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

Percentage Accurate: 77.1% → 99.5%

Time: 9.3s

Alternatives: 8

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: 77.1% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;-\mathsf{fma}\left(\log \left(-y\right) - \log \left(-x\right), x, z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-310)
   (- (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 <= -5e-310) {
		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 <= -5e-310)
		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, -5e-310], (-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 < -4.999999999999985e-310

   1. Initial program 79.9%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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. frac-2neg N/A

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

      4. log-div N/A

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

      5. lower--.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-log.f64 N/A

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

      9. lower-neg.f64 99.4

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. associate-+l- N/A

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

      4. sub0-neg N/A

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

      5. sub-neg N/A

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

      6. *-lft-identity N/A

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

      7. mul-1-neg N/A

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

      8. *-rgt-identity N/A

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

      9. *-inverses N/A

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

      10. associate-/l* N/A

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

      11. associate-*l/ N/A

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

      12. associate-*r/ N/A

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

      13. distribute-rgt-in N/A

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

      14. lower-neg.f64 N/A

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

   7. Applied rewrites 99.5%

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

   if -4.999999999999985e-310 < y

   1. Initial program 79.5%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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 99.5

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

   4. Applied rewrites 99.5%

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

Alternative 2: 87.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;-z\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (<= t_0 (- INFINITY))
     (- z)
     (if (<= t_0 5e+292) (- t_0 z) (* (- (log x) (log y)) x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = -z;
	} else if (t_0 <= 5e+292) {
		tmp = t_0 - z;
	} else {
		tmp = (log(x) - log(y)) * x;
	}
	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 = -z;
	} else if (t_0 <= 5e+292) {
		tmp = t_0 - z;
	} else {
		tmp = (Math.log(x) - Math.log(y)) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = -z
	elif t_0 <= 5e+292:
		tmp = t_0 - z
	else:
		tmp = (math.log(x) - math.log(y)) * x
	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(-z);
	elseif (t_0 <= 5e+292)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(Float64(log(x) - log(y)) * x);
	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 = -z;
	elseif (t_0 <= 5e+292)
		tmp = t_0 - z;
	else
		tmp = (log(x) - log(y)) * x;
	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)], (-z), If[LessEqual[t$95$0, 5e+292], N[(t$95$0 - z), $MachinePrecision], N[(N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 9.7%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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 44.5

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

   5. Applied rewrites 44.5%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 4.9999999999999996e292

   1. Initial program 99.8%

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

   if 4.9999999999999996e292 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 14.1%

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. log-rec N/A

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

      5. remove-double-neg N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. log-rec N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-log.f64 N/A

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

      13. lower-log.f64 51.5

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

   5. Applied rewrites 51.5%

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

Alternative 3: 87.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 2 \cdot 10^{+298}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 2e+298))) (- 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 <= 2e+298)) {
		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 <= 2e+298)) {
		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 <= 2e+298):
		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 <= 2e+298))
		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 <= 2e+298)))
		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, 2e+298]], $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 1.9999999999999999e298 < (*.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 44.9

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

   5. Applied rewrites 44.9%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 1.9999999999999999e298

   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 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 2 \cdot 10^{+298}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+158}:\\ \;\;\;\;\left(\log \left(-x\right) - \log \left(-y\right)\right) \cdot x\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-307}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.85e+158)
   (* (- (log (- x)) (log (- y))) x)
   (if (<= x -1.05e-190)
     (- (* x (log (/ x y))) z)
     (if (<= x -4e-307) (- z) (- (* x (- (log x) (log y))) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.85e+158) {
		tmp = (log(-x) - log(-y)) * x;
	} else if (x <= -1.05e-190) {
		tmp = (x * log((x / y))) - z;
	} else if (x <= -4e-307) {
		tmp = -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 <= (-1.85d+158)) then
        tmp = (log(-x) - log(-y)) * x
    else if (x <= (-1.05d-190)) then
        tmp = (x * log((x / y))) - z
    else if (x <= (-4d-307)) then
        tmp = -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 <= -1.85e+158) {
		tmp = (Math.log(-x) - Math.log(-y)) * x;
	} else if (x <= -1.05e-190) {
		tmp = (x * Math.log((x / y))) - z;
	} else if (x <= -4e-307) {
		tmp = -z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.85e+158:
		tmp = (math.log(-x) - math.log(-y)) * x
	elif x <= -1.05e-190:
		tmp = (x * math.log((x / y))) - z
	elif x <= -4e-307:
		tmp = -z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.85e+158)
		tmp = Float64(Float64(log(Float64(-x)) - log(Float64(-y))) * x);
	elseif (x <= -1.05e-190)
		tmp = Float64(Float64(x * log(Float64(x / y))) - z);
	elseif (x <= -4e-307)
		tmp = Float64(-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 <= -1.85e+158)
		tmp = (log(-x) - log(-y)) * x;
	elseif (x <= -1.05e-190)
		tmp = (x * log((x / y))) - z;
	elseif (x <= -4e-307)
		tmp = -z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.85e+158], N[(N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -1.05e-190], N[(N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, -4e-307], (-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 < -1.85000000000000005e158

   1. Initial program 57.4%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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. frac-2neg N/A

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

      4. log-div N/A

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

      5. lower--.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-log.f64 N/A

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

      9. lower-neg.f64 98.9

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

   4. Applied rewrites 98.9%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower-neg.f64 94.9

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

   7. Applied rewrites 94.9%

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

   if -1.85000000000000005e158 < x < -1.04999999999999996e-190

   1. Initial program 91.0%

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

   if -1.04999999999999996e-190 < x < -3.99999999999999964e-307

   1. Initial program 78.0%

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

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

      2. lower-neg.f64 93.0

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

   5. Applied rewrites 93.0%

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

   if -3.99999999999999964e-307 < x

   1. Initial program 79.5%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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 99.5

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

   4. Applied rewrites 99.5%

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

Alternative 5: 88.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+247}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\left(-x\right) \cdot \log \left(\frac{y}{x}\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.35e+247)
   (- z)
   (if (<= y -5e-310)
     (- (* (- x) (log (/ y x))) z)
     (- (* x (- (log x) (log y))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+247) {
		tmp = -z;
	} else if (y <= -5e-310) {
		tmp = (-x * log((y / x))) - 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 <= (-1.35d+247)) then
        tmp = -z
    else if (y <= (-5d-310)) then
        tmp = (-x * log((y / x))) - 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 <= -1.35e+247) {
		tmp = -z;
	} else if (y <= -5e-310) {
		tmp = (-x * Math.log((y / x))) - z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.35e+247:
		tmp = -z
	elif y <= -5e-310:
		tmp = (-x * math.log((y / x))) - z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.35e+247)
		tmp = Float64(-z);
	elseif (y <= -5e-310)
		tmp = Float64(Float64(Float64(-x) * log(Float64(y / x))) - 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 <= -1.35e+247)
		tmp = -z;
	elseif (y <= -5e-310)
		tmp = (-x * log((y / x))) - z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.35e+247], (-z), If[LessEqual[y, -5e-310], N[(N[((-x) * N[Log[N[(y / x), $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 3 regimes

2. if y < -1.35e247

   1. Initial program 40.4%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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 90.1

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

   5. Applied rewrites 90.1%

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

   if -1.35e247 < y < -4.999999999999985e-310

   1. Initial program 83.0%

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

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

      4. log-rec N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower-/.f64 83.6

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

   4. Applied rewrites 83.6%

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

   if -4.999999999999985e-310 < y

   1. Initial program 79.5%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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 99.5

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

   4. Applied rewrites 99.5%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+247}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\left(-x\right) \cdot \log \left(\frac{y}{x}\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -520000000 \lor \neg \left(z \leq 3.6 \cdot 10^{+18}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log \left(\frac{y}{x}\right) \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -520000000.0) (not (<= z 3.6e+18)))
   (- z)
   (* (log (/ y x)) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -520000000.0) || !(z <= 3.6e+18)) {
		tmp = -z;
	} else {
		tmp = log((y / x)) * -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 <= (-520000000.0d0)) .or. (.not. (z <= 3.6d+18))) then
        tmp = -z
    else
        tmp = log((y / x)) * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -520000000.0) || !(z <= 3.6e+18)) {
		tmp = -z;
	} else {
		tmp = Math.log((y / x)) * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -520000000.0) or not (z <= 3.6e+18):
		tmp = -z
	else:
		tmp = math.log((y / x)) * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -520000000.0) || !(z <= 3.6e+18))
		tmp = Float64(-z);
	else
		tmp = Float64(log(Float64(y / x)) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -520000000.0) || ~((z <= 3.6e+18)))
		tmp = -z;
	else
		tmp = log((y / x)) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -520000000.0], N[Not[LessEqual[z, 3.6e+18]], $MachinePrecision]], (-z), N[(N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e8 or 3.6e18 < z

   1. Initial program 85.1%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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 78.3

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

   5. Applied rewrites 78.3%

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

   if -5.2e8 < z < 3.6e18

   1. Initial program 73.7%

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

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

      4. log-rec N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower-/.f64 73.6

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

   4. Applied rewrites 73.6%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-neg.f64 62.1

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

   7. Applied rewrites 62.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -520000000 \lor \neg \left(z \leq 3.6 \cdot 10^{+18}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log \left(\frac{y}{x}\right) \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+66} \lor \neg \left(x \leq 2.7 \cdot 10^{+54}\right):\\ \;\;\;\;\log \left(\frac{x}{y}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45e+66) (not (<= x 2.7e+54))) (* (log (/ x y)) x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45e+66) || !(x <= 2.7e+54)) {
		tmp = log((x / y)) * x;
	} else {
		tmp = -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 <= (-1.45d+66)) .or. (.not. (x <= 2.7d+54))) then
        tmp = log((x / y)) * x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45e+66) || !(x <= 2.7e+54)) {
		tmp = Math.log((x / y)) * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.45e+66) or not (x <= 2.7e+54):
		tmp = math.log((x / y)) * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45e+66) || !(x <= 2.7e+54))
		tmp = Float64(log(Float64(x / y)) * x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.45e+66) || ~((x <= 2.7e+54)))
		tmp = log((x / y)) * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45e+66], N[Not[LessEqual[x, 2.7e+54]], $MachinePrecision]], N[(N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999993e66 or 2.70000000000000011e54 < x

   1. Initial program 75.6%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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 62.9

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

   5. Applied rewrites 62.9%

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

   if -1.44999999999999993e66 < x < 2.70000000000000011e54

   1. Initial program 82.5%

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

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

      2. lower-neg.f64 75.4

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

   5. Applied rewrites 75.4%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+66} \lor \neg \left(x \leq 2.7 \cdot 10^{+54}\right):\\ \;\;\;\;\log \left(\frac{x}{y}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.6% 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 79.7%

   \[x \cdot \log \left(\frac{x}{y}\right) - z \]
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 51.4

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

5. Applied rewrites 51.4%

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

Developer Target 1: 89.0% 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 2024299 
(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))