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

Percentage Accurate: 77.7% → 91.1%

Time: 3.0s

Alternatives: 4

Speedup: N/A×

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    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: 91.1% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-177}:\\ \;\;\;\;x \cdot \log \left({y}^{-1} \cdot x\right) - z\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-308}:\\ \;\;\;\;-1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y \cdot -1, x, \log x \cdot x\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.8e-177)
   (- (* x (log (* (pow y -1.0) x))) z)
   (if (<= x -2e-308)
     (* -1.0 z)
     (- (fma (* (log y) -1.0) x (* (log x) x)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8e-177) {
		tmp = (x * log((pow(y, -1.0) * x))) - z;
	} else if (x <= -2e-308) {
		tmp = -1.0 * z;
	} else {
		tmp = fma((log(y) * -1.0), x, (log(x) * x)) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.8e-177)
		tmp = Float64(Float64(x * log(Float64((y ^ -1.0) * x))) - z);
	elseif (x <= -2e-308)
		tmp = Float64(-1.0 * z);
	else
		tmp = Float64(fma(Float64(log(y) * -1.0), x, Float64(log(x) * x)) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.8e-177], N[(N[(x * N[Log[N[(N[Power[y, -1.0], $MachinePrecision] * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, -2e-308], N[(-1.0 * z), $MachinePrecision], N[(N[(N[(N[Log[y], $MachinePrecision] * -1.0), $MachinePrecision] * x + N[(N[Log[x], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.79999999999999987e-177

   1. Initial program 81.5%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. inv-pow N/A

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

      11. lower-pow.f64 81.5

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

   3. Applied rewrites 81.5%

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

   if -2.79999999999999987e-177 < x < -1.9999999999999998e-308

   1. Initial program 64.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 88.4

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

   4. Applied rewrites 88.4%

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

   if -1.9999999999999998e-308 < x

   1. Initial program 77.4%

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

   3. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y \cdot -1, x, \log x \cdot x\right)} - z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 87.1% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log x \cdot x\\ t_1 := x \cdot \log \left(\frac{x}{y}\right) - z\\ t_2 := x \cdot \log y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{{t\_0}^{2} - t\_2 \cdot t\_2}{t\_0 - t\_2 \cdot -1} - z\\ \mathbf{elif}\;t\_1 \leq 10^{+302}:\\ \;\;\;\;x \cdot \log \left({y}^{-1} \cdot x\right) - z\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log x) x))
        (t_1 (- (* x (log (/ x y))) z))
        (t_2 (* x (log y))))
   (if (<= t_1 (- INFINITY))
     (- (/ (- (pow t_0 2.0) (* t_2 t_2)) (- t_0 (* t_2 -1.0))) z)
     (if (<= t_1 1e+302) (- (* x (log (* (pow y -1.0) x))) z) (* -1.0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = log(x) * x;
	double t_1 = (x * log((x / y))) - z;
	double t_2 = x * log(y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((pow(t_0, 2.0) - (t_2 * t_2)) / (t_0 - (t_2 * -1.0))) - z;
	} else if (t_1 <= 1e+302) {
		tmp = (x * log((pow(y, -1.0) * x))) - z;
	} else {
		tmp = -1.0 * z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log(x) * x;
	double t_1 = (x * Math.log((x / y))) - z;
	double t_2 = x * Math.log(y);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((Math.pow(t_0, 2.0) - (t_2 * t_2)) / (t_0 - (t_2 * -1.0))) - z;
	} else if (t_1 <= 1e+302) {
		tmp = (x * Math.log((Math.pow(y, -1.0) * x))) - z;
	} else {
		tmp = -1.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log(x) * x
	t_1 = (x * math.log((x / y))) - z
	t_2 = x * math.log(y)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((math.pow(t_0, 2.0) - (t_2 * t_2)) / (t_0 - (t_2 * -1.0))) - z
	elif t_1 <= 1e+302:
		tmp = (x * math.log((math.pow(y, -1.0) * x))) - z
	else:
		tmp = -1.0 * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(log(x) * x)
	t_1 = Float64(Float64(x * log(Float64(x / y))) - z)
	t_2 = Float64(x * log(y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64((t_0 ^ 2.0) - Float64(t_2 * t_2)) / Float64(t_0 - Float64(t_2 * -1.0))) - z);
	elseif (t_1 <= 1e+302)
		tmp = Float64(Float64(x * log(Float64((y ^ -1.0) * x))) - z);
	else
		tmp = Float64(-1.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log(x) * x;
	t_1 = (x * log((x / y))) - z;
	t_2 = x * log(y);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (((t_0 ^ 2.0) - (t_2 * t_2)) / (t_0 - (t_2 * -1.0))) - z;
	elseif (t_1 <= 1e+302)
		tmp = (x * log(((y ^ -1.0) * x))) - z;
	else
		tmp = -1.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[x], $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[Power[t$95$0, 2.0], $MachinePrecision] - N[(t$95$2 * t$95$2), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 - N[(t$95$2 * -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[t$95$1, 1e+302], N[(N[(x * N[Log[N[(N[Power[y, -1.0], $MachinePrecision] * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(-1.0 * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.3%

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

   3. Applied rewrites 42.4%

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

   if -inf.0 < (-.f64 (*.f64 x (log.f64 (/.f64 x y))) z) < 1.0000000000000001e302

   1. Initial program 99.7%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. inv-pow N/A

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

      11. lower-pow.f64 99.7

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

   3. Applied rewrites 99.7%

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

   if 1.0000000000000001e302 < (-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)

   1. Initial program 10.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 47.6

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

   4. Applied rewrites 47.6%

      \[\leadsto \color{blue}{-1 \cdot z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 86.5% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;-1 \cdot z\\ \mathbf{elif}\;t\_0 \leq 10^{+302}:\\ \;\;\;\;x \cdot \log \left({y}^{-1} \cdot x\right) - z\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (log (/ x y))) z)))
   (if (<= t_0 (- INFINITY))
     (* -1.0 z)
     (if (<= t_0 1e+302) (- (* x (log (* (pow y -1.0) x))) z) (* -1.0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = (x * log((x / y))) - z;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = -1.0 * z;
	} else if (t_0 <= 1e+302) {
		tmp = (x * log((pow(y, -1.0) * x))) - z;
	} else {
		tmp = -1.0 * z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * Math.log((x / y))) - z;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = -1.0 * z;
	} else if (t_0 <= 1e+302) {
		tmp = (x * Math.log((Math.pow(y, -1.0) * x))) - z;
	} else {
		tmp = -1.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * math.log((x / y))) - z
	tmp = 0
	if t_0 <= -math.inf:
		tmp = -1.0 * z
	elif t_0 <= 1e+302:
		tmp = (x * math.log((math.pow(y, -1.0) * x))) - z
	else:
		tmp = -1.0 * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * log(Float64(x / y))) - z)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(-1.0 * z);
	elseif (t_0 <= 1e+302)
		tmp = Float64(Float64(x * log(Float64((y ^ -1.0) * x))) - z);
	else
		tmp = Float64(-1.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * log((x / y))) - z;
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = -1.0 * z;
	elseif (t_0 <= 1e+302)
		tmp = (x * log(((y ^ -1.0) * x))) - z;
	else
		tmp = -1.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(-1.0 * z), $MachinePrecision], If[LessEqual[t$95$0, 1e+302], N[(N[(x * N[Log[N[(N[Power[y, -1.0], $MachinePrecision] * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(-1.0 * z), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 (/.f64 x y))) z) < -inf.0 or 1.0000000000000001e302 < (-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)

   1. Initial program 8.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 47.3

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

   4. Applied rewrites 47.3%

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

   if -inf.0 < (-.f64 (*.f64 x (log.f64 (/.f64 x y))) z) < 1.0000000000000001e302

   1. Initial program 99.7%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. inv-pow N/A

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

      11. lower-pow.f64 99.7

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

   3. Applied rewrites 99.7%

      \[\leadsto x \cdot \log \color{blue}{\left({y}^{-1} \cdot x\right)} - z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 50.5% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ -1 \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* -1.0 z))

C

double code(double x, double y, double z) {
	return -1.0 * z;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (-1.0d0) * z
end function

Java

public static double code(double x, double y, double z) {
	return -1.0 * z;
}

Python

def code(x, y, z):
	return -1.0 * z

Julia

function code(x, y, z)
	return Float64(-1.0 * z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = -1.0 * z;
end

Wolfram

code[x_, y_, z_] := N[(-1.0 * z), $MachinePrecision]

Derivation

1. Initial program 77.7%

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

2. Taylor expanded in x around 0

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

   1. lower-*.f64 50.5

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

4. Applied rewrites 50.5%

   \[\leadsto \color{blue}{-1 \cdot z} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025093 
(FPCore (x y z)
  :name "Numeric.SpecFunctions.Extra:bd0 from math-functions-0.1.5.2"
  :precision binary64
  (- (* x (log (/ x y))) z))