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

Percentage Accurate: 77.7% → 99.5%

Time: 11.2s

Alternatives: 10

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.7% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-310}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e-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 (y <= -2e-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 (y <= (-2d-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 (y <= -2e-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 y <= -2e-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 (y <= -2e-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 (y <= -2e-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[y, -2e-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 y < -1.999999999999994e-310

   1. Initial program 77.1%

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

   3. Taylor expanded in y around -inf 99.5%

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

      1. metadata-eval 99.5%

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

      2. distribute-neg-frac 99.5%

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

      3. distribute-frac-neg2 99.5%

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

      4. log-rec 99.5%

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

      5. sub-neg 99.5%

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

      6. neg-mul-1 99.5%

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

   5. Simplified 99.5%

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

   if -1.999999999999994e-310 < y

   1. Initial program 74.0%

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

   3. Taylor expanded in x around 0 99.7%

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

      1. log-rec 99.7%

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

      2. neg-mul-1 99.7%

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

      3. neg-mul-1 99.7%

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

      4. sub-neg 99.7%

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

   5. Simplified 99.7%

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

Alternative 2: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\frac{x}{y}\right)\\ t_1 := x \cdot t\_0\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+253}:\\ \;\;\;\;\mathsf{fma}\left(x, t\_0, -z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (log (/ x y))) (t_1 (* x t_0)))
   (if (<= t_1 (- INFINITY))
     (- z)
     (if (<= t_1 5e+253) (fma x t_0 (- z)) (* x (- (log x) (log y)))))))

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)) {
		tmp = -z;
	} else if (t_1 <= 5e+253) {
		tmp = fma(x, t_0, -z);
	} else {
		tmp = x * (log(x) - log(y));
	}
	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))
		tmp = Float64(-z);
	elseif (t_1 <= 5e+253)
		tmp = fma(x, t_0, Float64(-z));
	else
		tmp = Float64(x * Float64(log(x) - log(y)));
	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[LessEqual[t$95$1, (-Infinity)], (-z), If[LessEqual[t$95$1, 5e+253], N[(x * t$95$0 + (-z)), $MachinePrecision], N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 9.1%

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

   3. Taylor expanded in x around 0 48.7%

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

      1. mul-1-neg 48.7%

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

   5. Simplified 48.7%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 4.9999999999999997e253

   1. Initial program 99.8%

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

      1. fma-neg 99.8%

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

   3. Simplified 99.8%

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

   if 4.9999999999999997e253 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 14.7%

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

      1. add-cube-cbrt 14.5%

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

      2. pow3 14.5%

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

   4. Applied egg-rr 14.5%

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

   5. Taylor expanded in x around inf 64.9%

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

      1. log-rec 64.9%

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

      2. mul-1-neg 64.9%

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

      3. log-rec 64.9%

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

      4. remove-double-div 64.9%

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

      5. +-commutative 64.9%

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

      6. sub-neg 64.9%

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

   7. Simplified 64.9%

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

Alternative 3: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;-z\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+253}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (<= t_0 (- INFINITY))
     (- z)
     (if (<= t_0 5e+253) (- t_0 z) (* x (- (log x) (log y)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = -z;
	} else if (t_0 <= 5e+253) {
		tmp = t_0 - z;
	} else {
		tmp = x * (log(x) - log(y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log((x / y));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = -z;
	} else if (t_0 <= 5e+253) {
		tmp = t_0 - z;
	} else {
		tmp = x * (Math.log(x) - Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = -z
	elif t_0 <= 5e+253:
		tmp = t_0 - z
	else:
		tmp = x * (math.log(x) - math.log(y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(Float64(x / y)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(-z);
	elseif (t_0 <= 5e+253)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(x * Float64(log(x) - log(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log((x / y));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = -z;
	elseif (t_0 <= 5e+253)
		tmp = t_0 - z;
	else
		tmp = x * (log(x) - log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], (-z), If[LessEqual[t$95$0, 5e+253], N[(t$95$0 - z), $MachinePrecision], N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 9.1%

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

   3. Taylor expanded in x around 0 48.7%

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

      1. mul-1-neg 48.7%

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

   5. Simplified 48.7%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 4.9999999999999997e253

   1. Initial program 99.8%

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

   if 4.9999999999999997e253 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 14.7%

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

      1. add-cube-cbrt 14.5%

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

      2. pow3 14.5%

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

   4. Applied egg-rr 14.5%

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

   5. Taylor expanded in x around inf 64.9%

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

      1. log-rec 64.9%

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

      2. mul-1-neg 64.9%

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

      3. log-rec 64.9%

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

      4. remove-double-div 64.9%

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

      5. +-commutative 64.9%

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

      6. sub-neg 64.9%

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

   7. Simplified 64.9%

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

Alternative 4: 86.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 2 \cdot 10^{+289}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 2e+289))) (- 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+289)) {
		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+289)) {
		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+289):
		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+289))
		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+289)))
		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+289]], $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 2.0000000000000001e289 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 7.7%

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

   3. Taylor expanded in x around 0 45.3%

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

      1. mul-1-neg 45.3%

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

   5. Simplified 45.3%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 2.0000000000000001e289

   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 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 2 \cdot 10^{+289}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-98}:\\ \;\;\;\;\left(-z\right) - x \cdot \log \left(\frac{y}{x}\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-140}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(x, \log \left(\frac{x}{y}\right), -z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.75e+196)
   (* x (- (log (- x)) (log (- y))))
   (if (<= x -2.3e-98)
     (- (- z) (* x (log (/ y x))))
     (if (<= x 3.5e-140)
       (- z)
       (if (<= x 8.2e+139)
         (fma x (log (/ x y)) (- z))
         (* x (- (log x) (log y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e+196) {
		tmp = x * (log(-x) - log(-y));
	} else if (x <= -2.3e-98) {
		tmp = -z - (x * log((y / x)));
	} else if (x <= 3.5e-140) {
		tmp = -z;
	} else if (x <= 8.2e+139) {
		tmp = fma(x, log((x / y)), -z);
	} else {
		tmp = x * (log(x) - log(y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.75e+196)
		tmp = Float64(x * Float64(log(Float64(-x)) - log(Float64(-y))));
	elseif (x <= -2.3e-98)
		tmp = Float64(Float64(-z) - Float64(x * log(Float64(y / x))));
	elseif (x <= 3.5e-140)
		tmp = Float64(-z);
	elseif (x <= 8.2e+139)
		tmp = fma(x, log(Float64(x / y)), Float64(-z));
	else
		tmp = Float64(x * Float64(log(x) - log(y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.75e+196], N[(x * N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.3e-98], N[((-z) - N[(x * N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-140], (-z), If[LessEqual[x, 8.2e+139], N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision] + (-z)), $MachinePrecision], N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.7499999999999999e196

   1. Initial program 60.6%

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

   3. Taylor expanded in z around 0 57.1%

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

   4. Taylor expanded in y around -inf 91.7%

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

      1. metadata-eval 99.0%

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

      2. distribute-neg-frac 99.0%

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

      3. distribute-frac-neg2 99.0%

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

      4. log-rec 99.0%

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

      5. sub-neg 99.0%

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

      6. neg-mul-1 99.0%

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

   6. Simplified 91.7%

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

   if -1.7499999999999999e196 < x < -2.30000000000000001e-98

   1. Initial program 87.9%

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

      1. clear-num 87.9%

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

      2. neg-log 91.4%

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

   4. Applied egg-rr 91.4%

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

   if -2.30000000000000001e-98 < x < 3.4999999999999998e-140

   1. Initial program 63.0%

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

   3. Taylor expanded in x around 0 87.3%

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

      1. mul-1-neg 87.3%

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

   5. Simplified 87.3%

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

   if 3.4999999999999998e-140 < x < 8.2000000000000004e139

   1. Initial program 92.8%

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

      1. fma-neg 92.8%

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

   3. Simplified 92.8%

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

   if 8.2000000000000004e139 < x

   1. Initial program 57.5%

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

      1. add-cube-cbrt 56.7%

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

      2. pow3 56.6%

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

   4. Applied egg-rr 56.6%

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

   5. Taylor expanded in x around inf 96.7%

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

      1. log-rec 96.7%

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

      2. mul-1-neg 96.7%

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

      3. log-rec 96.7%

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

      4. remove-double-div 96.7%

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

      5. +-commutative 96.7%

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

      6. sub-neg 96.7%

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

   7. Simplified 96.7%

      \[\leadsto \color{blue}{x \cdot \left(\log x - \log y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-98}:\\ \;\;\;\;\left(-z\right) - x \cdot \log \left(\frac{y}{x}\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-140}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(x, \log \left(\frac{x}{y}\right), -z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+195}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-98}:\\ \;\;\;\;\left(-z\right) - x \cdot \log \left(\frac{y}{x}\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-309}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.5e+195)
   (* x (- (log (- x)) (log (- y))))
   (if (<= x -3e-98)
     (- (- z) (* x (log (/ y x))))
     (if (<= x -5e-309) (- z) (- (* x (- (log x) (log y))) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.5e+195) {
		tmp = x * (log(-x) - log(-y));
	} else if (x <= -3e-98) {
		tmp = -z - (x * log((y / x)));
	} else if (x <= -5e-309) {
		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 <= (-8.5d+195)) then
        tmp = x * (log(-x) - log(-y))
    else if (x <= (-3d-98)) then
        tmp = -z - (x * log((y / x)))
    else if (x <= (-5d-309)) 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 <= -8.5e+195) {
		tmp = x * (Math.log(-x) - Math.log(-y));
	} else if (x <= -3e-98) {
		tmp = -z - (x * Math.log((y / x)));
	} else if (x <= -5e-309) {
		tmp = -z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.5e+195:
		tmp = x * (math.log(-x) - math.log(-y))
	elif x <= -3e-98:
		tmp = -z - (x * math.log((y / x)))
	elif x <= -5e-309:
		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 <= -8.5e+195)
		tmp = Float64(x * Float64(log(Float64(-x)) - log(Float64(-y))));
	elseif (x <= -3e-98)
		tmp = Float64(Float64(-z) - Float64(x * log(Float64(y / x))));
	elseif (x <= -5e-309)
		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 <= -8.5e+195)
		tmp = x * (log(-x) - log(-y));
	elseif (x <= -3e-98)
		tmp = -z - (x * log((y / x)));
	elseif (x <= -5e-309)
		tmp = -z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.5e+195], N[(x * N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3e-98], N[((-z) - N[(x * N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5e-309], (-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 < -8.5e195

   1. Initial program 60.6%

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

   3. Taylor expanded in z around 0 57.1%

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

   4. Taylor expanded in y around -inf 91.7%

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

      1. metadata-eval 99.0%

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

      2. distribute-neg-frac 99.0%

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

      3. distribute-frac-neg2 99.0%

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

      4. log-rec 99.0%

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

      5. sub-neg 99.0%

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

      6. neg-mul-1 99.0%

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

   6. Simplified 91.7%

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

   if -8.5e195 < x < -3e-98

   1. Initial program 87.9%

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

      1. clear-num 87.9%

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

      2. neg-log 91.4%

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

   4. Applied egg-rr 91.4%

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

   if -3e-98 < x < -4.9999999999999995e-309

   1. Initial program 71.3%

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

   3. Taylor expanded in x around 0 89.6%

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

      1. mul-1-neg 89.6%

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

   5. Simplified 89.6%

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

   if -4.9999999999999995e-309 < x

   1. Initial program 74.0%

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

   3. Taylor expanded in x around 0 99.7%

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

      1. log-rec 99.7%

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

      2. neg-mul-1 99.7%

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

      3. neg-mul-1 99.7%

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

      4. sub-neg 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+195}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-98}:\\ \;\;\;\;\left(-z\right) - x \cdot \log \left(\frac{y}{x}\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-309}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+36} \lor \neg \left(x \leq 1.22 \cdot 10^{+59}\right):\\ \;\;\;\;x \cdot \left(-\log \left(\frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.3e+36) (not (<= x 1.22e+59))) (* x (- (log (/ y x)))) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.3e+36) || !(x <= 1.22e+59)) {
		tmp = x * -log((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 <= (-4.3d+36)) .or. (.not. (x <= 1.22d+59))) then
        tmp = x * -log((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 <= -4.3e+36) || !(x <= 1.22e+59)) {
		tmp = x * -Math.log((y / x));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.3e+36) or not (x <= 1.22e+59):
		tmp = x * -math.log((y / x))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.3e+36) || !(x <= 1.22e+59))
		tmp = Float64(x * Float64(-log(Float64(y / x))));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.3e+36) || ~((x <= 1.22e+59)))
		tmp = x * -log((y / x));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.3e+36], N[Not[LessEqual[x, 1.22e+59]], $MachinePrecision]], N[(x * (-N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -4.30000000000000005e36 or 1.22e59 < x

   1. Initial program 70.2%

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

      1. clear-num 70.2%

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

      2. neg-log 74.1%

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

   4. Applied egg-rr 74.1%

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

   5. Taylor expanded in z around 0 61.5%

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

      1. associate-*r* 61.5%

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

      2. neg-mul-1 61.5%

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

   7. Simplified 61.5%

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

   if -4.30000000000000005e36 < x < 1.22e59

   1. Initial program 79.2%

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

   3. Taylor expanded in x around 0 76.1%

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

      1. mul-1-neg 76.1%

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

   5. Simplified 76.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+36} \lor \neg \left(x \leq 1.22 \cdot 10^{+59}\right):\\ \;\;\;\;x \cdot \left(-\log \left(\frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+34} \lor \neg \left(x \leq 5.4 \cdot 10^{+57}\right):\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1e+34) (not (<= x 5.4e+57))) (* x (log (/ x y))) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e+34) || !(x <= 5.4e+57)) {
		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 ((x <= (-1d+34)) .or. (.not. (x <= 5.4d+57))) 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 ((x <= -1e+34) || !(x <= 5.4e+57)) {
		tmp = x * Math.log((x / y));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1e+34) or not (x <= 5.4e+57):
		tmp = x * math.log((x / y))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1e+34) || !(x <= 5.4e+57))
		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 ((x <= -1e+34) || ~((x <= 5.4e+57)))
		tmp = x * log((x / y));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1e+34], N[Not[LessEqual[x, 5.4e+57]], $MachinePrecision]], N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -9.99999999999999946e33 or 5.3999999999999997e57 < x

   1. Initial program 70.2%

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

   3. Taylor expanded in z around 0 58.5%

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

   if -9.99999999999999946e33 < x < 5.3999999999999997e57

   1. Initial program 79.2%

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

   3. Taylor expanded in x around 0 76.1%

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

      1. mul-1-neg 76.1%

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

   5. Simplified 76.1%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+34} \lor \neg \left(x \leq 5.4 \cdot 10^{+57}\right):\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.7% 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 75.3%

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

3. Taylor expanded in x around 0 50.3%

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

   1. mul-1-neg 50.3%

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

5. Simplified 50.3%

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

Alternative 10: 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 75.3%

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

3. Taylor expanded in x around 0 50.3%

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

   1. mul-1-neg 50.3%

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

5. Simplified 50.3%

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

   1. neg-sub0 50.3%

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

   2. sub-neg 50.3%

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

   3. add-sqr-sqrt 26.1%

      \[\leadsto 0 + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}} \]

   4. sqrt-unprod 15.7%

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

   5. sqr-neg 15.7%

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

   6. sqrt-unprod 1.2%

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

   7. add-sqr-sqrt 2.1%

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

7. Applied egg-rr 2.1%

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

   1. +-lft-identity 2.1%

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

9. Simplified 2.1%

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

Developer Target 1: 88.1% 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 2024141 
(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))