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

Percentage Accurate: 61.1% → 98.2%

Time: 18.7s

Alternatives: 9

Speedup: 211.0×

• could not determine a ground truth

  1. x = 1.9067339511933494e-42
  2. y = 3.812421406878155e-159
  3. z = 118690618716731.23
  4. t = -4.538125385566937e+238

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.1% 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: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Initial program 62.9%

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

   1. sub-neg 62.9%

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

   2. neg-mul-1 62.9%

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

   3. *-commutative 62.9%

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

   4. cancel-sign-sub 62.9%

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

   5. *-commutative 62.9%

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

   6. mul-1-neg 62.9%

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

   7. remove-double-neg 62.9%

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

3. Simplified 98.9%

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

4. Final simplification 98.9%

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

Alternative 2: 90.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+19} \lor \neg \left(y \leq 8.2 \cdot 10^{-22}\right):\\ \;\;\;\;x + \frac{\frac{-1}{t}}{0.5 + \frac{\frac{1}{z}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{expm1}\left(z\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e+19) (not (<= y 8.2e-22)))
   (+ x (/ (/ -1.0 t) (+ 0.5 (/ (/ 1.0 z) y))))
   (- x (* (expm1 z) (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+19) || !(y <= 8.2e-22)) {
		tmp = x + ((-1.0 / t) / (0.5 + ((1.0 / z) / y)));
	} else {
		tmp = x - (expm1(z) * (y / t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+19) || !(y <= 8.2e-22)) {
		tmp = x + ((-1.0 / t) / (0.5 + ((1.0 / z) / y)));
	} else {
		tmp = x - (Math.expm1(z) * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e+19) or not (y <= 8.2e-22):
		tmp = x + ((-1.0 / t) / (0.5 + ((1.0 / z) / y)))
	else:
		tmp = x - (math.expm1(z) * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e+19) || !(y <= 8.2e-22))
		tmp = Float64(x + Float64(Float64(-1.0 / t) / Float64(0.5 + Float64(Float64(1.0 / z) / y))));
	else
		tmp = Float64(x - Float64(expm1(z) * Float64(y / t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e+19], N[Not[LessEqual[y, 8.2e-22]], $MachinePrecision]], N[(x + N[(N[(-1.0 / t), $MachinePrecision] / N[(0.5 + N[(N[(1.0 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(Exp[z] - 1), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8e19 or 8.1999999999999999e-22 < y

   1. Initial program 29.1%

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

      1. sub-neg 29.1%

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

      2. neg-mul-1 29.1%

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

      3. *-commutative 29.1%

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

      4. cancel-sign-sub 29.1%

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

      5. *-commutative 29.1%

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

      6. mul-1-neg 29.1%

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

      7. remove-double-neg 29.1%

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

   3. Simplified 99.8%

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

      1. div-inv 99.8%

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

      2. *-commutative 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-/r/ 99.7%

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

      2. div-inv 99.7%

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

      3. associate-/r* 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in y around 0 58.7%

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

      1. expm1-def 75.3%

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

   10. Simplified 75.3%

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

   11. Taylor expanded in z around 0 75.3%

       \[\leadsto x - \frac{\frac{1}{t}}{0.5 + \color{blue}{\frac{1}{y \cdot z}}} \]
   12. Step-by-step derivation

       1. *-commutative 75.3%

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

       2. associate-/r* 75.3%

          \[\leadsto x - \frac{\frac{1}{t}}{0.5 + \color{blue}{\frac{\frac{1}{z}}{y}}} \]

   13. Simplified 75.3%

       \[\leadsto x - \frac{\frac{1}{t}}{0.5 + \color{blue}{\frac{\frac{1}{z}}{y}}} \]

   if -3.8e19 < y < 8.1999999999999999e-22

   1. Initial program 84.3%

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

      1. sub-neg 84.3%

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

      2. neg-mul-1 84.3%

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

      3. *-commutative 84.3%

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

      4. cancel-sign-sub 84.3%

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

      5. *-commutative 84.3%

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

      6. mul-1-neg 84.3%

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

      7. remove-double-neg 84.3%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 92.3%

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

      1. associate-/l* 92.3%

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

      2. associate-/r/ 92.3%

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

      3. expm1-def 99.4%

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

   6. Simplified 99.4%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+19} \lor \neg \left(y \leq 8.2 \cdot 10^{-22}\right):\\ \;\;\;\;x + \frac{\frac{-1}{t}}{0.5 + \frac{\frac{1}{z}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{expm1}\left(z\right) \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3: 87.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -70000000:\\ \;\;\;\;x + \frac{\frac{-1}{t}}{0.5 + \left(\frac{1}{y \cdot z} - \frac{0.5}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{-1}{t}}{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -70000000.0)
   (+ x (/ (/ -1.0 t) (+ 0.5 (- (/ 1.0 (* y z)) (/ 0.5 y)))))
   (+ x (/ (/ -1.0 t) (/ (/ 1.0 y) (expm1 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -70000000.0) {
		tmp = x + ((-1.0 / t) / (0.5 + ((1.0 / (y * z)) - (0.5 / y))));
	} else {
		tmp = x + ((-1.0 / t) / ((1.0 / y) / expm1(z)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -70000000.0) {
		tmp = x + ((-1.0 / t) / (0.5 + ((1.0 / (y * z)) - (0.5 / y))));
	} else {
		tmp = x + ((-1.0 / t) / ((1.0 / y) / Math.expm1(z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -70000000.0:
		tmp = x + ((-1.0 / t) / (0.5 + ((1.0 / (y * z)) - (0.5 / y))))
	else:
		tmp = x + ((-1.0 / t) / ((1.0 / y) / math.expm1(z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -70000000.0)
		tmp = Float64(x + Float64(Float64(-1.0 / t) / Float64(0.5 + Float64(Float64(1.0 / Float64(y * z)) - Float64(0.5 / y)))));
	else
		tmp = Float64(x + Float64(Float64(-1.0 / t) / Float64(Float64(1.0 / y) / expm1(z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -70000000.0], N[(x + N[(N[(-1.0 / t), $MachinePrecision] / N[(0.5 + N[(N[(1.0 / N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(0.5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(-1.0 / t), $MachinePrecision] / N[(N[(1.0 / y), $MachinePrecision] / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7e7

   1. Initial program 37.5%

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

      1. sub-neg 37.5%

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

      2. neg-mul-1 37.5%

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

      3. *-commutative 37.5%

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

      4. cancel-sign-sub 37.5%

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

      5. *-commutative 37.5%

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

      6. mul-1-neg 37.5%

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

      7. remove-double-neg 37.5%

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

   3. Simplified 99.9%

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

      1. div-inv 99.8%

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

      2. *-commutative 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-/r/ 99.7%

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

      2. div-inv 99.7%

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

      3. associate-/r* 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in y around 0 63.4%

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

      1. expm1-def 72.1%

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

   10. Simplified 72.1%

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

   11. Taylor expanded in z around 0 72.1%

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

       1. associate-*r/ 72.1%

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

       2. metadata-eval 72.1%

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

   13. Simplified 72.1%

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

   if -7e7 < y

   1. Initial program 71.2%

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

      1. sub-neg 71.2%

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

      2. neg-mul-1 71.2%

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

      3. *-commutative 71.2%

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

      4. cancel-sign-sub 71.2%

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

      5. *-commutative 71.2%

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

      6. mul-1-neg 71.2%

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

      7. remove-double-neg 71.2%

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

   3. Simplified 98.6%

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

      1. div-inv 98.6%

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

      2. *-commutative 98.6%

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

   5. Applied egg-rr 98.6%

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

      1. associate-/r/ 98.5%

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

      2. div-inv 98.4%

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

      3. associate-/r* 98.4%

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

   7. Applied egg-rr 98.4%

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

   8. Taylor expanded in y around 0 84.4%

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

      1. associate-/r* 84.4%

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

      2. expm1-def 94.0%

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

   10. Simplified 94.0%

       \[\leadsto x - \frac{\frac{1}{t}}{\color{blue}{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -70000000:\\ \;\;\;\;x + \frac{\frac{-1}{t}}{0.5 + \left(\frac{1}{y \cdot z} - \frac{0.5}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{-1}{t}}{\frac{\frac{1}{y}}{\mathsf{expm1}\left(z\right)}}\\ \end{array} \]

Alternative 4: 89.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ x + \frac{\frac{-1}{t}}{0.5 + \frac{1}{y \cdot \mathsf{expm1}\left(z\right)}} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (/ (/ -1.0 t) (+ 0.5 (/ 1.0 (* y (expm1 z)))))))

C

double code(double x, double y, double z, double t) {
	return x + ((-1.0 / t) / (0.5 + (1.0 / (y * expm1(z)))));
}

Java

public static double code(double x, double y, double z, double t) {
	return x + ((-1.0 / t) / (0.5 + (1.0 / (y * Math.expm1(z)))));
}

Python

def code(x, y, z, t):
	return x + ((-1.0 / t) / (0.5 + (1.0 / (y * math.expm1(z)))))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(-1.0 / t) / Float64(0.5 + Float64(1.0 / Float64(y * expm1(z))))))
end

Wolfram

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

Derivation

1. Initial program 62.9%

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

   1. sub-neg 62.9%

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

   2. neg-mul-1 62.9%

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

   3. *-commutative 62.9%

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

   4. cancel-sign-sub 62.9%

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

   5. *-commutative 62.9%

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

   6. mul-1-neg 62.9%

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

   7. remove-double-neg 62.9%

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

3. Simplified 98.9%

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

   1. div-inv 98.9%

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

   2. *-commutative 98.9%

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

5. Applied egg-rr 98.9%

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

   1. associate-/r/ 98.8%

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

   2. div-inv 98.7%

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

   3. associate-/r* 98.8%

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

7. Applied egg-rr 98.8%

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

8. Taylor expanded in y around 0 79.3%

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

   1. expm1-def 89.3%

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

10. Simplified 89.3%

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

11. Final simplification 89.3%

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

Alternative 5: 82.8% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{-1}{t}}{0.5 + \frac{\frac{1}{z}}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e+62) x (+ x (/ (/ -1.0 t) (+ 0.5 (/ (/ 1.0 z) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+62) {
		tmp = x;
	} else {
		tmp = x + ((-1.0 / t) / (0.5 + ((1.0 / z) / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.8d+62)) then
        tmp = x
    else
        tmp = x + (((-1.0d0) / t) / (0.5d0 + ((1.0d0 / z) / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+62) {
		tmp = x;
	} else {
		tmp = x + ((-1.0 / t) / (0.5 + ((1.0 / z) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e+62:
		tmp = x
	else:
		tmp = x + ((-1.0 / t) / (0.5 + ((1.0 / z) / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e+62)
		tmp = x;
	else
		tmp = Float64(x + Float64(Float64(-1.0 / t) / Float64(0.5 + Float64(Float64(1.0 / z) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e+62)
		tmp = x;
	else
		tmp = x + ((-1.0 / t) / (0.5 + ((1.0 / z) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e+62], x, N[(x + N[(N[(-1.0 / t), $MachinePrecision] / N[(0.5 + N[(N[(1.0 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e62

   1. Initial program 83.2%

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

      1. sub-neg 83.2%

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

      2. neg-mul-1 83.2%

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

      3. *-commutative 83.2%

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

      4. cancel-sign-sub 83.2%

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

      5. *-commutative 83.2%

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

      6. mul-1-neg 83.2%

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

      7. remove-double-neg 83.2%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 70.2%

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

   if -1.8e62 < z

   1. Initial program 56.9%

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

      1. sub-neg 56.9%

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

      2. neg-mul-1 56.9%

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

      3. *-commutative 56.9%

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

      4. cancel-sign-sub 56.9%

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

      5. *-commutative 56.9%

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

      6. mul-1-neg 56.9%

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

      7. remove-double-neg 56.9%

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

   3. Simplified 98.6%

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

      1. div-inv 98.6%

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

      2. *-commutative 98.6%

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

   5. Applied egg-rr 98.6%

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

      1. associate-/r/ 98.6%

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

      2. div-inv 98.4%

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

      3. associate-/r* 98.5%

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

   7. Applied egg-rr 98.5%

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

   8. Taylor expanded in y around 0 76.6%

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

      1. expm1-def 89.7%

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

   10. Simplified 89.7%

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

   11. Taylor expanded in z around 0 88.9%

       \[\leadsto x - \frac{\frac{1}{t}}{0.5 + \color{blue}{\frac{1}{y \cdot z}}} \]
   12. Step-by-step derivation

       1. *-commutative 88.9%

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

       2. associate-/r* 88.9%

          \[\leadsto x - \frac{\frac{1}{t}}{0.5 + \color{blue}{\frac{\frac{1}{z}}{y}}} \]

   13. Simplified 88.9%

       \[\leadsto x - \frac{\frac{1}{t}}{0.5 + \color{blue}{\frac{\frac{1}{z}}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{-1}{t}}{0.5 + \frac{\frac{1}{z}}{y}}\\ \end{array} \]

Alternative 6: 84.2% accurate, 12.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.9%

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

   1. sub-neg 62.9%

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

   2. neg-mul-1 62.9%

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

   3. *-commutative 62.9%

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

   4. cancel-sign-sub 62.9%

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

   5. *-commutative 62.9%

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

   6. mul-1-neg 62.9%

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

   7. remove-double-neg 62.9%

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

3. Simplified 98.9%

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

   1. div-inv 98.9%

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

   2. *-commutative 98.9%

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

5. Applied egg-rr 98.9%

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

   1. associate-/r/ 98.8%

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

   2. div-inv 98.7%

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

   3. associate-/r* 98.8%

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

7. Applied egg-rr 98.8%

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

8. Taylor expanded in y around 0 79.3%

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

   1. expm1-def 89.3%

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

10. Simplified 89.3%

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

11. Taylor expanded in z around 0 85.6%

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

    1. associate-*r/ 85.6%

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

    2. metadata-eval 85.6%

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

13. Simplified 85.6%

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

14. Final simplification 85.6%

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

Alternative 7: 82.0% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3200000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3200000.0) x (- x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3200000.0) {
		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 <= (-3200000.0d0)) 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 <= -3200000.0) {
		tmp = x;
	} else {
		tmp = x - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3200000.0:
		tmp = x
	else:
		tmp = x - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3200000.0)
		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 <= -3200000.0)
		tmp = x;
	else
		tmp = x - (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3200000.0], x, N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e6

   1. Initial program 84.5%

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

      1. sub-neg 84.5%

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

      2. neg-mul-1 84.5%

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

      3. *-commutative 84.5%

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

      4. cancel-sign-sub 84.5%

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

      5. *-commutative 84.5%

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

      6. mul-1-neg 84.5%

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

      7. remove-double-neg 84.5%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 72.1%

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

   if -3.2e6 < z

   1. Initial program 54.8%

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

      1. sub-neg 54.8%

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

      2. neg-mul-1 54.8%

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

      3. *-commutative 54.8%

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

      4. cancel-sign-sub 54.8%

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

      5. *-commutative 54.8%

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

      6. mul-1-neg 54.8%

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

      7. remove-double-neg 54.8%

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

   3. Simplified 98.6%

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

      1. div-inv 98.5%

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

      2. *-commutative 98.5%

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

   5. Applied egg-rr 98.5%

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

      1. associate-/r/ 98.5%

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

      2. div-inv 98.3%

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

      3. associate-/r* 98.4%

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

   7. Applied egg-rr 98.4%

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

   8. Taylor expanded in y around 0 75.7%

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

      1. expm1-def 89.5%

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

   10. Simplified 89.5%

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

   11. Taylor expanded in z around 0 87.4%

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

       1. associate-*r/ 88.7%

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

   13. Simplified 88.7%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3200000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 8: 82.0% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -900000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -900000.0) x (- x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -900000.0) {
		tmp = x;
	} else {
		tmp = x - (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-900000.0d0)) then
        tmp = x
    else
        tmp = x - (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -900000.0) {
		tmp = x;
	} else {
		tmp = x - (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -900000.0:
		tmp = x
	else:
		tmp = x - (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -900000.0)
		tmp = x;
	else
		tmp = Float64(x - Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -900000.0)
		tmp = x;
	else
		tmp = x - (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -900000.0], x, N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9e5

   1. Initial program 84.5%

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

      1. sub-neg 84.5%

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

      2. neg-mul-1 84.5%

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

      3. *-commutative 84.5%

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

      4. cancel-sign-sub 84.5%

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

      5. *-commutative 84.5%

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

      6. mul-1-neg 84.5%

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

      7. remove-double-neg 84.5%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 72.1%

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

   if -9e5 < z

   1. Initial program 54.8%

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

      1. sub-neg 54.8%

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

      2. neg-mul-1 54.8%

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

      3. *-commutative 54.8%

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

      4. cancel-sign-sub 54.8%

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

      5. *-commutative 54.8%

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

      6. mul-1-neg 54.8%

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

      7. remove-double-neg 54.8%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 87.4%

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

      1. associate-/l* 88.8%

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

   6. Simplified 88.8%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -900000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 9: 71.1% accurate, 211.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.9%

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

   1. sub-neg 62.9%

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

   2. neg-mul-1 62.9%

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

   3. *-commutative 62.9%

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

   4. cancel-sign-sub 62.9%

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

   5. *-commutative 62.9%

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

   6. mul-1-neg 62.9%

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

   7. remove-double-neg 62.9%

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

3. Simplified 98.9%

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

4. Taylor expanded in x around inf 74.3%

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

5. Final simplification 74.3%

   \[\leadsto x \]

Developer target: 74.4% 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 2023336 
(FPCore (x y z t)
  :name "System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2"
  :precision binary64

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

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