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

Percentage Accurate: 77.1% → 99.7%

Time: 13.5s

Alternatives: 9

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: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) \cdot 3\right) - z \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (- (* x (* (log (/ (cbrt x) (cbrt y))) 3.0)) z))

C

double code(double x, double y, double z) {
	return (x * (log((cbrt(x) / cbrt(y))) * 3.0)) - z;
}

Java

public static double code(double x, double y, double z) {
	return (x * (Math.log((Math.cbrt(x) / Math.cbrt(y))) * 3.0)) - z;
}

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(log(Float64(cbrt(x) / cbrt(y))) * 3.0)) - z)
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[Log[N[(N[Power[x, 1/3], $MachinePrecision] / N[Power[y, 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 79.1%

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

   1. add-cube-cbrt 79.1%

      \[\leadsto x \cdot \log \color{blue}{\left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y}}\right)} - z \]

   2. associate-*l* 79.1%

      \[\leadsto x \cdot \log \color{blue}{\left(\sqrt[3]{\frac{x}{y}} \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right)\right)} - z \]

   3. log-prod 79.0%

      \[\leadsto x \cdot \color{blue}{\left(\log \left(\sqrt[3]{\frac{x}{y}}\right) + \log \left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right)\right)} - z \]

   4. pow2 79.0%

      \[\leadsto x \cdot \left(\log \left(\sqrt[3]{\frac{x}{y}}\right) + \log \color{blue}{\left({\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}\right)}\right) - z \]

   5. metadata-eval 79.0%

      \[\leadsto x \cdot \left(\log \left(\sqrt[3]{\frac{x}{y}}\right) + \log \left({\left(\sqrt[3]{\frac{x}{y}}\right)}^{\color{blue}{\left(1 + 1\right)}}\right)\right) - z \]

   6. log-pow 79.0%

      \[\leadsto x \cdot \left(\log \left(\sqrt[3]{\frac{x}{y}}\right) + \color{blue}{\left(1 + 1\right) \cdot \log \left(\sqrt[3]{\frac{x}{y}}\right)}\right) - z \]

   7. metadata-eval 79.0%

      \[\leadsto x \cdot \left(\log \left(\sqrt[3]{\frac{x}{y}}\right) + \color{blue}{2} \cdot \log \left(\sqrt[3]{\frac{x}{y}}\right)\right) - z \]

3. Applied egg-rr 79.0%

   \[\leadsto x \cdot \color{blue}{\left(\log \left(\sqrt[3]{\frac{x}{y}}\right) + 2 \cdot \log \left(\sqrt[3]{\frac{x}{y}}\right)\right)} - z \]
4. Step-by-step derivation

   1. distribute-rgt1-in 79.0%

      \[\leadsto x \cdot \color{blue}{\left(\left(2 + 1\right) \cdot \log \left(\sqrt[3]{\frac{x}{y}}\right)\right)} - z \]

   2. metadata-eval 79.0%

      \[\leadsto x \cdot \left(\color{blue}{3} \cdot \log \left(\sqrt[3]{\frac{x}{y}}\right)\right) - z \]

   3. *-commutative 79.0%

      \[\leadsto x \cdot \color{blue}{\left(\log \left(\sqrt[3]{\frac{x}{y}}\right) \cdot 3\right)} - z \]

5. Simplified 79.0%

   \[\leadsto x \cdot \color{blue}{\left(\log \left(\sqrt[3]{\frac{x}{y}}\right) \cdot 3\right)} - z \]
6. Step-by-step derivation

   1. cbrt-div 99.7%

      \[\leadsto x \cdot \left(\log \color{blue}{\left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)} \cdot 3\right) - z \]

   2. div-inv 99.7%

      \[\leadsto x \cdot \left(\log \color{blue}{\left(\sqrt[3]{x} \cdot \frac{1}{\sqrt[3]{y}}\right)} \cdot 3\right) - z \]

7. Applied egg-rr 99.7%

   \[\leadsto x \cdot \left(\log \color{blue}{\left(\sqrt[3]{x} \cdot \frac{1}{\sqrt[3]{y}}\right)} \cdot 3\right) - z \]
8. Step-by-step derivation

   1. associate-*r/ 99.7%

      \[\leadsto x \cdot \left(\log \color{blue}{\left(\frac{\sqrt[3]{x} \cdot 1}{\sqrt[3]{y}}\right)} \cdot 3\right) - z \]

   2. *-rgt-identity 99.7%

      \[\leadsto x \cdot \left(\log \left(\frac{\color{blue}{\sqrt[3]{x}}}{\sqrt[3]{y}}\right) \cdot 3\right) - z \]

9. Simplified 99.7%

   \[\leadsto x \cdot \left(\log \color{blue}{\left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)} \cdot 3\right) - z \]

10. Final simplification 99.7%

    \[\leadsto x \cdot \left(\log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) \cdot 3\right) - z \]

Alternative 2: 88.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\frac{x}{y}\right)\\ t_1 := x \cdot t_0\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+301}\right):\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_0, x, -z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (log (/ x y))) (t_1 (* x t_0)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+301)))
     (- (* x (log (* x y))) z)
     (fma t_0 x (- z)))))

C

double code(double x, double y, double z) {
	double t_0 = log((x / y));
	double t_1 = x * t_0;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+301)) {
		tmp = (x * log((x * y))) - z;
	} else {
		tmp = fma(t_0, x, -z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = log(Float64(x / y))
	t_1 = Float64(x * t_0)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+301))
		tmp = Float64(Float64(x * log(Float64(x * y))) - z);
	else
		tmp = fma(t_0, x, Float64(-z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(x * t$95$0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+301]], $MachinePrecision]], N[(N[(x * N[Log[N[(x * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(t$95$0 * x + (-z)), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 1.00000000000000005e301 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 7.0%

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

      1. log-div 54.2%

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

   3. Applied egg-rr 54.2%

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

      1. sub-neg 54.2%

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

      2. distribute-rgt-in 54.2%

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

   5. Applied egg-rr 54.2%

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

      1. distribute-rgt-out 54.2%

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

      2. sub-neg 54.2%

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

      3. diff-log 7.0%

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

      4. *-commutative 7.0%

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

      5. clear-num 7.0%

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

      6. associate-/r/ 7.0%

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

      7. add-exp-log 3.1%

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

      8. neg-log 3.1%

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

      9. add-sqr-sqrt 2.7%

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

      10. sqrt-unprod 23.8%

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

      11. sqr-neg 23.8%

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

      12. sqrt-unprod 21.1%

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

      13. add-sqr-sqrt 24.8%

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

      14. add-exp-log 51.0%

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

   7. Applied egg-rr 51.0%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 1.00000000000000005e301

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. fma-neg 99.8%

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

   3. Applied egg-rr 99.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 10^{+301}\right):\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log \left(\frac{x}{y}\right), x, -z\right)\\ \end{array} \]

Alternative 3: 88.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq 10^{+301}\right):\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 1e+301)))
     (- (* x (log (* x y))) 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 <= 1e+301)) {
		tmp = (x * log((x * y))) - 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 <= 1e+301)) {
		tmp = (x * Math.log((x * y))) - 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 <= 1e+301):
		tmp = (x * math.log((x * y))) - 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 <= 1e+301))
		tmp = Float64(Float64(x * log(Float64(x * y))) - 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 <= 1e+301)))
		tmp = (x * log((x * y))) - 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, 1e+301]], $MachinePrecision]], N[(N[(x * N[Log[N[(x * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], 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 1.00000000000000005e301 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 7.0%

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

      1. log-div 54.2%

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

   3. Applied egg-rr 54.2%

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

      1. sub-neg 54.2%

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

      2. distribute-rgt-in 54.2%

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

   5. Applied egg-rr 54.2%

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

      1. distribute-rgt-out 54.2%

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

      2. sub-neg 54.2%

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

      3. diff-log 7.0%

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

      4. *-commutative 7.0%

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

      5. clear-num 7.0%

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

      6. associate-/r/ 7.0%

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

      7. add-exp-log 3.1%

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

      8. neg-log 3.1%

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

      9. add-sqr-sqrt 2.7%

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

      10. sqrt-unprod 23.8%

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

      11. sqr-neg 23.8%

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

      12. sqrt-unprod 21.1%

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

      13. add-sqr-sqrt 24.8%

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

      14. add-exp-log 51.0%

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

   7. Applied egg-rr 51.0%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 1.00000000000000005e301

   1. Initial program 99.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 10^{+301}\right):\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]

Alternative 4: 86.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;-z\\ \mathbf{elif}\;t_0 \leq 10^{+301}:\\ \;\;\;\;t_0 - z\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (<= t_0 (- INFINITY)) (- z) (if (<= t_0 1e+301) (- t_0 z) (- 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 = -z;
	} else if (t_0 <= 1e+301) {
		tmp = t_0 - z;
	} else {
		tmp = -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 = -z;
	} else if (t_0 <= 1e+301) {
		tmp = t_0 - z;
	} else {
		tmp = -z;
	}
	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 <= 1e+301:
		tmp = t_0 - z
	else:
		tmp = -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(-z);
	elseif (t_0 <= 1e+301)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(-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 = -z;
	elseif (t_0 <= 1e+301)
		tmp = t_0 - z;
	else
		tmp = -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)], (-z), If[LessEqual[t$95$0, 1e+301], N[(t$95$0 - z), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 1.00000000000000005e301 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 7.0%

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

   2. Taylor expanded in x around 0 45.6%

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

      1. neg-mul-1 45.6%

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

   4. Simplified 45.6%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 1.00000000000000005e301

   1. Initial program 99.8%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \cdot \log \left(\frac{x}{y}\right) \leq 10^{+301}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 5: 90.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(-\log \left(\frac{y}{x}\right)\right) - z\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-305}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.6e-170)
   (- (* x (- (log (/ y x)))) z)
   (if (<= x -1e-305) (- z) (- (* x (- (log x) (log y))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.6e-170) {
		tmp = (x * -log((y / x))) - z;
	} else if (x <= -1e-305) {
		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 <= (-3.6d-170)) then
        tmp = (x * -log((y / x))) - z
    else if (x <= (-1d-305)) 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 <= -3.6e-170) {
		tmp = (x * -Math.log((y / x))) - z;
	} else if (x <= -1e-305) {
		tmp = -z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.6e-170:
		tmp = (x * -math.log((y / x))) - z
	elif x <= -1e-305:
		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 <= -3.6e-170)
		tmp = Float64(Float64(x * Float64(-log(Float64(y / x)))) - z);
	elseif (x <= -1e-305)
		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 <= -3.6e-170)
		tmp = (x * -log((y / x))) - z;
	elseif (x <= -1e-305)
		tmp = -z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.6e-170], N[(N[(x * (-N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, -1e-305], (-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 < -3.6000000000000003e-170

   1. Initial program 85.3%

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

      1. clear-num 85.3%

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

      2. neg-log 87.4%

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

   3. Applied egg-rr 87.4%

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

   if -3.6000000000000003e-170 < x < -9.99999999999999996e-306

   1. Initial program 59.3%

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

   2. Taylor expanded in x around 0 96.5%

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

      1. neg-mul-1 96.5%

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

   4. Simplified 96.5%

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

   if -9.99999999999999996e-306 < x

   1. Initial program 78.7%

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

      1. log-div 99.3%

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

   3. Applied egg-rr 99.3%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(-\log \left(\frac{y}{x}\right)\right) - z\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-305}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \]

Alternative 6: 99.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5e-310], N[(N[(x * N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $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 x < -4.999999999999985e-310

   1. Initial program 79.5%

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

      1. frac-2neg 79.5%

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

      2. log-div 99.6%

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

   3. Applied egg-rr 99.6%

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

   if -4.999999999999985e-310 < x

   1. Initial program 78.7%

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

      1. log-div 99.3%

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

   3. Applied egg-rr 99.3%

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

4. Final simplification 99.4%

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

Alternative 7: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{-45}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.75e-45) (- z) (if (<= z 1.35e+29) (* x (log (/ x y))) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.75e-45) {
		tmp = -z;
	} else if (z <= 1.35e+29) {
		tmp = x * log((x / y));
	} 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 (z <= (-2.75d-45)) then
        tmp = -z
    else if (z <= 1.35d+29) then
        tmp = x * log((x / y))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.75e-45) {
		tmp = -z;
	} else if (z <= 1.35e+29) {
		tmp = x * Math.log((x / y));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.75e-45:
		tmp = -z
	elif z <= 1.35e+29:
		tmp = x * math.log((x / y))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.75e-45)
		tmp = Float64(-z);
	elseif (z <= 1.35e+29)
		tmp = Float64(x * log(Float64(x / y)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.75e-45)
		tmp = -z;
	elseif (z <= 1.35e+29)
		tmp = x * log((x / y));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.75e-45], (-z), If[LessEqual[z, 1.35e+29], N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -2.75000000000000015e-45 or 1.35e29 < z

   1. Initial program 74.0%

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

   2. Taylor expanded in x around 0 70.6%

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

      1. neg-mul-1 70.6%

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

   4. Simplified 70.6%

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

   if -2.75000000000000015e-45 < z < 1.35e29

   1. Initial program 85.2%

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

      1. flip-- 62.0%

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

      2. clear-num 61.9%

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

      3. fma-def 61.9%

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

      4. pow2 61.9%

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

   3. Applied egg-rr 61.9%

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

   4. Taylor expanded in x around inf 46.9%

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

      1. associate-/r* 46.9%

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

      2. log-rec 46.9%

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

      3. +-commutative 46.9%

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

      4. mul-1-neg 46.9%

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

      5. log-rec 46.9%

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

      6. remove-double-neg 46.9%

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

      7. sub-neg 46.9%

         \[\leadsto \frac{1}{\frac{\frac{1}{x}}{\color{blue}{\log x - \log y}}} \]

      8. log-div 70.7%

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

   6. Simplified 70.7%

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

      1. clear-num 70.8%

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

      2. div-inv 70.9%

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

      3. remove-double-div 71.0%

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

   8. Applied egg-rr 71.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{-45}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 49.3% accurate, 53.5× 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 79.1%

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

2. Taylor expanded in x around 0 47.8%

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

   1. neg-mul-1 47.8%

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

4. Simplified 47.8%

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

5. Final simplification 47.8%

   \[\leadsto -z \]

Alternative 9: 2.3% accurate, 107.0× 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 z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 79.1%

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

   1. flip-- 47.4%

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

   2. clear-num 47.3%

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

   3. fma-def 47.3%

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

   4. pow2 47.3%

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

3. Applied egg-rr 47.3%

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

4. Taylor expanded in x around 0 47.6%

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

   1. associate-/r/ 47.8%

      \[\leadsto \color{blue}{\frac{1}{-1} \cdot z} \]

   2. metadata-eval 47.8%

      \[\leadsto \color{blue}{-1} \cdot z \]

   3. neg-mul-1 47.8%

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

   4. neg-sub0 47.8%

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

   5. metadata-eval 47.8%

      \[\leadsto \color{blue}{\log 1} - z \]

   6. sub-neg 47.8%

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

   7. add-sqr-sqrt 23.8%

      \[\leadsto \log 1 + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}} \]

   8. sqrt-unprod 14.7%

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

   9. sqr-neg 14.7%

      \[\leadsto \log 1 + \sqrt{\color{blue}{z \cdot z}} \]

   10. sqrt-unprod 1.3%

       \[\leadsto \log 1 + \color{blue}{\sqrt{z} \cdot \sqrt{z}} \]

   11. add-sqr-sqrt 2.4%

       \[\leadsto \log 1 + \color{blue}{z} \]

   12. metadata-eval 2.4%

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

6. Applied egg-rr 2.4%

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

   1. +-lft-identity 2.4%

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

8. Simplified 2.4%

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

9. Final simplification 2.4%

   \[\leadsto z \]

Developer target: 88.2% 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 2023279 
(FPCore (x y z)
  :name "Numeric.SpecFunctions.Extra:bd0 from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< y 7.595077799083773e-308) (- (* x (log (/ x y))) z) (- (* x (- (log x) (log y))) z))

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