Numeric.SpecFunctions.Extra:bd0 from math-functions-0.1.5.2

Percentage Accurate: 77.6% → 99.4%

Time: 13.1s

Alternatives: 10

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-311}:\\ \;\;\;\;x \cdot \left(\log \left(0 - x\right) - \log \left(0 - y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log x, x, 0 - \left(z + x \cdot \log y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-311)
   (- (* x (- (log (- 0.0 x)) (log (- 0.0 y)))) z)
   (fma (log x) x (- 0.0 (+ z (* x (log y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-311) {
		tmp = (x * (log((0.0 - x)) - log((0.0 - y)))) - z;
	} else {
		tmp = fma(log(x), x, (0.0 - (z + (x * log(y)))));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-311)
		tmp = Float64(Float64(x * Float64(log(Float64(0.0 - x)) - log(Float64(0.0 - y)))) - z);
	else
		tmp = fma(log(x), x, Float64(0.0 - Float64(z + Float64(x * log(y)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-311], N[(N[(x * N[(N[Log[N[(0.0 - x), $MachinePrecision]], $MachinePrecision] - N[Log[N[(0.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[x], $MachinePrecision] * x + N[(0.0 - N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000023e-311

   1. Initial program 81.9%

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

      1. frac-2neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log \left(\frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(y\right)}\right)\right), z\right) \]

      2. log-div N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(\log \left(\mathsf{neg}\left(x\right)\right) - \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\log \left(\mathsf{neg}\left(x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      4. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(\mathsf{neg}\left(x\right)\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(0 - x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(\log 1 - x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(\log 1, x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      9. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), z\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\left(0 - y\right)\right)\right)\right), z\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\left(\log 1 - y\right)\right)\right)\right), z\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\mathsf{\_.f64}\left(\log 1, y\right)\right)\right)\right), z\right) \]

      13. metadata-eval 99.3%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, y\right)\right)\right)\right), z\right) \]

   4. Applied egg-rr 99.3%

      \[\leadsto x \cdot \color{blue}{\left(\log \left(0 - x\right) - \log \left(0 - y\right)\right)} - z \]

   if -5.00000000000023e-311 < y

   1. Initial program 77.8%

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\log \left(\frac{x}{y}\right), \color{blue}{x}, \left(\mathsf{neg}\left(z\right)\right)\right) \]

      4. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(\left(\frac{x}{y}\right)\right), x, \left(\mathsf{neg}\left(z\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(x, y\right)\right), x, \left(\mathsf{neg}\left(z\right)\right)\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(x, y\right)\right), x, \left(0 - z\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(x, y\right)\right), x, \left(\log 1 - z\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(x, y\right)\right), x, \mathsf{\_.f64}\left(\log 1, z\right)\right) \]

      9. metadata-eval 77.8%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(x, y\right)\right), x, \mathsf{\_.f64}\left(0, z\right)\right) \]

   4. Applied egg-rr 77.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log \left(\frac{x}{y}\right), x, 0 - z\right)} \]
   5. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \log \left(\frac{x}{y}\right) + \left(\color{blue}{0} - z\right) \]

      2. diff-log N/A

         \[\leadsto x \cdot \left(\log x - \log y\right) + \left(0 - z\right) \]

      3. sub-neg N/A

         \[\leadsto x \cdot \left(\log x + \left(\mathsf{neg}\left(\log y\right)\right)\right) + \left(0 - z\right) \]

      4. distribute-rgt-out N/A

         \[\leadsto \left(\log x \cdot x + \left(\mathsf{neg}\left(\log y\right)\right) \cdot x\right) + \left(\color{blue}{0} - z\right) \]

      5. sub0-neg N/A

         \[\leadsto \left(\log x \cdot x + \left(0 - \log y\right) \cdot x\right) + \left(0 - z\right) \]

      6. sub0-neg N/A

         \[\leadsto \left(\log x \cdot x + \left(0 - \log y\right) \cdot x\right) + \left(\mathsf{neg}\left(z\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \left(\log x \cdot x + \left(0 - \log y\right) \cdot x\right) - \color{blue}{z} \]

      8. associate--l+ N/A

         \[\leadsto \log x \cdot x + \color{blue}{\left(\left(0 - \log y\right) \cdot x - z\right)} \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\log x, \color{blue}{x}, \left(\left(0 - \log y\right) \cdot x - z\right)\right) \]

      10. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(x\right), x, \left(\left(0 - \log y\right) \cdot x - z\right)\right) \]

      11. +-lft-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(x\right), x, \left(\left(0 - \log y\right) \cdot x - \left(0 + z\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(x\right), x, \mathsf{\_.f64}\left(\left(\left(0 - \log y\right) \cdot x\right), \left(0 + z\right)\right)\right) \]

      13. sub0-neg N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(x\right), x, \mathsf{\_.f64}\left(\left(\left(\mathsf{neg}\left(\log y\right)\right) \cdot x\right), \left(0 + z\right)\right)\right) \]

      14. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(x\right), x, \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\log y \cdot x\right)\right), \left(0 + z\right)\right)\right) \]

      15. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(x\right), x, \mathsf{\_.f64}\left(\mathsf{neg.f64}\left(\left(\log y \cdot x\right)\right), \left(0 + z\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(x\right), x, \mathsf{\_.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(\log y, x\right)\right), \left(0 + z\right)\right)\right) \]

      17. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(x\right), x, \mathsf{\_.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(y\right), x\right)\right), \left(0 + z\right)\right)\right) \]

      18. +-lft-identity 99.7%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(x\right), x, \mathsf{\_.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(y\right), x\right)\right), z\right)\right) \]

   6. Applied egg-rr 99.7%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-311}:\\ \;\;\;\;x \cdot \left(\log \left(0 - x\right) - \log \left(0 - y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log x, x, 0 - \left(z + x \cdot \log y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{+282}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log x - x \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (<= t_0 (- INFINITY))
     (- 0.0 z)
     (if (<= t_0 4e+282) (- t_0 z) (- (* x (log x)) (* x (log y)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = 0.0 - z;
	} else if (t_0 <= 4e+282) {
		tmp = t_0 - z;
	} else {
		tmp = (x * log(x)) - (x * log(y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log((x / y));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = 0.0 - z;
	} else if (t_0 <= 4e+282) {
		tmp = t_0 - z;
	} else {
		tmp = (x * Math.log(x)) - (x * Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = 0.0 - z
	elif t_0 <= 4e+282:
		tmp = t_0 - z
	else:
		tmp = (x * math.log(x)) - (x * math.log(y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(Float64(x / y)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(0.0 - z);
	elseif (t_0 <= 4e+282)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(Float64(x * log(x)) - Float64(x * log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log((x / y));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = 0.0 - z;
	elseif (t_0 <= 4e+282)
		tmp = t_0 - z;
	else
		tmp = (x * log(x)) - (x * log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(0.0 - z), $MachinePrecision], If[LessEqual[t$95$0, 4e+282], N[(t$95$0 - z), $MachinePrecision], N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0

   1. Initial program 13.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 55.5%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 55.5%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. +-lft-identity N/A

         \[\leadsto \mathsf{neg}\left(\left(0 + z\right)\right) \]

      3. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(0 + z\right)\right) \]

      4. +-lft-identity 55.5%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 55.5%

      \[\leadsto \color{blue}{-z} \]

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 4.00000000000000013e282

   1. Initial program 99.5%

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

   if 4.00000000000000013e282 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 19.6%

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

   3. Taylor expanded in x around inf

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

      1. distribute-rgt-in N/A

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

      2. mul-1-neg N/A

         \[\leadsto \log \left(\frac{1}{y}\right) \cdot x + \left(\mathsf{neg}\left(\log \left(\frac{1}{x}\right)\right)\right) \cdot x \]

      3. log-rec N/A

         \[\leadsto \log \left(\frac{1}{y}\right) \cdot x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log x\right)\right)\right)\right) \cdot x \]

      4. remove-double-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. +-commutative N/A

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

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\log x + \log \left(\frac{1}{y}\right)\right)}\right) \]

      8. log-rec N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\log x + \left(\mathsf{neg}\left(\log y\right)\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\log x - \color{blue}{\log y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\log x, \color{blue}{\log y}\right)\right) \]

      11. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(x\right), \log \color{blue}{y}\right)\right) \]

      12. log-lowering-log.f64 54.6%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(x\right), \mathsf{log.f64}\left(y\right)\right)\right) \]

   5. Simplified 54.6%

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

      1. sub-neg N/A

         \[\leadsto x \cdot \left(\log x + \color{blue}{\left(\mathsf{neg}\left(\log y\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto x \cdot \left(\left(\mathsf{neg}\left(\log y\right)\right) + \color{blue}{\log x}\right) \]

      3. distribute-rgt-out N/A

         \[\leadsto \left(\mathsf{neg}\left(\log y\right)\right) \cdot x + \color{blue}{\log x \cdot x} \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\log y\right)\right), \color{blue}{x}, \left(\log x \cdot x\right)\right) \]

      5. sub0-neg N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(0 - \log y\right), x, \left(\log x \cdot x\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(0, \log y\right), x, \left(\log x \cdot x\right)\right) \]

      7. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{log.f64}\left(y\right)\right), x, \left(\log x \cdot x\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{log.f64}\left(y\right)\right), x, \left(x \cdot \log x\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{log.f64}\left(y\right)\right), x, \mathsf{*.f64}\left(x, \log x\right)\right) \]

      10. log-lowering-log.f64 54.8%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{log.f64}\left(y\right)\right), x, \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(x\right)\right)\right) \]

   7. Applied egg-rr 54.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0 - \log y, x, x \cdot \log x\right)} \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x \cdot \log x + \color{blue}{\left(0 - \log y\right) \cdot x} \]

      2. sub0-neg N/A

         \[\leadsto x \cdot \log x + \left(\mathsf{neg}\left(\log y\right)\right) \cdot x \]

      3. distribute-lft-neg-out N/A

         \[\leadsto x \cdot \log x + \left(\mathsf{neg}\left(\log y \cdot x\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto x \cdot \log x - \color{blue}{\log y \cdot x} \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \log x\right), \color{blue}{\left(\log y \cdot x\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log x\right), \left(\color{blue}{\log y} \cdot x\right)\right) \]

      7. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(x\right)\right), \left(\log y \cdot x\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(x\right)\right), \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y \cdot x\right)\right)\right)\right)\right) \]

      9. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(x\right)\right), \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right) \cdot x\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(x\right)\right), \left(\mathsf{neg}\left(x \cdot \left(\mathsf{neg}\left(\log y\right)\right)\right)\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(x\right)\right), \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log y\right)\right)\right)\right)}\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(x\right)\right), \left(x \cdot \log y\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(x\right)\right), \mathsf{*.f64}\left(x, \color{blue}{\log y}\right)\right) \]

      14. log-lowering-log.f64 54.8%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(x\right)\right), \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right)\right) \]

   9. Applied egg-rr 54.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;x \cdot \log \left(\frac{x}{y}\right) \leq 4 \cdot 10^{+282}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log x - x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;t\_0 \leq 10^{+291}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (<= t_0 (- INFINITY))
     (- 0.0 z)
     (if (<= t_0 1e+291) (- t_0 z) (* x (- (log x) (log y)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = 0.0 - z;
	} else if (t_0 <= 1e+291) {
		tmp = t_0 - z;
	} else {
		tmp = x * (log(x) - log(y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log((x / y));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = 0.0 - z;
	} else if (t_0 <= 1e+291) {
		tmp = t_0 - z;
	} else {
		tmp = x * (Math.log(x) - Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = 0.0 - z
	elif t_0 <= 1e+291:
		tmp = t_0 - z
	else:
		tmp = x * (math.log(x) - math.log(y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(Float64(x / y)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(0.0 - z);
	elseif (t_0 <= 1e+291)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(x * Float64(log(x) - log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log((x / y));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = 0.0 - z;
	elseif (t_0 <= 1e+291)
		tmp = t_0 - z;
	else
		tmp = x * (log(x) - log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(0.0 - z), $MachinePrecision], If[LessEqual[t$95$0, 1e+291], N[(t$95$0 - z), $MachinePrecision], N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0

   1. Initial program 13.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 55.5%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 55.5%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. +-lft-identity N/A

         \[\leadsto \mathsf{neg}\left(\left(0 + z\right)\right) \]

      3. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(0 + z\right)\right) \]

      4. +-lft-identity 55.5%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 55.5%

      \[\leadsto \color{blue}{-z} \]

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 9.9999999999999996e290

   1. Initial program 99.5%

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

   if 9.9999999999999996e290 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 11.0%

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

   3. Taylor expanded in x around inf

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

      1. distribute-rgt-in N/A

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

      2. mul-1-neg N/A

         \[\leadsto \log \left(\frac{1}{y}\right) \cdot x + \left(\mathsf{neg}\left(\log \left(\frac{1}{x}\right)\right)\right) \cdot x \]

      3. log-rec N/A

         \[\leadsto \log \left(\frac{1}{y}\right) \cdot x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log x\right)\right)\right)\right) \cdot x \]

      4. remove-double-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. +-commutative N/A

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

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\log x + \log \left(\frac{1}{y}\right)\right)}\right) \]

      8. log-rec N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\log x + \left(\mathsf{neg}\left(\log y\right)\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\log x - \color{blue}{\log y}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\log x, \color{blue}{\log y}\right)\right) \]

      11. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(x\right), \log \color{blue}{y}\right)\right) \]

      12. log-lowering-log.f64 50.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(x\right), \mathsf{log.f64}\left(y\right)\right)\right) \]

   5. Simplified 50.0%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;x \cdot \log \left(\frac{x}{y}\right) \leq 10^{+291}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;t\_0 \leq 10^{+291}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (<= t_0 (- INFINITY))
     (- 0.0 z)
     (if (<= t_0 1e+291) (- t_0 z) (- 0.0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = 0.0 - z;
	} else if (t_0 <= 1e+291) {
		tmp = t_0 - z;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log((x / y));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = 0.0 - z;
	} else if (t_0 <= 1e+291) {
		tmp = t_0 - z;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = 0.0 - z
	elif t_0 <= 1e+291:
		tmp = t_0 - z
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(Float64(x / y)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(0.0 - z);
	elseif (t_0 <= 1e+291)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log((x / y));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = 0.0 - z;
	elseif (t_0 <= 1e+291)
		tmp = t_0 - z;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(0.0 - z), $MachinePrecision], If[LessEqual[t$95$0, 1e+291], N[(t$95$0 - z), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 9.9999999999999996e290 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 12.5%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 52.4%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 52.4%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. +-lft-identity N/A

         \[\leadsto \mathsf{neg}\left(\left(0 + z\right)\right) \]

      3. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(0 + z\right)\right) \]

      4. +-lft-identity 52.4%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 52.4%

      \[\leadsto \color{blue}{-z} \]

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 9.9999999999999996e290

   1. Initial program 99.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;x \cdot \log \left(\frac{x}{y}\right) \leq 10^{+291}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+277}:\\ \;\;\;\;x \cdot \left(\log \left(0 - x\right) + \log \left(\frac{-1}{y}\right)\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-307}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e+277)
   (* x (+ (log (- 0.0 x)) (log (/ -1.0 y))))
   (if (<= x -1.75e-114)
     (- (* x (log (/ x y))) z)
     (if (<= x -1e-307) (- 0.0 z) (- (* x (- (log x) (log y))) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+277) {
		tmp = x * (log((0.0 - x)) + log((-1.0 / y)));
	} else if (x <= -1.75e-114) {
		tmp = (x * log((x / y))) - z;
	} else if (x <= -1e-307) {
		tmp = 0.0 - z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.3d+277)) then
        tmp = x * (log((0.0d0 - x)) + log(((-1.0d0) / y)))
    else if (x <= (-1.75d-114)) then
        tmp = (x * log((x / y))) - z
    else if (x <= (-1d-307)) then
        tmp = 0.0d0 - z
    else
        tmp = (x * (log(x) - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+277) {
		tmp = x * (Math.log((0.0 - x)) + Math.log((-1.0 / y)));
	} else if (x <= -1.75e-114) {
		tmp = (x * Math.log((x / y))) - z;
	} else if (x <= -1e-307) {
		tmp = 0.0 - z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e+277:
		tmp = x * (math.log((0.0 - x)) + math.log((-1.0 / y)))
	elif x <= -1.75e-114:
		tmp = (x * math.log((x / y))) - z
	elif x <= -1e-307:
		tmp = 0.0 - z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e+277)
		tmp = Float64(x * Float64(log(Float64(0.0 - x)) + log(Float64(-1.0 / y))));
	elseif (x <= -1.75e-114)
		tmp = Float64(Float64(x * log(Float64(x / y))) - z);
	elseif (x <= -1e-307)
		tmp = Float64(0.0 - z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.3e+277)
		tmp = x * (log((0.0 - x)) + log((-1.0 / y)));
	elseif (x <= -1.75e-114)
		tmp = (x * log((x / y))) - z;
	elseif (x <= -1e-307)
		tmp = 0.0 - z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e+277], N[(x * N[(N[Log[N[(0.0 - x), $MachinePrecision]], $MachinePrecision] + N[Log[N[(-1.0 / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.75e-114], N[(N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, -1e-307], N[(0.0 - z), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.29999999999999994e277

   1. Initial program 58.1%

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

   3. Taylor expanded in x around -inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\log \left(\frac{-1}{y}\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\log \left(\frac{-1}{y}\right), \color{blue}{\left(-1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right)\right) \]

      3. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\log \left(\frac{-1}{\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)}\right), \left(-1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right) \]

      4. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\log \left(\mathsf{neg}\left(\frac{-1}{\mathsf{neg}\left(y\right)}\right)\right), \left(-1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\log \left(\frac{\mathsf{neg}\left(-1\right)}{\mathsf{neg}\left(y\right)}\right), \left(-1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\log \left(\frac{1}{\mathsf{neg}\left(y\right)}\right), \left(-1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right) \]

      7. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\left(\frac{1}{\mathsf{neg}\left(y\right)}\right)\right), \left(\color{blue}{-1} \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\left(\frac{\mathsf{neg}\left(-1\right)}{\mathsf{neg}\left(y\right)}\right)\right), \left(-1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right) \]

      9. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\left(\mathsf{neg}\left(\frac{-1}{\mathsf{neg}\left(y\right)}\right)\right)\right), \left(-1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\left(\frac{-1}{\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)}\right)\right), \left(-1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\left(\frac{-1}{y}\right)\right), \left(-1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(-1, y\right)\right), \left(-1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(-1, y\right)\right), \left(\mathsf{neg}\left(\log \left(\frac{-1}{x}\right)\right)\right)\right)\right) \]

      14. log-rec N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(-1, y\right)\right), \log \left(\frac{1}{\frac{-1}{x}}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(-1, y\right)\right), \log \left(\frac{1}{\frac{\frac{1}{-1}}{x}}\right)\right)\right) \]

      16. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(-1, y\right)\right), \log \left(\frac{1}{\frac{1}{-1 \cdot x}}\right)\right)\right) \]

      17. remove-double-div N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(-1, y\right)\right), \log \left(-1 \cdot x\right)\right)\right) \]

      18. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(-1, y\right)\right), \mathsf{log.f64}\left(\left(-1 \cdot x\right)\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(-1, y\right)\right), \mathsf{log.f64}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)\right) \]

      20. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(-1, y\right)\right), \mathsf{log.f64}\left(\left(0 - x\right)\right)\right)\right) \]

      21. --lowering--.f64 99.2%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{log.f64}\left(\mathsf{/.f64}\left(-1, y\right)\right), \mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right)\right)\right) \]

   5. Simplified 99.2%

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

   if -1.29999999999999994e277 < x < -1.75e-114

   1. Initial program 91.4%

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

   if -1.75e-114 < x < -9.99999999999999909e-308

   1. Initial program 68.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 87.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 87.3%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. +-lft-identity N/A

         \[\leadsto \mathsf{neg}\left(\left(0 + z\right)\right) \]

      3. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(0 + z\right)\right) \]

      4. +-lft-identity 87.3%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 87.3%

      \[\leadsto \color{blue}{-z} \]

   if -9.99999999999999909e-308 < x

   1. Initial program 77.8%

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

      1. log-div N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(\log x - \log y\right)\right), z\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\log x, \log y\right)\right), z\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(x\right), \log y\right)\right), z\right) \]

      4. log-lowering-log.f64 99.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(x\right), \mathsf{log.f64}\left(y\right)\right)\right), z\right) \]

   4. Applied egg-rr 99.6%

      \[\leadsto x \cdot \color{blue}{\left(\log x - \log y\right)} - z \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+277}:\\ \;\;\;\;x \cdot \left(\log \left(0 - x\right) + \log \left(\frac{-1}{y}\right)\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-307}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.75e-114)
   (- (* x (log (/ x y))) z)
   (if (<= x -5e-310) (- 0.0 z) (- (* x (- (log x) (log y))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e-114) {
		tmp = (x * log((x / y))) - z;
	} else if (x <= -5e-310) {
		tmp = 0.0 - z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.75d-114)) then
        tmp = (x * log((x / y))) - z
    else if (x <= (-5d-310)) then
        tmp = 0.0d0 - z
    else
        tmp = (x * (log(x) - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e-114) {
		tmp = (x * Math.log((x / y))) - z;
	} else if (x <= -5e-310) {
		tmp = 0.0 - z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.75e-114:
		tmp = (x * math.log((x / y))) - z
	elif x <= -5e-310:
		tmp = 0.0 - z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.75e-114)
		tmp = Float64(Float64(x * log(Float64(x / y))) - z);
	elseif (x <= -5e-310)
		tmp = Float64(0.0 - z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.75e-114)
		tmp = (x * log((x / y))) - z;
	elseif (x <= -5e-310)
		tmp = 0.0 - z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.75e-114], N[(N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, -5e-310], N[(0.0 - z), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75e-114

   1. Initial program 86.8%

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

   if -1.75e-114 < x < -4.999999999999985e-310

   1. Initial program 68.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 87.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 87.3%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. +-lft-identity N/A

         \[\leadsto \mathsf{neg}\left(\left(0 + z\right)\right) \]

      3. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(0 + z\right)\right) \]

      4. +-lft-identity 87.3%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 87.3%

      \[\leadsto \color{blue}{-z} \]

   if -4.999999999999985e-310 < x

   1. Initial program 77.8%

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

      1. log-div N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(\log x - \log y\right)\right), z\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\log x, \log y\right)\right), z\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(x\right), \log y\right)\right), z\right) \]

      4. log-lowering-log.f64 99.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(x\right), \mathsf{log.f64}\left(y\right)\right)\right), z\right) \]

   4. Applied egg-rr 99.6%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-311}:\\ \;\;\;\;x \cdot \left(\log \left(0 - x\right) - \log \left(0 - y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x \cdot \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-311)
   (- (* x (- (log (- 0.0 x)) (log (- 0.0 y)))) z)
   (- (- (* x (log x)) (* x (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-311) {
		tmp = (x * (log((0.0 - x)) - log((0.0 - y)))) - z;
	} else {
		tmp = ((x * log(x)) - (x * log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5d-311)) then
        tmp = (x * (log((0.0d0 - x)) - log((0.0d0 - y)))) - z
    else
        tmp = ((x * log(x)) - (x * log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-311) {
		tmp = (x * (Math.log((0.0 - x)) - Math.log((0.0 - y)))) - z;
	} else {
		tmp = ((x * Math.log(x)) - (x * Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e-311:
		tmp = (x * (math.log((0.0 - x)) - math.log((0.0 - y)))) - z
	else:
		tmp = ((x * math.log(x)) - (x * math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-311)
		tmp = Float64(Float64(x * Float64(log(Float64(0.0 - x)) - log(Float64(0.0 - y)))) - z);
	else
		tmp = Float64(Float64(Float64(x * log(x)) - Float64(x * log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e-311)
		tmp = (x * (log((0.0 - x)) - log((0.0 - y)))) - z;
	else
		tmp = ((x * log(x)) - (x * log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-311], N[(N[(x * N[(N[Log[N[(0.0 - x), $MachinePrecision]], $MachinePrecision] - N[Log[N[(0.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000023e-311

   1. Initial program 81.9%

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

      1. frac-2neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log \left(\frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(y\right)}\right)\right), z\right) \]

      2. log-div N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(\log \left(\mathsf{neg}\left(x\right)\right) - \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\log \left(\mathsf{neg}\left(x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      4. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(\mathsf{neg}\left(x\right)\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(0 - x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(\log 1 - x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(\log 1, x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      9. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), z\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\left(0 - y\right)\right)\right)\right), z\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\left(\log 1 - y\right)\right)\right)\right), z\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\mathsf{\_.f64}\left(\log 1, y\right)\right)\right)\right), z\right) \]

      13. metadata-eval 99.3%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, y\right)\right)\right)\right), z\right) \]

   4. Applied egg-rr 99.3%

      \[\leadsto x \cdot \color{blue}{\left(\log \left(0 - x\right) - \log \left(0 - y\right)\right)} - z \]

   if -5.00000000000023e-311 < y

   1. Initial program 77.8%

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

      1. log-div N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\log x - \log y\right)\right), z\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\log x + \left(\mathsf{neg}\left(\log y\right)\right)\right)\right), z\right) \]

      3. distribute-rgt-in N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\log x \cdot x + \left(\mathsf{neg}\left(\log y\right)\right) \cdot x\right), z\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\log x \cdot x\right), \left(\left(\mathsf{neg}\left(\log y\right)\right) \cdot x\right)\right), z\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\log x, x\right), \left(\left(\mathsf{neg}\left(\log y\right)\right) \cdot x\right)\right), z\right) \]

      6. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(x\right), x\right), \left(\left(\mathsf{neg}\left(\log y\right)\right) \cdot x\right)\right), z\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(x\right), x\right), \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\log y\right)\right), x\right)\right), z\right) \]

      8. neg-log N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(x\right), x\right), \mathsf{*.f64}\left(\log \left(\frac{1}{y}\right), x\right)\right), z\right) \]

      9. log-div N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(x\right), x\right), \mathsf{*.f64}\left(\left(\log 1 - \log y\right), x\right)\right), z\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(x\right), x\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\log 1, \log y\right), x\right)\right), z\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(x\right), x\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \log y\right), x\right)\right), z\right) \]

      12. log-lowering-log.f64 99.7%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(x\right), x\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{log.f64}\left(y\right)\right), x\right)\right), z\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(\log x \cdot x + \left(0 - \log y\right) \cdot x\right)} - z \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-311}:\\ \;\;\;\;x \cdot \left(\log \left(0 - x\right) - \log \left(0 - y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x \cdot \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-311}:\\ \;\;\;\;x \cdot \left(\log \left(0 - x\right) - \log \left(0 - y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-311)
   (- (* x (- (log (- 0.0 x)) (log (- 0.0 y)))) z)
   (- (* x (- (log x) (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-311) {
		tmp = (x * (log((0.0 - x)) - log((0.0 - y)))) - z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5d-311)) then
        tmp = (x * (log((0.0d0 - x)) - log((0.0d0 - y)))) - z
    else
        tmp = (x * (log(x) - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-311) {
		tmp = (x * (Math.log((0.0 - x)) - Math.log((0.0 - y)))) - z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e-311:
		tmp = (x * (math.log((0.0 - x)) - math.log((0.0 - y)))) - z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-311)
		tmp = Float64(Float64(x * Float64(log(Float64(0.0 - x)) - log(Float64(0.0 - y)))) - z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e-311)
		tmp = (x * (log((0.0 - x)) - log((0.0 - y)))) - z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-311], N[(N[(x * N[(N[Log[N[(0.0 - x), $MachinePrecision]], $MachinePrecision] - N[Log[N[(0.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000023e-311

   1. Initial program 81.9%

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

      1. frac-2neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log \left(\frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(y\right)}\right)\right), z\right) \]

      2. log-div N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(\log \left(\mathsf{neg}\left(x\right)\right) - \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\log \left(\mathsf{neg}\left(x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      4. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(\mathsf{neg}\left(x\right)\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(0 - x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(\log 1 - x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(\log 1, x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \log \left(\mathsf{neg}\left(y\right)\right)\right)\right), z\right) \]

      9. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), z\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\left(0 - y\right)\right)\right)\right), z\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\left(\log 1 - y\right)\right)\right)\right), z\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\mathsf{\_.f64}\left(\log 1, y\right)\right)\right)\right), z\right) \]

      13. metadata-eval 99.3%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, x\right)\right), \mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, y\right)\right)\right)\right), z\right) \]

   4. Applied egg-rr 99.3%

      \[\leadsto x \cdot \color{blue}{\left(\log \left(0 - x\right) - \log \left(0 - y\right)\right)} - z \]

   if -5.00000000000023e-311 < y

   1. Initial program 77.8%

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

      1. log-div N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(\log x - \log y\right)\right), z\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\log x, \log y\right)\right), z\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(x\right), \log y\right)\right), z\right) \]

      4. log-lowering-log.f64 99.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(x\right), \mathsf{log.f64}\left(y\right)\right)\right), z\right) \]

   4. Applied egg-rr 99.6%

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

Alternative 9: 64.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+81}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+51}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (<= x -7e+81) t_0 (if (<= x 5.2e+51) (- 0.0 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if (x <= -7e+81) {
		tmp = t_0;
	} else if (x <= 5.2e+51) {
		tmp = 0.0 - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * log((x / y))
    if (x <= (-7d+81)) then
        tmp = t_0
    else if (x <= 5.2d+51) then
        tmp = 0.0d0 - z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log((x / y));
	double tmp;
	if (x <= -7e+81) {
		tmp = t_0;
	} else if (x <= 5.2e+51) {
		tmp = 0.0 - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if x <= -7e+81:
		tmp = t_0
	elif x <= 5.2e+51:
		tmp = 0.0 - z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(Float64(x / y)))
	tmp = 0.0
	if (x <= -7e+81)
		tmp = t_0;
	elseif (x <= 5.2e+51)
		tmp = Float64(0.0 - z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log((x / y));
	tmp = 0.0;
	if (x <= -7e+81)
		tmp = t_0;
	elseif (x <= 5.2e+51)
		tmp = 0.0 - z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+81], t$95$0, If[LessEqual[x, 5.2e+51], N[(0.0 - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.0000000000000001e81 or 5.2000000000000002e51 < x

   1. Initial program 78.2%

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

   3. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\log \left(\frac{x}{y}\right)}\right) \]

      2. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(\left(\frac{x}{y}\right)\right)\right) \]

      3. /-lowering-/.f64 62.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(\mathsf{/.f64}\left(x, y\right)\right)\right) \]

   5. Simplified 62.6%

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

   if -7.0000000000000001e81 < x < 5.2000000000000002e51

   1. Initial program 81.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 79.9%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 79.9%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. +-lft-identity N/A

         \[\leadsto \mathsf{neg}\left(\left(0 + z\right)\right) \]

      3. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(0 + z\right)\right) \]

      4. +-lft-identity 79.9%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 79.9%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+51}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.8% accurate, 35.7× speedup

Math

\[\begin{array}{l} \\ 0 - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- 0.0 z))

C

double code(double x, double y, double z) {
	return 0.0 - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.0d0 - z
end function

Java

public static double code(double x, double y, double z) {
	return 0.0 - z;
}

Python

def code(x, y, z):
	return 0.0 - z

Julia

function code(x, y, z)
	return Float64(0.0 - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.0 - z;
end

Wolfram

code[x_, y_, z_] := N[(0.0 - z), $MachinePrecision]

Derivation

1. Initial program 79.8%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-1 \cdot z} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(z\right) \]

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{z} \]

   3. --lowering--.f64 55.2%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

5. Simplified 55.2%

   \[\leadsto \color{blue}{0 - z} \]
6. Step-by-step derivation

   1. sub0-neg N/A

      \[\leadsto \mathsf{neg}\left(z\right) \]

   2. +-lft-identity N/A

      \[\leadsto \mathsf{neg}\left(\left(0 + z\right)\right) \]

   3. neg-lowering-neg.f64 N/A

      \[\leadsto \mathsf{neg.f64}\left(\left(0 + z\right)\right) \]

   4. +-lft-identity 55.2%

      \[\leadsto \mathsf{neg.f64}\left(z\right) \]

7. Applied egg-rr 55.2%

   \[\leadsto \color{blue}{-z} \]

8. Final simplification 55.2%

   \[\leadsto 0 - z \]
9. Add Preprocessing

Developer Target 1: 88.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.595077799083773 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< y 7.595077799083773e-308)
   (- (* x (log (/ x y))) z)
   (- (* x (- (log x) (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y < 7.595077799083773e-308) {
		tmp = (x * log((x / y))) - z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y < 7.595077799083773d-308) then
        tmp = (x * log((x / y))) - z
    else
        tmp = (x * (log(x) - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y < 7.595077799083773e-308) {
		tmp = (x * Math.log((x / y))) - z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y < 7.595077799083773e-308:
		tmp = (x * math.log((x / y))) - z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y < 7.595077799083773e-308)
		tmp = Float64(Float64(x * log(Float64(x / y))) - z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y < 7.595077799083773e-308)
		tmp = (x * log((x / y))) - z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[y, 7.595077799083773e-308], N[(N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Reproduce

herbie shell --seed 2024191 
(FPCore (x y z)
  :name "Numeric.SpecFunctions.Extra:bd0 from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y 7595077799083773/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (log (/ x y))) z) (- (* x (- (log x) (log y))) z)))

  (- (* x (log (/ x y))) z))