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

Percentage Accurate: 77.5% → 99.5%

Time: 2.6s

Alternatives: 8

Speedup: 0.7×

Specification

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (- (* 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)
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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * (ln((x / y)))) - z
END code

Initial Program: 77.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (- (* 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)
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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * (ln((x / y)))) - z
END code

Alternative 1: 99.5% accurate, 0.7× speedup

Math

\[x \cdot \left(\log \left(\left|x\right|\right) - \log \left(\left|y\right|\right)\right) - z \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (- (* x (- (log (fabs x)) (log (fabs y)))) z))

C

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

Fortran

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(abs(x)) - log(abs(y)))) - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * ((ln((abs(x)))) - (ln((abs(y)))))) - z
END code

Derivation

1. Initial program 77.5%

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

3. Applied rewrites 99.5%

   \[\leadsto x \cdot \left(\log \left(\left|x\right|\right) - \log \left(\left|y\right|\right)\right) - z \]
4. Add Preprocessing

Alternative 2: 89.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ t_1 := \left(-z\right) - \log \left(\left|y\right|\right) \cdot x\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t\_0 - z\\ \mathbf{elif}\;t\_0 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-0.6931471805599453 + \log \left(2 \cdot \left|\frac{x}{y}\right|\right)\right) - z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (log (/ x y)))) (t_1 (- (- z) (* (log (fabs y)) x))))
  (if (<= t_0 (- INFINITY))
    t_1
    (if (<= t_0 5e+305)
      (- t_0 z)
      (if (<= t_0 INFINITY)
        t_1
        (-
         (* x (+ -0.6931471805599453 (log (* 2.0 (fabs (/ x y))))))
         z))))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double t_1 = -z - (log(fabs(y)) * x);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= 5e+305) {
		tmp = t_0 - z;
	} else if (t_0 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x * (-0.6931471805599453 + log((2.0 * fabs((x / y)))))) - z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log((x / y));
	double t_1 = -z - (Math.log(Math.abs(y)) * x);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= 5e+305) {
		tmp = t_0 - z;
	} else if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x * (-0.6931471805599453 + Math.log((2.0 * Math.abs((x / y)))))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	t_1 = -z - (math.log(math.fabs(y)) * x)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= 5e+305:
		tmp = t_0 - z
	elif t_0 <= math.inf:
		tmp = t_1
	else:
		tmp = (x * (-0.6931471805599453 + math.log((2.0 * math.fabs((x / y)))))) - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(Float64(x / y)))
	t_1 = Float64(Float64(-z) - Float64(log(abs(y)) * x))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= 5e+305)
		tmp = Float64(t_0 - z);
	elseif (t_0 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(-0.6931471805599453 + log(Float64(2.0 * abs(Float64(x / y)))))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log((x / y));
	t_1 = -z - (log(abs(y)) * x);
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= 5e+305)
		tmp = t_0 - z;
	elseif (t_0 <= Inf)
		tmp = t_1;
	else
		tmp = (x * (-0.6931471805599453 + log((2.0 * abs((x / y)))))) - 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]}, Block[{t$95$1 = N[((-z) - N[(N[Log[N[Abs[y], $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, 5e+305], N[(t$95$0 - z), $MachinePrecision], If[LessEqual[t$95$0, Infinity], t$95$1, N[(N[(x * N[(-0.6931471805599453 + N[Log[N[(2.0 * N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 5.0000000000000001e305 < (*.f64 x (log.f64 (/.f64 x y))) < +inf.0

   1. Initial program 77.5%

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

   3. Applied rewrites 77.3%

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(x, -\log \left(\left|y\right|\right), -1 \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 56.1%

      \[\leadsto \mathsf{fma}\left(x, -\log \left(\left|y\right|\right), -1 \cdot z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.1%

       \[\leadsto \left(-z\right) - \log \left(\left|y\right|\right) \cdot x \]

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 5.0000000000000001e305

   1. Initial program 77.5%

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

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

   1. Initial program 77.5%

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

   3. Applied rewrites 77.4%

      \[\leadsto x \cdot \left(\log 0.5 + \log \left(2 \cdot \left|\frac{x}{y}\right|\right)\right) - z \]

   4. Evaluated real constant 77.4%

      \[\leadsto x \cdot \left(-0.6931471805599453 + \log \left(2 \cdot \left|\frac{x}{y}\right|\right)\right) - z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 89.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \log \left(\left|y\right|\right)\\ \mathbf{if}\;x \leq -2.355915687297802 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(\log \left(\left|x\right|\right) - t\_0\right)\\ \mathbf{elif}\;x \leq 2.8137445995672254 \cdot 10^{-161}:\\ \;\;\;\;\left(-z\right) - t\_0 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(\log \left(\frac{y}{x}\right), x, z\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (log (fabs y))))
  (if (<= x -2.355915687297802e+103)
    (* x (- (log (fabs x)) t_0))
    (if (<= x 2.8137445995672254e-161)
      (- (- z) (* t_0 x))
      (- (fma (log (/ y x)) x z))))))

C

double code(double x, double y, double z) {
	double t_0 = log(fabs(y));
	double tmp;
	if (x <= -2.355915687297802e+103) {
		tmp = x * (log(fabs(x)) - t_0);
	} else if (x <= 2.8137445995672254e-161) {
		tmp = -z - (t_0 * x);
	} else {
		tmp = -fma(log((y / x)), x, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = log(abs(y))
	tmp = 0.0
	if (x <= -2.355915687297802e+103)
		tmp = Float64(x * Float64(log(abs(x)) - t_0));
	elseif (x <= 2.8137445995672254e-161)
		tmp = Float64(Float64(-z) - Float64(t_0 * x));
	else
		tmp = Float64(-fma(log(Float64(y / x)), x, z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Log[N[Abs[y], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -2.355915687297802e+103], N[(x * N[(N[Log[N[Abs[x], $MachinePrecision]], $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8137445995672254e-161], N[((-z) - N[(t$95$0 * x), $MachinePrecision]), $MachinePrecision], (-N[(N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision] * x + z), $MachinePrecision])]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (ln((abs(y)))) IN
		LET tmp_1 = IF (x <= (28137445995672253562512624737083075467871722688081150561045570433355418598974045848749464618581113674214239986917381003183495732912523378855005351017915104944135221922492677044423270498506304507910846050405961709953595085845023293031406382864848301060160398810126406302010553858186105785533340929880096615262152964992587675570251398212465169186773775200446966971552454934804064911484967892452146998039097525179386138916015625e-585)) THEN ((- z) - (t_0 * x)) ELSE (- (((ln((y / x))) * x) + z)) ENDIF IN
		LET tmp = IF (x <= (-23559156872978018068070270347616667727337560578668702045675392005501681056632747131401300369999568830464)) THEN (x * ((ln((abs(x)))) - t_0)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if x < -2.3559156872978018e103

   1. Initial program 77.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 39.6%

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

   6. Applied rewrites 50.6%

      \[\leadsto x \cdot \left(\log \left(\left|x\right|\right) - \log \left(\left|y\right|\right)\right) \]

   if -2.3559156872978018e103 < x < 2.8137445995672254e-161

   1. Initial program 77.5%

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

   3. Applied rewrites 77.3%

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(x, -\log \left(\left|y\right|\right), -1 \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 56.1%

      \[\leadsto \mathsf{fma}\left(x, -\log \left(\left|y\right|\right), -1 \cdot z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.1%

       \[\leadsto \left(-z\right) - \log \left(\left|y\right|\right) \cdot x \]

   if 2.8137445995672254e-161 < x

   1. Initial program 77.5%

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

   3. Applied rewrites 77.3%

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

Alternative 4: 79.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ t_1 := \left(-z\right) - \log \left(\left|y\right|\right) \cdot x\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (log (/ x y)))) (t_1 (- (- z) (* (log (fabs y)) x))))
  (if (<= t_0 (- INFINITY)) t_1 (if (<= t_0 5e+305) (- t_0 z) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double t_1 = -z - (log(fabs(y)) * x);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= 5e+305) {
		tmp = t_0 - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log((x / y));
	double t_1 = -z - (Math.log(Math.abs(y)) * x);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= 5e+305) {
		tmp = t_0 - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	t_1 = -z - (math.log(math.fabs(y)) * x)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= 5e+305:
		tmp = t_0 - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(Float64(x / y)))
	t_1 = Float64(Float64(-z) - Float64(log(abs(y)) * x))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= 5e+305)
		tmp = Float64(t_0 - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log((x / y));
	t_1 = -z - (log(abs(y)) * x);
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= 5e+305)
		tmp = t_0 - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-z) - N[(N[Log[N[Abs[y], $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, 5e+305], N[(t$95$0 - z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 5.0000000000000001e305 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 77.5%

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

   3. Applied rewrites 77.3%

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(x, -\log \left(\left|y\right|\right), -1 \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 56.1%

      \[\leadsto \mathsf{fma}\left(x, -\log \left(\left|y\right|\right), -1 \cdot z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.1%

       \[\leadsto \left(-z\right) - \log \left(\left|y\right|\right) \cdot x \]

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 5.0000000000000001e305

   1. Initial program 77.5%

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

Alternative 5: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 1679.4032864083838:\\ \;\;\;\;\left(-z\right) - \log \left(\left|y\right|\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-x \cdot \log \left(\frac{y}{x}\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x 1679.4032864083838)
  (- (- z) (* (log (fabs y)) x))
  (- (* x (log (/ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1679.4032864083838) {
		tmp = -z - (log(fabs(y)) * x);
	} else {
		tmp = -(x * log((y / x)));
	}
	return tmp;
}

Fortran

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
    real(8) :: tmp
    if (x <= 1679.4032864083838d0) then
        tmp = -z - (log(abs(y)) * x)
    else
        tmp = -(x * log((y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1679.4032864083838) {
		tmp = -z - (Math.log(Math.abs(y)) * x);
	} else {
		tmp = -(x * Math.log((y / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1679.4032864083838:
		tmp = -z - (math.log(math.fabs(y)) * x)
	else:
		tmp = -(x * math.log((y / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1679.4032864083838)
		tmp = Float64(Float64(-z) - Float64(log(abs(y)) * x));
	else
		tmp = Float64(-Float64(x * log(Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1679.4032864083838)
		tmp = -z - (log(abs(y)) * x);
	else
		tmp = -(x * log((y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1679.4032864083838], N[((-z) - N[(N[Log[N[Abs[y], $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], (-N[(x * N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision])]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp = IF (x <= (1679403286408383792149834334850311279296875e-39)) THEN ((- z) - ((ln((abs(y)))) * x)) ELSE (- (x * (ln((y / x))))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 1679.4032864083838

   1. Initial program 77.5%

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

   3. Applied rewrites 77.3%

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(x, -\log \left(\left|y\right|\right), -1 \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 56.1%

      \[\leadsto \mathsf{fma}\left(x, -\log \left(\left|y\right|\right), -1 \cdot z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.1%

       \[\leadsto \left(-z\right) - \log \left(\left|y\right|\right) \cdot x \]

   if 1679.4032864083838 < x

   1. Initial program 77.5%

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

   3. Applied rewrites 77.3%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 40.0%

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

Alternative 6: 60.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 1679.4032864083838:\\ \;\;\;\;\left(-z\right) - \log \left(\left|y\right|\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x 1679.4032864083838)
  (- (- z) (* (log (fabs y)) x))
  (* x (log (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1679.4032864083838) {
		tmp = -z - (log(fabs(y)) * x);
	} else {
		tmp = x * log((x / y));
	}
	return tmp;
}

Fortran

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
    real(8) :: tmp
    if (x <= 1679.4032864083838d0) then
        tmp = -z - (log(abs(y)) * x)
    else
        tmp = x * log((x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1679.4032864083838) {
		tmp = -z - (Math.log(Math.abs(y)) * x);
	} else {
		tmp = x * Math.log((x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1679.4032864083838:
		tmp = -z - (math.log(math.fabs(y)) * x)
	else:
		tmp = x * math.log((x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1679.4032864083838)
		tmp = Float64(Float64(-z) - Float64(log(abs(y)) * x));
	else
		tmp = Float64(x * log(Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1679.4032864083838)
		tmp = -z - (log(abs(y)) * x);
	else
		tmp = x * log((x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1679.4032864083838], N[((-z) - N[(N[Log[N[Abs[y], $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp = IF (x <= (1679403286408383792149834334850311279296875e-39)) THEN ((- z) - ((ln((abs(y)))) * x)) ELSE (x * (ln((x / y)))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 1679.4032864083838

   1. Initial program 77.5%

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

   3. Applied rewrites 77.3%

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(x, -\log \left(\left|y\right|\right), -1 \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 56.1%

      \[\leadsto \mathsf{fma}\left(x, -\log \left(\left|y\right|\right), -1 \cdot z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.1%

       \[\leadsto \left(-z\right) - \log \left(\left|y\right|\right) \cdot x \]

   if 1679.4032864083838 < x

   1. Initial program 77.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 39.6%

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

Alternative 7: 56.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 2.9204912009210902 \cdot 10^{-27}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x 2.9204912009210902e-27) (- z) (* x (log (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.9204912009210902e-27) {
		tmp = -z;
	} else {
		tmp = x * log((x / y));
	}
	return tmp;
}

Fortran

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
    real(8) :: tmp
    if (x <= 2.9204912009210902d-27) then
        tmp = -z
    else
        tmp = x * log((x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.9204912009210902e-27) {
		tmp = -z;
	} else {
		tmp = x * Math.log((x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2.9204912009210902e-27:
		tmp = -z
	else:
		tmp = x * math.log((x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.9204912009210902e-27)
		tmp = Float64(-z);
	else
		tmp = Float64(x * log(Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2.9204912009210902e-27)
		tmp = -z;
	else
		tmp = x * log((x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.9204912009210902e-27], (-z), N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp = IF (x <= (29204912009210902147782043151277405701569921261933593239206745097622202993192797038091157446615397930145263671875e-139)) THEN (- z) ELSE (x * (ln((x / y)))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 2.9204912009210902e-27

   1. Initial program 77.5%

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

   3. Applied rewrites 77.3%

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

   4. Taylor expanded in x around 0

      \[\leadsto -z \]
   5. Step-by-step derivation

   6. Applied rewrites 50.2%

      \[\leadsto -z \]

   if 2.9204912009210902e-27 < x

   1. Initial program 77.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 39.6%

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

Alternative 8: 50.2% accurate, 8.2× speedup

Math

\[-z \]

FPCore

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

C

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

Fortran

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 = -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)

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	- z
END code

Derivation

1. Initial program 77.5%

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

3. Applied rewrites 77.3%

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

4. Taylor expanded in x around 0

   \[\leadsto -z \]
5. Step-by-step derivation

6. Applied rewrites 50.2%

   \[\leadsto -z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Numeric.SpecFunctions.Extra:bd0 from math-functions-0.1.5.2"
  :precision binary64
  (- (* x (log (/ x y))) z))