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

Percentage Accurate: 77.8% → 99.5%

Time: 7.9s

Alternatives: 7

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: 77.8% 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: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-311}:\\ \;\;\;\;-\mathsf{fma}\left(\log \left(-y\right) - \log \left(-x\right), x, z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e-311)
   (- (fma (- (log (- y)) (log (- x))) x z))
   (- (* x (- (log x) (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e-311) {
		tmp = -fma((log(-y) - log(-x)), x, z);
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4e-311)
		tmp = Float64(-fma(Float64(log(Float64(-y)) - log(Float64(-x))), x, z));
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4e-311], (-N[(N[(N[Log[(-y)], $MachinePrecision] - N[Log[(-x)], $MachinePrecision]), $MachinePrecision] * x + 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 < -3.99999999999979e-311

   1. Initial program 74.8%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. distribute-lft-in N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

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

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

      10. *-inverses N/A

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

      11. fp-cancel-sign-sub N/A

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

      12. *-rgt-identity N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.6%

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

   if -3.99999999999979e-311 < y

   1. Initial program 74.8%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. log-div N/A

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

      4. lower--.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 99.7

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

   4. Applied rewrites 99.7%

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

Alternative 2: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 5e+306))) (- z) (- t_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)) || !(t_0 <= 5e+306)) {
		tmp = -z;
	} else {
		tmp = t_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) || !(t_0 <= 5e+306)) {
		tmp = -z;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if (t_0 <= -math.inf) or not (t_0 <= 5e+306):
		tmp = -z
	else:
		tmp = t_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)) || !(t_0 <= 5e+306))
		tmp = Float64(-z);
	else
		tmp = Float64(t_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) || ~((t_0 <= 5e+306)))
		tmp = -z;
	else
		tmp = t_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[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, 5e+306]], $MachinePrecision]], (-z), N[(t$95$0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 4.99999999999999993e306 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 9.6%

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

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

      2. lower-neg.f64 45.8

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

   5. Applied rewrites 45.8%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 4.99999999999999993e306

   1. Initial program 99.8%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(\log \left(\frac{y}{x}\right), x, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 5e+306)))
     (- z)
     (- (fma (log (/ y x)) x z)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if ((t_0 <= -((double) INFINITY)) || !(t_0 <= 5e+306)) {
		tmp = -z;
	} else {
		tmp = -fma(log((y / x)), x, 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)) || !(t_0 <= 5e+306))
		tmp = Float64(-z);
	else
		tmp = Float64(-fma(log(Float64(y / x)), x, z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, 5e+306]], $MachinePrecision]], (-z), (-N[(N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision] * x + z), $MachinePrecision])]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 4.99999999999999993e306 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 9.6%

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

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

      2. lower-neg.f64 45.8

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

   5. Applied rewrites 45.8%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 4.99999999999999993e306

   1. Initial program 99.8%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. distribute-lft-in N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

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

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

      10. *-inverses N/A

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

      11. fp-cancel-sign-sub N/A

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

      12. *-rgt-identity N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 52.2%

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

   7. Applied rewrites 97.7%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(\log \left(\frac{y}{x}\right), x, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+109}:\\ \;\;\;\;\left(\log \left(-x\right) - \log \left(-y\right)\right) \cdot x\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-143}:\\ \;\;\;\;-\mathsf{fma}\left(\log \left(\frac{y}{x}\right), x, z\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.5e+109)
   (* (- (log (- x)) (log (- y))) x)
   (if (<= x -6e-143)
     (- (fma (log (/ y x)) x z))
     (if (<= x -4e-308) (- z) (- (* x (- (log x) (log y))) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e+109) {
		tmp = (log(-x) - log(-y)) * x;
	} else if (x <= -6e-143) {
		tmp = -fma(log((y / x)), x, z);
	} else if (x <= -4e-308) {
		tmp = -z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5e+109)
		tmp = Float64(Float64(log(Float64(-x)) - log(Float64(-y))) * x);
	elseif (x <= -6e-143)
		tmp = Float64(-fma(log(Float64(y / x)), x, z));
	elseif (x <= -4e-308)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5e+109], N[(N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -6e-143], (-N[(N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision] * x + z), $MachinePrecision]), If[LessEqual[x, -4e-308], (-z), 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 < -1.50000000000000008e109

   1. Initial program 64.7%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 91.0%

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

   if -1.50000000000000008e109 < x < -5.9999999999999997e-143

   1. Initial program 92.1%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. distribute-lft-in N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

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

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

      10. *-inverses N/A

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

      11. fp-cancel-sign-sub N/A

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

      12. *-rgt-identity N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.5%

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

   7. Applied rewrites 92.1%

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

   if -5.9999999999999997e-143 < x < -4.00000000000000013e-308

   1. Initial program 64.3%

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

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

      2. lower-neg.f64 91.2

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

   5. Applied rewrites 91.2%

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

   if -4.00000000000000013e-308 < x

   1. Initial program 74.8%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. log-div N/A

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

      4. lower--.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 99.7

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

   4. Applied rewrites 99.7%

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

Alternative 5: 90.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-143}:\\ \;\;\;\;-\mathsf{fma}\left(\log \left(\frac{y}{x}\right), x, z\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6e-143)
   (- (fma (log (/ y x)) x z))
   (if (<= x -4e-308) (- z) (- (* x (- (log x) (log y))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6e-143) {
		tmp = -fma(log((y / x)), x, z);
	} else if (x <= -4e-308) {
		tmp = -z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6e-143)
		tmp = Float64(-fma(log(Float64(y / x)), x, z));
	elseif (x <= -4e-308)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6e-143], (-N[(N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision] * x + z), $MachinePrecision]), If[LessEqual[x, -4e-308], (-z), 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 < -5.9999999999999997e-143

   1. Initial program 79.1%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. distribute-lft-in N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

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

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

      10. *-inverses N/A

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

      11. fp-cancel-sign-sub N/A

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

      12. *-rgt-identity N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.4%

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

   7. Applied rewrites 79.1%

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

   if -5.9999999999999997e-143 < x < -4.00000000000000013e-308

   1. Initial program 64.3%

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

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

      2. lower-neg.f64 91.2

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

   5. Applied rewrites 91.2%

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

   if -4.00000000000000013e-308 < x

   1. Initial program 74.8%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. log-div N/A

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

      4. lower--.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 99.7

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

   4. Applied rewrites 99.7%

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

Alternative 6: 68.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+34} \lor \neg \left(z \leq 5.6 \cdot 10^{-36}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log \left(\frac{x}{y}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e+34) (not (<= z 5.6e-36))) (- z) (* (log (/ x y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e+34) || !(z <= 5.6e-36)) {
		tmp = -z;
	} else {
		tmp = log((x / y)) * x;
	}
	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 ((z <= (-2.4d+34)) .or. (.not. (z <= 5.6d-36))) then
        tmp = -z
    else
        tmp = log((x / y)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e+34) || !(z <= 5.6e-36)) {
		tmp = -z;
	} else {
		tmp = Math.log((x / y)) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e+34) or not (z <= 5.6e-36):
		tmp = -z
	else:
		tmp = math.log((x / y)) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.4e+34) || !(z <= 5.6e-36))
		tmp = Float64(-z);
	else
		tmp = Float64(log(Float64(x / y)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.4e+34) || ~((z <= 5.6e-36)))
		tmp = -z;
	else
		tmp = log((x / y)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e+34], N[Not[LessEqual[z, 5.6e-36]], $MachinePrecision]], (-z), N[(N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.39999999999999987e34 or 5.6000000000000002e-36 < z

   1. Initial program 71.1%

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

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

      2. lower-neg.f64 77.8

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

   5. Applied rewrites 77.8%

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

   if -2.39999999999999987e34 < z < 5.6000000000000002e-36

   1. Initial program 78.7%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-/.f64 63.1

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

   5. Applied rewrites 63.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+34} \lor \neg \left(z \leq 5.6 \cdot 10^{-36}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log \left(\frac{x}{y}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.2% accurate, 40.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return -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 = -z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 74.8%

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

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

   2. lower-neg.f64 50.6

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

5. Applied rewrites 50.6%

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

Developer Target 1: 87.8% accurate, 0.6× 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 2024326 
(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))