Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, B

Percentage Accurate: 72.4% → 99.4%

Time: 8.1s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 1 - \log \left(1 - \frac{x - y}{1 - y}\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))

C

double code(double x, double y) {
	return 1.0 - log((1.0 - ((x - y) / (1.0 - y))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 - log((1.0d0 - ((x - y) / (1.0d0 - y))))
end function

Java

public static double code(double x, double y) {
	return 1.0 - Math.log((1.0 - ((x - y) / (1.0 - y))));
}

Python

def code(x, y):
	return 1.0 - math.log((1.0 - ((x - y) / (1.0 - y))))

Julia

function code(x, y)
	return Float64(1.0 - log(Float64(1.0 - Float64(Float64(x - y) / Float64(1.0 - y)))))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 - log((1.0 - ((x - y) / (1.0 - y))));
end

Wolfram

code[x_, y_] := N[(1.0 - N[Log[N[(1.0 - N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 72.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - \log \left(1 - \frac{x - y}{1 - y}\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))

C

double code(double x, double y) {
	return 1.0 - log((1.0 - ((x - y) / (1.0 - y))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 - log((1.0d0 - ((x - y) / (1.0d0 - y))))
end function

Java

public static double code(double x, double y) {
	return 1.0 - Math.log((1.0 - ((x - y) / (1.0 - y))));
}

Python

def code(x, y):
	return 1.0 - math.log((1.0 - ((x - y) / (1.0 - y))))

Julia

function code(x, y)
	return Float64(1.0 - log(Float64(1.0 - Float64(Float64(x - y) / Float64(1.0 - y)))))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 - log((1.0 - ((x - y) / (1.0 - y))));
end

Wolfram

code[x_, y_] := N[(1.0 - N[Log[N[(1.0 - N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{1 - y} \leq 0.004:\\ \;\;\;\;1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(y \cdot \frac{e}{x + -1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (- x y) (- 1.0 y)) 0.004)
   (- 1.0 (log1p (/ (- x y) (+ y -1.0))))
   (log (* y (/ E (+ x -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (((x - y) / (1.0 - y)) <= 0.004) {
		tmp = 1.0 - log1p(((x - y) / (y + -1.0)));
	} else {
		tmp = log((y * (((double) M_E) / (x + -1.0))));
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (((x - y) / (1.0 - y)) <= 0.004) {
		tmp = 1.0 - Math.log1p(((x - y) / (y + -1.0)));
	} else {
		tmp = Math.log((y * (Math.E / (x + -1.0))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x - y) / (1.0 - y)) <= 0.004:
		tmp = 1.0 - math.log1p(((x - y) / (y + -1.0)))
	else:
		tmp = math.log((y * (math.e / (x + -1.0))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(1.0 - y)) <= 0.004)
		tmp = Float64(1.0 - log1p(Float64(Float64(x - y) / Float64(y + -1.0))));
	else
		tmp = log(Float64(y * Float64(exp(1) / Float64(x + -1.0))));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 0.004], N[(1.0 - N[Log[1 + N[(N[(x - y), $MachinePrecision] / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Log[N[(y * N[(E / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y)) < 0.0040000000000000001

   1. Initial program 100.0%

      \[1 - \log \left(1 - \frac{x - y}{1 - y}\right) \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. log1p-define 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{0 - \left(1 - y\right)}}\right) \]

      5. associate--r- 100.0%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{\left(0 - 1\right) + y}}\right) \]

      6. metadata-eval 100.0%

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

      7. +-commutative 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)} \]
   4. Add Preprocessing

   if 0.0040000000000000001 < (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y))

   1. Initial program 7.3%

      \[1 - \log \left(1 - \frac{x - y}{1 - y}\right) \]
   2. Step-by-step derivation

      1. sub-neg 7.3%

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

      2. log1p-define 7.3%

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

      3. distribute-neg-frac2 7.3%

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

      4. neg-sub0 7.3%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{0 - \left(1 - y\right)}}\right) \]

      5. associate--r- 7.3%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{\left(0 - 1\right) + y}}\right) \]

      6. metadata-eval 7.3%

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

      7. +-commutative 7.3%

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

   3. Simplified 7.3%

      \[\leadsto \color{blue}{1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 80.8%

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

      1. mul-1-neg 80.8%

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

      2. sub-neg 80.8%

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

      3. metadata-eval 80.8%

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

   7. Simplified 80.8%

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

      1. add-log-exp 80.8%

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

      2. exp-diff 80.8%

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

      3. sum-log 100.0%

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

      4. add-exp-log 100.0%

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

      5. associate-*r/ 100.0%

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

      6. add-sqr-sqrt 81.3%

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

      7. sqrt-unprod 78.2%

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

      8. sqr-neg 78.2%

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

      9. sqrt-unprod 0.0%

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

      10. add-sqr-sqrt 0.0%

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

      11. *-commutative 0.0%

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

      12. neg-mul-1 0.0%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-unprod 14.1%

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

      15. sqr-neg 14.1%

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

      16. sqrt-unprod 18.8%

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

      17. add-sqr-sqrt 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. metadata-eval 100.0%

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

       2. sub-neg 100.0%

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

       3. associate-/r/ 100.0%

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

       4. exp-1-e 100.0%

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

       5. sub-neg 100.0%

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

       6. metadata-eval 100.0%

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

       7. +-commutative 100.0%

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

   11. Simplified 100.0%

       \[\leadsto \color{blue}{\log \left(\frac{e}{-1 + x} \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{1 - y} \leq 0.004:\\ \;\;\;\;1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(y \cdot \frac{e}{x + -1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\log \left(y \cdot \frac{e}{x + -1}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) - \mathsf{log1p}\left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.7) (not (<= y 1.0)))
   (log (* y (/ E (+ x -1.0))))
   (- (- 1.0 y) (log1p (- x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.7) || !(y <= 1.0)) {
		tmp = log((y * (((double) M_E) / (x + -1.0))));
	} else {
		tmp = (1.0 - y) - log1p(-x);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.7) || !(y <= 1.0)) {
		tmp = Math.log((y * (Math.E / (x + -1.0))));
	} else {
		tmp = (1.0 - y) - Math.log1p(-x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.7) or not (y <= 1.0):
		tmp = math.log((y * (math.e / (x + -1.0))))
	else:
		tmp = (1.0 - y) - math.log1p(-x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.7) || !(y <= 1.0))
		tmp = log(Float64(y * Float64(exp(1) / Float64(x + -1.0))));
	else
		tmp = Float64(Float64(1.0 - y) - log1p(Float64(-x)));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.7], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[Log[N[(y * N[(E / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] - N[Log[1 + (-x)], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.69999999999999996 or 1 < y

   1. Initial program 34.1%

      \[1 - \log \left(1 - \frac{x - y}{1 - y}\right) \]
   2. Step-by-step derivation

      1. sub-neg 34.1%

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

      2. log1p-define 34.1%

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

      3. distribute-neg-frac2 34.1%

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

      4. neg-sub0 34.1%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{0 - \left(1 - y\right)}}\right) \]

      5. associate--r- 34.1%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{\left(0 - 1\right) + y}}\right) \]

      6. metadata-eval 34.1%

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

      7. +-commutative 34.1%

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

   3. Simplified 34.1%

      \[\leadsto \color{blue}{1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. sub-neg 73.5%

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

      3. metadata-eval 73.5%

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

   7. Simplified 73.5%

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

      1. add-log-exp 73.5%

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

      2. exp-diff 73.5%

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

      3. sum-log 99.3%

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

      4. add-exp-log 99.3%

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

      5. associate-*r/ 99.3%

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

      6. add-sqr-sqrt 74.2%

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

      7. sqrt-unprod 62.8%

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

      8. sqr-neg 62.8%

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

      9. sqrt-unprod 0.0%

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

      10. add-sqr-sqrt 0.0%

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

      11. *-commutative 0.0%

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

      12. neg-mul-1 0.0%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-unprod 16.1%

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

      15. sqr-neg 16.1%

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

      16. sqrt-unprod 25.1%

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

      17. add-sqr-sqrt 99.3%

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

   9. Applied egg-rr 99.3%

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

       1. metadata-eval 99.3%

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

       2. sub-neg 99.3%

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

       3. associate-/r/ 99.3%

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

       4. exp-1-e 99.3%

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

       5. sub-neg 99.3%

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

       6. metadata-eval 99.3%

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

       7. +-commutative 99.3%

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

   11. Simplified 99.3%

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

   if -1.69999999999999996 < y < 1

   1. Initial program 100.0%

      \[1 - \log \left(1 - \frac{x - y}{1 - y}\right) \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. log1p-define 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{0 - \left(1 - y\right)}}\right) \]

      5. associate--r- 100.0%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{\left(0 - 1\right) + y}}\right) \]

      6. metadata-eval 100.0%

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

      7. +-commutative 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 99.1%

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

   7. Simplified 99.1%

      \[\leadsto \color{blue}{\left(1 - y\right) - \mathsf{log1p}\left(-x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\log \left(y \cdot \frac{e}{x + -1}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) - \mathsf{log1p}\left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13.2:\\ \;\;\;\;1 - \log \left(\frac{-1}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) - \mathsf{log1p}\left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -13.2) (- 1.0 (log (/ -1.0 y))) (- (- 1.0 y) (log1p (- x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -13.2) {
		tmp = 1.0 - log((-1.0 / y));
	} else {
		tmp = (1.0 - y) - log1p(-x);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -13.2) {
		tmp = 1.0 - Math.log((-1.0 / y));
	} else {
		tmp = (1.0 - y) - Math.log1p(-x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -13.2:
		tmp = 1.0 - math.log((-1.0 / y))
	else:
		tmp = (1.0 - y) - math.log1p(-x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -13.2)
		tmp = Float64(1.0 - log(Float64(-1.0 / y)));
	else
		tmp = Float64(Float64(1.0 - y) - log1p(Float64(-x)));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -13.2], N[(1.0 - N[Log[N[(-1.0 / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] - N[Log[1 + (-x)], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -13.199999999999999

   1. Initial program 28.1%

      \[1 - \log \left(1 - \frac{x - y}{1 - y}\right) \]
   2. Step-by-step derivation

      1. sub-neg 28.1%

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

      2. log1p-define 28.1%

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

      3. distribute-neg-frac2 28.1%

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

      4. neg-sub0 28.1%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{0 - \left(1 - y\right)}}\right) \]

      5. associate--r- 28.1%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{\left(0 - 1\right) + y}}\right) \]

      6. metadata-eval 28.1%

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

      7. +-commutative 28.1%

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

   3. Simplified 28.1%

      \[\leadsto \color{blue}{1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. sub-neg 98.7%

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

      3. metadata-eval 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in x around 0 65.8%

      \[\leadsto 1 - \color{blue}{\log \left(\frac{-1}{y}\right)} \]

   if -13.199999999999999 < y

   1. Initial program 94.1%

      \[1 - \log \left(1 - \frac{x - y}{1 - y}\right) \]
   2. Step-by-step derivation

      1. sub-neg 94.1%

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

      2. log1p-define 94.1%

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

      3. distribute-neg-frac2 94.1%

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

      4. neg-sub0 94.1%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{0 - \left(1 - y\right)}}\right) \]

      5. associate--r- 94.1%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{\left(0 - 1\right) + y}}\right) \]

      6. metadata-eval 94.1%

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

      7. +-commutative 94.1%

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

   3. Simplified 94.1%

      \[\leadsto \color{blue}{1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 87.0%

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

   7. Simplified 87.0%

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

Alternative 4: 79.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -165000000:\\ \;\;\;\;1 - \log \left(\frac{-1}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 - \mathsf{log1p}\left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -165000000.0) (- 1.0 (log (/ -1.0 y))) (- 1.0 (log1p (- x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -165000000.0) {
		tmp = 1.0 - log((-1.0 / y));
	} else {
		tmp = 1.0 - log1p(-x);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -165000000.0) {
		tmp = 1.0 - Math.log((-1.0 / y));
	} else {
		tmp = 1.0 - Math.log1p(-x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -165000000.0:
		tmp = 1.0 - math.log((-1.0 / y))
	else:
		tmp = 1.0 - math.log1p(-x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -165000000.0)
		tmp = Float64(1.0 - log(Float64(-1.0 / y)));
	else
		tmp = Float64(1.0 - log1p(Float64(-x)));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -165000000.0], N[(1.0 - N[Log[N[(-1.0 / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(1.0 - N[Log[1 + (-x)], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e8

   1. Initial program 27.0%

      \[1 - \log \left(1 - \frac{x - y}{1 - y}\right) \]
   2. Step-by-step derivation

      1. sub-neg 27.0%

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

      2. log1p-define 27.0%

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

      3. distribute-neg-frac2 27.0%

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

      4. neg-sub0 27.0%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{0 - \left(1 - y\right)}}\right) \]

      5. associate--r- 27.0%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{\left(0 - 1\right) + y}}\right) \]

      6. metadata-eval 27.0%

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

      7. +-commutative 27.0%

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

   3. Simplified 27.0%

      \[\leadsto \color{blue}{1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. sub-neg 99.1%

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

      3. metadata-eval 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in x around 0 66.8%

      \[\leadsto 1 - \color{blue}{\log \left(\frac{-1}{y}\right)} \]

   if -1.65e8 < y

   1. Initial program 94.1%

      \[1 - \log \left(1 - \frac{x - y}{1 - y}\right) \]
   2. Step-by-step derivation

      1. sub-neg 94.1%

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

      2. log1p-define 94.1%

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

      3. distribute-neg-frac2 94.1%

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

      4. neg-sub0 94.1%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{0 - \left(1 - y\right)}}\right) \]

      5. associate--r- 94.1%

         \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{\left(0 - 1\right) + y}}\right) \]

      6. metadata-eval 94.1%

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

      7. +-commutative 94.1%

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

   3. Simplified 94.1%

      \[\leadsto \color{blue}{1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 86.0%

      \[\leadsto 1 - \color{blue}{\log \left(1 + -1 \cdot x\right)} \]
   6. Step-by-step derivation

      1. log1p-define 86.0%

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

      2. mul-1-neg 86.0%

         \[\leadsto 1 - \mathsf{log1p}\left(\color{blue}{-x}\right) \]

   7. Simplified 86.0%

      \[\leadsto 1 - \color{blue}{\mathsf{log1p}\left(-x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 62.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ 1 - \mathsf{log1p}\left(-x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 1.0 (log1p (- x))))

C

double code(double x, double y) {
	return 1.0 - log1p(-x);
}

Java

public static double code(double x, double y) {
	return 1.0 - Math.log1p(-x);
}

Python

def code(x, y):
	return 1.0 - math.log1p(-x)

Julia

function code(x, y)
	return Float64(1.0 - log1p(Float64(-x)))
end

Wolfram

code[x_, y_] := N[(1.0 - N[Log[1 + (-x)], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.8%

   \[1 - \log \left(1 - \frac{x - y}{1 - y}\right) \]
2. Step-by-step derivation

   1. sub-neg 76.8%

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

   2. log1p-define 76.8%

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

   3. distribute-neg-frac2 76.8%

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

   4. neg-sub0 76.8%

      \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{0 - \left(1 - y\right)}}\right) \]

   5. associate--r- 76.8%

      \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{\left(0 - 1\right) + y}}\right) \]

   6. metadata-eval 76.8%

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

   7. +-commutative 76.8%

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

3. Simplified 76.8%

   \[\leadsto \color{blue}{1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 67.2%

   \[\leadsto 1 - \color{blue}{\log \left(1 + -1 \cdot x\right)} \]
6. Step-by-step derivation

   1. log1p-define 67.2%

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

   2. mul-1-neg 67.2%

      \[\leadsto 1 - \mathsf{log1p}\left(\color{blue}{-x}\right) \]

7. Simplified 67.2%

   \[\leadsto 1 - \color{blue}{\mathsf{log1p}\left(-x\right)} \]
8. Add Preprocessing

Alternative 6: 2.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ 1 - \mathsf{log1p}\left(-1\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 1.0 (log1p -1.0)))

C

double code(double x, double y) {
	return 1.0 - log1p(-1.0);
}

Java

public static double code(double x, double y) {
	return 1.0 - Math.log1p(-1.0);
}

Python

def code(x, y):
	return 1.0 - math.log1p(-1.0)

Julia

function code(x, y)
	return Float64(1.0 - log1p(-1.0))
end

Wolfram

code[x_, y_] := N[(1.0 - N[Log[1 + -1.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.8%

   \[1 - \log \left(1 - \frac{x - y}{1 - y}\right) \]
2. Step-by-step derivation

   1. sub-neg 76.8%

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

   2. log1p-define 76.8%

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

   3. distribute-neg-frac2 76.8%

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

   4. neg-sub0 76.8%

      \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{0 - \left(1 - y\right)}}\right) \]

   5. associate--r- 76.8%

      \[\leadsto 1 - \mathsf{log1p}\left(\frac{x - y}{\color{blue}{\left(0 - 1\right) + y}}\right) \]

   6. metadata-eval 76.8%

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

   7. +-commutative 76.8%

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

3. Simplified 76.8%

   \[\leadsto \color{blue}{1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 2.4%

   \[\leadsto 1 - \mathsf{log1p}\left(\color{blue}{-1}\right) \]
6. Add Preprocessing

Developer target: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \log \left(\frac{x}{y \cdot y} - \left(\frac{1}{y} - \frac{x}{y}\right)\right)\\ \mathbf{if}\;y < -81284752.61947241:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 3.0094271212461764 \cdot 10^{+25}:\\ \;\;\;\;\log \left(\frac{e^{1}}{1 - \frac{x - y}{1 - y}}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (log (- (/ x (* y y)) (- (/ 1.0 y) (/ x y)))))))
   (if (< y -81284752.61947241)
     t_0
     (if (< y 3.0094271212461764e+25)
       (log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
       t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 - log(((x / (y * y)) - ((1.0 / y) - (x / y))));
	double tmp;
	if (y < -81284752.61947241) {
		tmp = t_0;
	} else if (y < 3.0094271212461764e+25) {
		tmp = log((exp(1.0) / (1.0 - ((x - y) / (1.0 - y)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - log(((x / (y * y)) - ((1.0d0 / y) - (x / y))))
    if (y < (-81284752.61947241d0)) then
        tmp = t_0
    else if (y < 3.0094271212461764d+25) then
        tmp = log((exp(1.0d0) / (1.0d0 - ((x - y) / (1.0d0 - y)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - Math.log(((x / (y * y)) - ((1.0 / y) - (x / y))));
	double tmp;
	if (y < -81284752.61947241) {
		tmp = t_0;
	} else if (y < 3.0094271212461764e+25) {
		tmp = Math.log((Math.exp(1.0) / (1.0 - ((x - y) / (1.0 - y)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - math.log(((x / (y * y)) - ((1.0 / y) - (x / y))))
	tmp = 0
	if y < -81284752.61947241:
		tmp = t_0
	elif y < 3.0094271212461764e+25:
		tmp = math.log((math.exp(1.0) / (1.0 - ((x - y) / (1.0 - y)))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - log(Float64(Float64(x / Float64(y * y)) - Float64(Float64(1.0 / y) - Float64(x / y)))))
	tmp = 0.0
	if (y < -81284752.61947241)
		tmp = t_0;
	elseif (y < 3.0094271212461764e+25)
		tmp = log(Float64(exp(1.0) / Float64(1.0 - Float64(Float64(x - y) / Float64(1.0 - y)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - log(((x / (y * y)) - ((1.0 / y) - (x / y))));
	tmp = 0.0;
	if (y < -81284752.61947241)
		tmp = t_0;
	elseif (y < 3.0094271212461764e+25)
		tmp = log((exp(1.0) / (1.0 - ((x - y) / (1.0 - y)))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[Log[N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] - N[(N[(1.0 / y), $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[Less[y, -81284752.61947241], t$95$0, If[Less[y, 3.0094271212461764e+25], N[Log[N[(N[Exp[1.0], $MachinePrecision] / N[(1.0 - N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024103 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (if (< y -81284752.61947241) (- 1.0 (log (- (/ x (* y y)) (- (/ 1.0 y) (/ x y))))) (if (< y 3.0094271212461764e+25) (log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))) (- 1.0 (log (- (/ x (* y y)) (- (/ 1.0 y) (/ x y)))))))

  (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))