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

Percentage Accurate: 61.1% → 99.3%

Time: 18.3s

Alternatives: 8

Speedup: 11.3×

• could not determine a ground truth

  1. x = 1.909824876003581e+162
  2. y = 1.3969687448072756e-128
  3. z = 3.736341193378758e+267
  4. t = -21832370988501.582

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: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{z} \cdot y + \left(1 - y\right)\\ \mathbf{if}\;t\_1 \leq 0:\\ \;\;\;\;x - \frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot z\right)}}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x - \frac{1}{\frac{\mathsf{fma}\left(y \cdot t, 0.5, \frac{t}{\mathsf{expm1}\left(z\right)}\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log t\_1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (exp z) y) (- 1.0 y))))
   (if (<= t_1 0.0)
     (- x (/ 1.0 (/ t (log1p (* y z)))))
     (if (<= t_1 2.0)
       (- x (/ 1.0 (/ (fma (* y t) 0.5 (/ t (expm1 z))) y)))
       (- x (/ (log t_1) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (exp(z) * y) + (1.0 - y);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = x - (1.0 / (t / log1p((y * z))));
	} else if (t_1 <= 2.0) {
		tmp = x - (1.0 / (fma((y * t), 0.5, (t / expm1(z))) / y));
	} else {
		tmp = x - (log(t_1) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(exp(z) * y) + Float64(1.0 - y))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(x - Float64(1.0 / Float64(t / log1p(Float64(y * z)))));
	elseif (t_1 <= 2.0)
		tmp = Float64(x - Float64(1.0 / Float64(fma(Float64(y * t), 0.5, Float64(t / expm1(z))) / y)));
	else
		tmp = Float64(x - Float64(log(t_1) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[Exp[z], $MachinePrecision] * y), $MachinePrecision] + N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(x - N[(1.0 / N[(t / N[Log[1 + N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(x - N[(1.0 / N[(N[(N[(y * t), $MachinePrecision] * 0.5 + N[(t / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[t$95$1], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z))) < 0.0

   1. Initial program 1.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 1.9

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

      5. lift-log.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-neg N/A

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

      9. associate-+l+ N/A

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

      10. lower-log1p.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-neg.f64 58.3

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

   4. Applied rewrites 58.3%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 99.8

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

   7. Applied rewrites 99.8%

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

   if 0.0 < (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z))) < 2

   1. Initial program 81.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 81.1

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

      5. lift-log.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-neg N/A

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

      9. associate-+l+ N/A

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

      10. lower-log1p.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-neg.f64 93.0

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

   4. Applied rewrites 93.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

         \[\leadsto x - \frac{1}{\color{blue}{\frac{\frac{1}{2} \cdot \left(t \cdot y\right) + \frac{t}{e^{z} - 1}}{y}}} \]

      2. *-commutative N/A

         \[\leadsto x - \frac{1}{\frac{\color{blue}{\left(t \cdot y\right) \cdot \frac{1}{2}} + \frac{t}{e^{z} - 1}}{y}} \]

      3. lower-fma.f64 N/A

         \[\leadsto x - \frac{1}{\frac{\color{blue}{\mathsf{fma}\left(t \cdot y, \frac{1}{2}, \frac{t}{e^{z} - 1}\right)}}{y}} \]

      4. lower-*.f64 N/A

         \[\leadsto x - \frac{1}{\frac{\mathsf{fma}\left(\color{blue}{t \cdot y}, \frac{1}{2}, \frac{t}{e^{z} - 1}\right)}{y}} \]

      5. lower-/.f64 N/A

         \[\leadsto x - \frac{1}{\frac{\mathsf{fma}\left(t \cdot y, \frac{1}{2}, \color{blue}{\frac{t}{e^{z} - 1}}\right)}{y}} \]

      6. lower-expm1.f64 99.9

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

   7. Applied rewrites 99.9%

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

   if 2 < (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))

   1. Initial program 94.0%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Add Preprocessing
3. Recombined 3 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{z} \cdot y + \left(1 - y\right) \leq 0:\\ \;\;\;\;x - \frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot z\right)}}\\ \mathbf{elif}\;e^{z} \cdot y + \left(1 - y\right) \leq 2:\\ \;\;\;\;x - \frac{1}{\frac{\mathsf{fma}\left(y \cdot t, 0.5, \frac{t}{\mathsf{expm1}\left(z\right)}\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(e^{z} \cdot y + \left(1 - y\right)\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot z\right)}}\\ t_2 := \frac{\log \left(e^{z} \cdot y + \left(1 - y\right)\right)}{t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-284}:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right)}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ 1.0 (/ t (log1p (* y z))))))
        (t_2 (/ (log (+ (* (exp z) y) (- 1.0 y))) t)))
   (if (<= t_2 -2e-159)
     t_1
     (if (<= t_2 2e-284) (- x (* (/ (expm1 z) t) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (1.0 / (t / log1p((y * z))));
	double t_2 = log(((exp(z) * y) + (1.0 - y))) / t;
	double tmp;
	if (t_2 <= -2e-159) {
		tmp = t_1;
	} else if (t_2 <= 2e-284) {
		tmp = x - ((expm1(z) / t) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (1.0 / (t / Math.log1p((y * z))));
	double t_2 = Math.log(((Math.exp(z) * y) + (1.0 - y))) / t;
	double tmp;
	if (t_2 <= -2e-159) {
		tmp = t_1;
	} else if (t_2 <= 2e-284) {
		tmp = x - ((Math.expm1(z) / t) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (1.0 / (t / math.log1p((y * z))))
	t_2 = math.log(((math.exp(z) * y) + (1.0 - y))) / t
	tmp = 0
	if t_2 <= -2e-159:
		tmp = t_1
	elif t_2 <= 2e-284:
		tmp = x - ((math.expm1(z) / t) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(1.0 / Float64(t / log1p(Float64(y * z)))))
	t_2 = Float64(log(Float64(Float64(exp(z) * y) + Float64(1.0 - y))) / t)
	tmp = 0.0
	if (t_2 <= -2e-159)
		tmp = t_1;
	elseif (t_2 <= 2e-284)
		tmp = Float64(x - Float64(Float64(expm1(z) / t) * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(1.0 / N[(t / N[Log[1 + N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[N[(N[(N[Exp[z], $MachinePrecision] * y), $MachinePrecision] + N[(1.0 - y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-159], t$95$1, If[LessEqual[t$95$2, 2e-284], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) t) < -1.99999999999999998e-159 or 2.00000000000000007e-284 < (/.f64 (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) t)

   1. Initial program 25.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 25.9

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

      5. lift-log.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-neg N/A

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

      9. associate-+l+ N/A

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

      10. lower-log1p.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-neg.f64 67.8

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

   4. Applied rewrites 67.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 88.3

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

   7. Applied rewrites 88.3%

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

   if -1.99999999999999998e-159 < (/.f64 (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) t) < 2.00000000000000007e-284

   1. Initial program 82.2%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. div-sub N/A

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

      6. lower-/.f64 N/A

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

      7. lower-expm1.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\log \left(e^{z} \cdot y + \left(1 - y\right)\right)}{t} \leq -2 \cdot 10^{-159}:\\ \;\;\;\;x - \frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot z\right)}}\\ \mathbf{elif}\;\frac{\log \left(e^{z} \cdot y + \left(1 - y\right)\right)}{t} \leq 2 \cdot 10^{-284}:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right)}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot z\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{z} \cdot y + \left(1 - y\right) \leq 0:\\ \;\;\;\;x - \frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{\frac{\mathsf{fma}\left(y \cdot t, 0.5, \frac{t}{\mathsf{expm1}\left(z\right)}\right)}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ (* (exp z) y) (- 1.0 y)) 0.0)
   (- x (/ 1.0 (/ t (log1p (* y z)))))
   (- x (/ 1.0 (/ (fma (* y t) 0.5 (/ t (expm1 z))) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((exp(z) * y) + (1.0 - y)) <= 0.0) {
		tmp = x - (1.0 / (t / log1p((y * z))));
	} else {
		tmp = x - (1.0 / (fma((y * t), 0.5, (t / expm1(z))) / y));
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z))) < 0.0

   1. Initial program 1.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 1.9

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

      5. lift-log.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-neg N/A

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

      9. associate-+l+ N/A

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

      10. lower-log1p.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-neg.f64 58.3

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

   4. Applied rewrites 58.3%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 99.8

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

   7. Applied rewrites 99.8%

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

   if 0.0 < (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))

   1. Initial program 82.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 82.9

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

      5. lift-log.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-neg N/A

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

      9. associate-+l+ N/A

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

      10. lower-log1p.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-neg.f64 93.1

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

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

         \[\leadsto x - \frac{1}{\color{blue}{\frac{\frac{1}{2} \cdot \left(t \cdot y\right) + \frac{t}{e^{z} - 1}}{y}}} \]

      2. *-commutative N/A

         \[\leadsto x - \frac{1}{\frac{\color{blue}{\left(t \cdot y\right) \cdot \frac{1}{2}} + \frac{t}{e^{z} - 1}}{y}} \]

      3. lower-fma.f64 N/A

         \[\leadsto x - \frac{1}{\frac{\color{blue}{\mathsf{fma}\left(t \cdot y, \frac{1}{2}, \frac{t}{e^{z} - 1}\right)}}{y}} \]

      4. lower-*.f64 N/A

         \[\leadsto x - \frac{1}{\frac{\mathsf{fma}\left(\color{blue}{t \cdot y}, \frac{1}{2}, \frac{t}{e^{z} - 1}\right)}{y}} \]

      5. lower-/.f64 N/A

         \[\leadsto x - \frac{1}{\frac{\mathsf{fma}\left(t \cdot y, \frac{1}{2}, \color{blue}{\frac{t}{e^{z} - 1}}\right)}{y}} \]

      6. lower-expm1.f64 94.3

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

   7. Applied rewrites 94.3%

      \[\leadsto x - \frac{1}{\color{blue}{\frac{\mathsf{fma}\left(t \cdot y, 0.5, \frac{t}{\mathsf{expm1}\left(z\right)}\right)}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{z} \cdot y + \left(1 - y\right) \leq 0:\\ \;\;\;\;x - \frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{\frac{\mathsf{fma}\left(y \cdot t, 0.5, \frac{t}{\mathsf{expm1}\left(z\right)}\right)}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- x (/ 1.0 (/ t (log1p (* y (expm1 z)))))))

C

double code(double x, double y, double z, double t) {
	return x - (1.0 / (t / log1p((y * expm1(z)))));
}

Java

public static double code(double x, double y, double z, double t) {
	return x - (1.0 / (t / Math.log1p((y * Math.expm1(z)))));
}

Python

def code(x, y, z, t):
	return x - (1.0 / (t / math.log1p((y * math.expm1(z)))))

Julia

function code(x, y, z, t)
	return Float64(x - Float64(1.0 / Float64(t / log1p(Float64(y * expm1(z))))))
end

Wolfram

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

Derivation

1. Initial program 63.9%

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

   1. lift-/.f64 N/A

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

   2. clear-num N/A

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

   3. lower-/.f64 N/A

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

   4. lower-/.f64 63.9

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

   5. lift-log.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. lift--.f64 N/A

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

   8. sub-neg N/A

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

   9. associate-+l+ N/A

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

   10. lower-log1p.f64 N/A

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

   11. +-commutative N/A

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

   12. lift-*.f64 N/A

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

   13. *-commutative N/A

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

   14. lower-fma.f64 N/A

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

   15. lower-neg.f64 84.9

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

4. Applied rewrites 84.9%

   \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\mathsf{log1p}\left(\mathsf{fma}\left(e^{z}, y, -y\right)\right)}}} \]
5. Step-by-step derivation

   1. lift-exp.f64 N/A

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

   2. lift-fma.f64 N/A

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

   3. lift-neg.f64 N/A

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

   4. neg-mul-1 N/A

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

   5. distribute-rgt-in N/A

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

   6. metadata-eval N/A

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

   7. sub-neg N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower-expm1.f64 98.5

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

6. Applied rewrites 98.5%

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

7. Final simplification 98.5%

   \[\leadsto x - \frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}} \]
8. Add Preprocessing

Alternative 5: 86.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+75}:\\ \;\;\;\;x - \frac{\log \left(\mathsf{fma}\left(z, y, 1\right)\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right)}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.4e+75)
   (- x (/ (log (fma z y 1.0)) t))
   (- x (* (/ (expm1 z) t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.4e+75) {
		tmp = x - (log(fma(z, y, 1.0)) / t);
	} else {
		tmp = x - ((expm1(z) / t) * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.4e+75)
		tmp = Float64(x - Float64(log(fma(z, y, 1.0)) / t));
	else
		tmp = Float64(x - Float64(Float64(expm1(z) / t) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.4e+75], N[(x - N[(N[Log[N[(z * y + 1.0), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.39999999999999969e75

   1. Initial program 48.9%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 69.4

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

   5. Applied rewrites 69.4%

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

   if -6.39999999999999969e75 < y

   1. Initial program 66.8%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. div-sub N/A

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

      6. lower-/.f64 N/A

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

      7. lower-expm1.f64 95.5

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

   5. Applied rewrites 95.5%

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

Alternative 6: 85.9% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Initial program 63.9%

   \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. associate-/l* N/A

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

   2. div-sub N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 N/A

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

   5. div-sub N/A

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

   6. lower-/.f64 N/A

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

   7. lower-expm1.f64 88.4

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

5. Applied rewrites 88.4%

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

Alternative 7: 83.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-118}:\\ \;\;\;\;x - \frac{1}{\frac{\mathsf{fma}\left(\frac{-0.5}{y}, \frac{\left(\left(y - y \cdot y\right) \cdot z\right) \cdot t}{y}, \frac{t}{y}\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{z}{t} \cdot \mathsf{fma}\left(z \cdot z, 0.25, -1\right)}{\mathsf{fma}\left(0.5, z, -1\right)} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.8e-118)
   (- x (/ 1.0 (/ (fma (/ -0.5 y) (/ (* (* (- y (* y y)) z) t) y) (/ t y)) z)))
   (- x (* (/ (* (/ z t) (fma (* z z) 0.25 -1.0)) (fma 0.5 z -1.0)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e-118) {
		tmp = x - (1.0 / (fma((-0.5 / y), ((((y - (y * y)) * z) * t) / y), (t / y)) / z));
	} else {
		tmp = x - ((((z / t) * fma((z * z), 0.25, -1.0)) / fma(0.5, z, -1.0)) * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.8e-118)
		tmp = Float64(x - Float64(1.0 / Float64(fma(Float64(-0.5 / y), Float64(Float64(Float64(Float64(y - Float64(y * y)) * z) * t) / y), Float64(t / y)) / z)));
	else
		tmp = Float64(x - Float64(Float64(Float64(Float64(z / t) * fma(Float64(z * z), 0.25, -1.0)) / fma(0.5, z, -1.0)) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.8e-118], N[(x - N[(1.0 / N[(N[(N[(-0.5 / y), $MachinePrecision] * N[(N[(N[(N[(y - N[(y * y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / y), $MachinePrecision] + N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(N[(z / t), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] * 0.25 + -1.0), $MachinePrecision]), $MachinePrecision] / N[(0.5 * z + -1.0), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999961e-118

   1. Initial program 70.5%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 70.4

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

      5. lift-log.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-neg N/A

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

      9. associate-+l+ N/A

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

      10. lower-log1p.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-neg.f64 91.4

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

   4. Applied rewrites 91.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

   7. Applied rewrites 70.5%

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

   if -5.79999999999999961e-118 < z

   1. Initial program 59.2%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. div-sub N/A

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

      6. lower-/.f64 N/A

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

      7. lower-expm1.f64 93.4

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

   5. Applied rewrites 93.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 94.1%

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

   10. Applied rewrites 94.1%

       \[\leadsto x - \frac{\mathsf{fma}\left(z \cdot z, 0.25, -1\right) \cdot \frac{z}{t}}{\mathsf{fma}\left(0.5, z, -1\right)} \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-118}:\\ \;\;\;\;x - \frac{1}{\frac{\mathsf{fma}\left(\frac{-0.5}{y}, \frac{\left(\left(y - y \cdot y\right) \cdot z\right) \cdot t}{y}, \frac{t}{y}\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{z}{t} \cdot \mathsf{fma}\left(z \cdot z, 0.25, -1\right)}{\mathsf{fma}\left(0.5, z, -1\right)} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.9% accurate, 11.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.9%

   \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. associate-/l* N/A

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

   2. div-sub N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 N/A

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

   5. div-sub N/A

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

   6. lower-/.f64 N/A

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

   7. lower-expm1.f64 88.4

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

5. Applied rewrites 88.4%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 76.9%

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

Developer Target 1: 74.9% accurate, 1.8× 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 2024270 
(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)))