-identity 77.7%

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

      10. distribute-lft-out-- 77.7%

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

      11. expm1-define 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 z around 0 88.0%

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

      1. associate-/l* 89.1%

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

   7. Simplified 89.1%

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

Alternative 13: 72.0% 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 65.8%

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

   1. associate-+l- 79.0%

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

   2. sub-neg 79.0%

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

   3. log1p-define 83.7%

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

   4. neg-sub0 83.7%

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

   5. associate-+l- 83.7%

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

   6. neg-sub0 83.7%

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

   7. +-commutative 83.7%

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

   8. unsub-neg 83.7%

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

   9. *-rgt-identity 83.7%

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

   10. distribute-lft-out-- 83.7%

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

   11. expm1-define 98.2%

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

3. Simplified 98.2%

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

5. Taylor expanded in x around inf 73.2%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 74.7% 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 2024135 
(FPCore (x y z t)
  :name "System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -288746230882079470000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- x (/ (/ (- 1/2) (* y t)) (* z z))) (* (/ (- 1/2) (* y t)) (/ (/ 2 z) (* z z)))) (- x (/ (log (+ 1 (* z y))) t))))

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