Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B

Percentage Accurate: 94.3% → 98.8%

Time: 6.6s

Alternatives: 23

Speedup: 1.2×

• 68.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (+
 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
 (/
  (+
   (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
   0.083333333333333)
  x)))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

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 - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $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 =
	((((x - (5e-1)) * (ln(x))) - x) + (918938533204670005005709754186682403087615966796875e-51)) + ((((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) + (8333333333333299564049667651488562114536762237548828125e-56)) / x)
END code

Initial Program: 94.3% accurate, 1.0× speedup

Math

\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (+
 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
 (/
  (+
   (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
   0.083333333333333)
  x)))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

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 - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $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 =
	((((x - (5e-1)) * (ln(x))) - x) + (918938533204670005005709754186682403087615966796875e-51)) + ((((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) + (8333333333333299564049667651488562114536762237548828125e-56)) / x)
END code

Alternative 1: 98.8% accurate, 1.0× speedup

Math

\[\frac{0.083333333333333}{x} + \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), \mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right)\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (+
 (/ 0.083333333333333 x)
 (fma
  (/ z x)
  (fma z (+ 0.0007936500793651 y) -0.0027777777777778)
  (fma (log x) (- x 0.5) (- 0.91893853320467 x)))))

C

double code(double x, double y, double z) {
	return (0.083333333333333 / x) + fma((z / x), fma(z, (0.0007936500793651 + y), -0.0027777777777778), fma(log(x), (x - 0.5), (0.91893853320467 - x)));
}

Julia

function code(x, y, z)
	return Float64(Float64(0.083333333333333 / x) + fma(Float64(z / x), fma(z, Float64(0.0007936500793651 + y), -0.0027777777777778), fma(log(x), Float64(x - 0.5), Float64(0.91893853320467 - x))))
end

Wolfram

code[x_, y_, z_] := N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(N[(z / x), $MachinePrecision] * N[(z * N[(0.0007936500793651 + y), $MachinePrecision] + -0.0027777777777778), $MachinePrecision] + N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $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 =
	((8333333333333299564049667651488562114536762237548828125e-56) / x) + (((z / x) * ((z * ((793650079365100014940070938251892584958113729953765869140625e-63) + y)) + (-2777777777777800001512975569539776188321411609649658203125e-60))) + (((ln(x)) * (x - (5e-1))) + ((918938533204670005005709754186682403087615966796875e-51) - x)))
END code

Derivation

1. Initial program 94.3%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Step-by-step derivation

3. Applied rewrites 98.8%

   \[\leadsto \frac{0.083333333333333}{x} + \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), \mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right)\right) \]
4. Add Preprocessing

Alternative 2: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)\\ \mathbf{if}\;x \leq 54438607786058.664:\\ \;\;\;\;\frac{\mathsf{fma}\left(t\_0, z, 0.083333333333333\right)}{x} + \mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{t\_0}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (fma z (+ 0.0007936500793651 y) -0.0027777777777778)))
  (if (<= x 54438607786058.664)
    (+
     (/ (fma t_0 z 0.083333333333333) x)
     (fma (log x) (- x 0.5) (- 0.91893853320467 x)))
    (fma z (/ t_0 x) (* -1.0 (* x (+ 1.0 (log (/ 1.0 x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(z, (0.0007936500793651 + y), -0.0027777777777778);
	double tmp;
	if (x <= 54438607786058.664) {
		tmp = (fma(t_0, z, 0.083333333333333) / x) + fma(log(x), (x - 0.5), (0.91893853320467 - x));
	} else {
		tmp = fma(z, (t_0 / x), (-1.0 * (x * (1.0 + log((1.0 / x))))));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(z, Float64(0.0007936500793651 + y), -0.0027777777777778)
	tmp = 0.0
	if (x <= 54438607786058.664)
		tmp = Float64(Float64(fma(t_0, z, 0.083333333333333) / x) + fma(log(x), Float64(x - 0.5), Float64(0.91893853320467 - x)));
	else
		tmp = fma(z, Float64(t_0 / x), Float64(-1.0 * Float64(x * Float64(1.0 + log(Float64(1.0 / x))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(0.0007936500793651 + y), $MachinePrecision] + -0.0027777777777778), $MachinePrecision]}, If[LessEqual[x, 54438607786058.664], N[(N[(N[(t$95$0 * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t$95$0 / x), $MachinePrecision] + N[(-1.0 * N[(x * N[(1.0 + N[Log[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $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 t_0 = ((z * ((793650079365100014940070938251892584958113729953765869140625e-63) + y)) + (-2777777777777800001512975569539776188321411609649658203125e-60)) IN
		LET tmp = IF (x <= (544386077860586640625e-7)) THEN ((((t_0 * z) + (8333333333333299564049667651488562114536762237548828125e-56)) / x) + (((ln(x)) * (x - (5e-1))) + ((918938533204670005005709754186682403087615966796875e-51) - x))) ELSE ((z * (t_0 / x)) + ((-1) * (x * ((1) + (ln(((1) / x))))))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 54438607786058.664

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 94.4%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} + \mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right) \]

   if 54438607786058.664 < x

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 97.9%

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, \frac{0.083333333333333}{x} - \mathsf{fma}\left(0.5 - x, \log x, x - 0.91893853320467\right)\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 76.3%

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)\\ \mathbf{if}\;x \leq 163.86616644949444:\\ \;\;\;\;\frac{\mathsf{fma}\left(t\_0, z, 0.083333333333333\right)}{x} + \mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{t\_0}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (fma z (+ 0.0007936500793651 y) -0.0027777777777778)))
  (if (<= x 163.86616644949444)
    (+
     (/ (fma t_0 z 0.083333333333333) x)
     (fma (log x) (- x 0.5) 0.91893853320467))
    (fma z (/ t_0 x) (* -1.0 (* x (+ 1.0 (log (/ 1.0 x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(z, (0.0007936500793651 + y), -0.0027777777777778);
	double tmp;
	if (x <= 163.86616644949444) {
		tmp = (fma(t_0, z, 0.083333333333333) / x) + fma(log(x), (x - 0.5), 0.91893853320467);
	} else {
		tmp = fma(z, (t_0 / x), (-1.0 * (x * (1.0 + log((1.0 / x))))));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(z, Float64(0.0007936500793651 + y), -0.0027777777777778)
	tmp = 0.0
	if (x <= 163.86616644949444)
		tmp = Float64(Float64(fma(t_0, z, 0.083333333333333) / x) + fma(log(x), Float64(x - 0.5), 0.91893853320467));
	else
		tmp = fma(z, Float64(t_0 / x), Float64(-1.0 * Float64(x * Float64(1.0 + log(Float64(1.0 / x))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(0.0007936500793651 + y), $MachinePrecision] + -0.0027777777777778), $MachinePrecision]}, If[LessEqual[x, 163.86616644949444], N[(N[(N[(t$95$0 * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision] + 0.91893853320467), $MachinePrecision]), $MachinePrecision], N[(z * N[(t$95$0 / x), $MachinePrecision] + N[(-1.0 * N[(x * N[(1.0 + N[Log[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $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 t_0 = ((z * ((793650079365100014940070938251892584958113729953765869140625e-63) + y)) + (-2777777777777800001512975569539776188321411609649658203125e-60)) IN
		LET tmp = IF (x <= (163866166449494443213552585802972316741943359375e-45)) THEN ((((t_0 * z) + (8333333333333299564049667651488562114536762237548828125e-56)) / x) + (((ln(x)) * (x - (5e-1))) + (918938533204670005005709754186682403087615966796875e-51))) ELSE ((z * (t_0 / x)) + ((-1) * (x * ((1) + (ln(((1) / x))))))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 163.86616644949444

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 94.4%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} + \mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} + \mathsf{fma}\left(\log x, x - 0.5, \frac{91893853320467}{100000000000000}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 72.8%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} + \mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467\right) \]

   if 163.86616644949444 < x

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 97.9%

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, \frac{0.083333333333333}{x} - \mathsf{fma}\left(0.5 - x, \log x, x - 0.91893853320467\right)\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 76.3%

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 163.86616644949444:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} + \mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), x \cdot \left(\log x - 1\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x 163.86616644949444)
  (+
   (/
    (fma
     (fma z (+ 0.0007936500793651 y) -0.0027777777777778)
     z
     0.083333333333333)
    x)
   (fma (log x) (- x 0.5) 0.91893853320467))
  (fma
   (/ z x)
   (fma (+ 0.0007936500793651 y) z -0.0027777777777778)
   (* x (- (log x) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 163.86616644949444) {
		tmp = (fma(fma(z, (0.0007936500793651 + y), -0.0027777777777778), z, 0.083333333333333) / x) + fma(log(x), (x - 0.5), 0.91893853320467);
	} else {
		tmp = fma((z / x), fma((0.0007936500793651 + y), z, -0.0027777777777778), (x * (log(x) - 1.0)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 163.86616644949444)
		tmp = Float64(Float64(fma(fma(z, Float64(0.0007936500793651 + y), -0.0027777777777778), z, 0.083333333333333) / x) + fma(log(x), Float64(x - 0.5), 0.91893853320467));
	else
		tmp = fma(Float64(z / x), fma(Float64(0.0007936500793651 + y), z, -0.0027777777777778), Float64(x * Float64(log(x) - 1.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 163.86616644949444], N[(N[(N[(N[(z * N[(0.0007936500793651 + y), $MachinePrecision] + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision] + N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision] + 0.91893853320467), $MachinePrecision]), $MachinePrecision], N[(N[(z / x), $MachinePrecision] * N[(N[(0.0007936500793651 + y), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] - 1.0), $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 <= (163866166449494443213552585802972316741943359375e-45)) THEN ((((((z * ((793650079365100014940070938251892584958113729953765869140625e-63) + y)) + (-2777777777777800001512975569539776188321411609649658203125e-60)) * z) + (8333333333333299564049667651488562114536762237548828125e-56)) / x) + (((ln(x)) * (x - (5e-1))) + (918938533204670005005709754186682403087615966796875e-51))) ELSE (((z / x) * ((((793650079365100014940070938251892584958113729953765869140625e-63) + y) * z) + (-2777777777777800001512975569539776188321411609649658203125e-60))) + (x * ((ln(x)) - (1)))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 163.86616644949444

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 94.4%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} + \mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} + \mathsf{fma}\left(\log x, x - 0.5, \frac{91893853320467}{100000000000000}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 72.8%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} + \mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467\right) \]

   if 163.86616644949444 < x

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 97.9%

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, \frac{0.083333333333333}{x} - \mathsf{fma}\left(0.5 - x, \log x, x - 0.91893853320467\right)\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 76.3%

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right) \]

   8. Applied rewrites 76.8%

      \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), -\left(\left(-\log x\right) + 1\right) \cdot x\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), x \cdot \left(\log x - 1\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 76.8%

       \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), x \cdot \left(\log x - 1\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 3.073278703382996:\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), x \cdot \left(\log x - 1\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x 3.073278703382996)
  (+
   (+ 0.91893853320467 (* -0.5 (log x)))
   (/
    (+
     (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
     0.083333333333333)
    x))
  (fma
   (/ z x)
   (fma (+ 0.0007936500793651 y) z -0.0027777777777778)
   (* x (- (log x) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.073278703382996) {
		tmp = (0.91893853320467 + (-0.5 * log(x))) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = fma((z / x), fma((0.0007936500793651 + y), z, -0.0027777777777778), (x * (log(x) - 1.0)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 3.073278703382996)
		tmp = Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x));
	else
		tmp = fma(Float64(z / x), fma(Float64(0.0007936500793651 + y), z, -0.0027777777777778), Float64(x * Float64(log(x) - 1.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 3.073278703382996], N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(z / x), $MachinePrecision] * N[(N[(0.0007936500793651 + y), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] + N[(x * N[(N[Log[x], $MachinePrecision] - 1.0), $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 <= (3073278703382996024373596810619346797466278076171875e-51)) THEN (((918938533204670005005709754186682403087615966796875e-51) + ((-5e-1) * (ln(x)))) + ((((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) + (8333333333333299564049667651488562114536762237548828125e-56)) / x)) ELSE (((z / x) * ((((793650079365100014940070938251892584958113729953765869140625e-63) + y) * z) + (-2777777777777800001512975569539776188321411609649658203125e-60))) + (x * ((ln(x)) - (1)))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 3.073278703382996

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 63.2%

      \[\leadsto \left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   if 3.073278703382996 < x

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 97.9%

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, \frac{0.083333333333333}{x} - \mathsf{fma}\left(0.5 - x, \log x, x - 0.91893853320467\right)\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 76.3%

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right) \]

   8. Applied rewrites 76.8%

      \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), -\left(\left(-\log x\right) + 1\right) \cdot x\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), x \cdot \left(\log x - 1\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 76.8%

       \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), x \cdot \left(\log x - 1\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 97.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right)\\ \mathbf{if}\;x \leq 2.7198285450017545:\\ \;\;\;\;\frac{\mathsf{fma}\left(t\_0, z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{x}, t\_0, x \cdot \left(\log x - 1\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (fma (+ 0.0007936500793651 y) z -0.0027777777777778)))
  (if (<= x 2.7198285450017545)
    (/ (fma t_0 z 0.083333333333333) x)
    (fma (/ z x) t_0 (* x (- (log x) 1.0))))))

C

double code(double x, double y, double z) {
	double t_0 = fma((0.0007936500793651 + y), z, -0.0027777777777778);
	double tmp;
	if (x <= 2.7198285450017545) {
		tmp = fma(t_0, z, 0.083333333333333) / x;
	} else {
		tmp = fma((z / x), t_0, (x * (log(x) - 1.0)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(0.0007936500793651 + y), z, -0.0027777777777778)
	tmp = 0.0
	if (x <= 2.7198285450017545)
		tmp = Float64(fma(t_0, z, 0.083333333333333) / x);
	else
		tmp = fma(Float64(z / x), t_0, Float64(x * Float64(log(x) - 1.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.0007936500793651 + y), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision]}, If[LessEqual[x, 2.7198285450017545], N[(N[(t$95$0 * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision], N[(N[(z / x), $MachinePrecision] * t$95$0 + N[(x * N[(N[Log[x], $MachinePrecision] - 1.0), $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 t_0 = ((((793650079365100014940070938251892584958113729953765869140625e-63) + y) * z) + (-2777777777777800001512975569539776188321411609649658203125e-60)) IN
		LET tmp = IF (x <= (271982854500175452727717129164375364780426025390625e-50)) THEN (((t_0 * z) + (8333333333333299564049667651488562114536762237548828125e-56)) / x) ELSE (((z / x) * t_0) + (x * ((ln(x)) - (1)))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 2.7198285450017545

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   8. Applied rewrites 63.6%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   if 2.7198285450017545 < x

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 97.9%

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, \frac{0.083333333333333}{x} - \mathsf{fma}\left(0.5 - x, \log x, x - 0.91893853320467\right)\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 76.3%

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right) \]

   8. Applied rewrites 76.8%

      \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), -\left(\left(-\log x\right) + 1\right) \cdot x\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), x \cdot \left(\log x - 1\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 76.8%

       \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), x \cdot \left(\log x - 1\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 91.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 175443438.37202394:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651, z, -0.0027777777777778\right), -\left(\left(-\log x\right) + 1\right) \cdot x\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x 175443438.37202394)
  (/
   (fma
    (fma (+ 0.0007936500793651 y) z -0.0027777777777778)
    z
    0.083333333333333)
   x)
  (fma
   (/ z x)
   (fma 0.0007936500793651 z -0.0027777777777778)
   (- (* (+ (- (log x)) 1.0) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 175443438.37202394) {
		tmp = fma(fma((0.0007936500793651 + y), z, -0.0027777777777778), z, 0.083333333333333) / x;
	} else {
		tmp = fma((z / x), fma(0.0007936500793651, z, -0.0027777777777778), -((-log(x) + 1.0) * x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 175443438.37202394)
		tmp = Float64(fma(fma(Float64(0.0007936500793651 + y), z, -0.0027777777777778), z, 0.083333333333333) / x);
	else
		tmp = fma(Float64(z / x), fma(0.0007936500793651, z, -0.0027777777777778), Float64(-Float64(Float64(Float64(-log(x)) + 1.0) * x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 175443438.37202394], N[(N[(N[(N[(0.0007936500793651 + y), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision], N[(N[(z / x), $MachinePrecision] * N[(0.0007936500793651 * z + -0.0027777777777778), $MachinePrecision] + (-N[(N[((-N[Log[x], $MachinePrecision]) + 1.0), $MachinePrecision] * x), $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 <= (17544343837202394008636474609375e-23)) THEN (((((((793650079365100014940070938251892584958113729953765869140625e-63) + y) * z) + (-2777777777777800001512975569539776188321411609649658203125e-60)) * z) + (8333333333333299564049667651488562114536762237548828125e-56)) / x) ELSE (((z / x) * (((793650079365100014940070938251892584958113729953765869140625e-63) * z) + (-2777777777777800001512975569539776188321411609649658203125e-60))) + (- (((- (ln(x))) + (1)) * x))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 175443438.37202394

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   8. Applied rewrites 63.6%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   if 175443438.37202394 < x

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 97.9%

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, \frac{0.083333333333333}{x} - \mathsf{fma}\left(0.5 - x, \log x, x - 0.91893853320467\right)\right) \]

   4. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 76.3%

      \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right)}{x}, -1 \cdot \left(x \cdot \left(1 + \log \left(\frac{1}{x}\right)\right)\right)\right) \]

   8. Applied rewrites 76.8%

      \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), -\left(\left(-\log x\right) + 1\right) \cdot x\right) \]

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(\frac{7936500793651}{10000000000000000}, z, -0.0027777777777778\right), -\left(\left(-\log x\right) + 1\right) \cdot x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 59.3%

       \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \mathsf{fma}\left(0.0007936500793651, z, -0.0027777777777778\right), -\left(\left(-\log x\right) + 1\right) \cdot x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z\\ t_1 := \left(0.0007936500793651 + y\right) \cdot \left(z \cdot \frac{z}{x}\right)\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 1.5 \cdot 10^{+53}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{1}{12.000000000000048 \cdot x}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z))
       (t_1 (* (+ 0.0007936500793651 y) (* z (/ z x)))))
  (if (<= t_0 -2e+16)
    t_1
    (if (<= t_0 1.5e+53)
      (+
       (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
       (/ 1.0 (* 12.000000000000048 x)))
      t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = (0.0007936500793651 + y) * (z * (z / x));
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 1.5e+53) {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (1.0 / (12.000000000000048 * x));
	} else {
		tmp = t_1;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z
    t_1 = (0.0007936500793651d0 + y) * (z * (z / x))
    if (t_0 <= (-2d+16)) then
        tmp = t_1
    else if (t_0 <= 1.5d+53) then
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (1.0d0 / (12.000000000000048d0 * x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = (0.0007936500793651 + y) * (z * (z / x));
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 1.5e+53) {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (1.0 / (12.000000000000048 * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z
	t_1 = (0.0007936500793651 + y) * (z * (z / x))
	tmp = 0
	if t_0 <= -2e+16:
		tmp = t_1
	elif t_0 <= 1.5e+53:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (1.0 / (12.000000000000048 * x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z)
	t_1 = Float64(Float64(0.0007936500793651 + y) * Float64(z * Float64(z / x)))
	tmp = 0.0
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 1.5e+53)
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(1.0 / Float64(12.000000000000048 * x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	t_1 = (0.0007936500793651 + y) * (z * (z / x));
	tmp = 0.0;
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 1.5e+53)
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (1.0 / (12.000000000000048 * x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.0007936500793651 + y), $MachinePrecision] * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+16], t$95$1, If[LessEqual[t$95$0, 1.5e+53], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(1.0 / N[(12.000000000000048 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

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 = ((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) IN
		LET t_1 = (((793650079365100014940070938251892584958113729953765869140625e-63) + y) * (z * (z / x))) IN
			LET tmp_1 = IF (t_0 <= (149999999999999998983142301154244196469256266291609600)) THEN (((((x - (5e-1)) * (ln(x))) - x) + (918938533204670005005709754186682403087615966796875e-51)) + ((1) / ((120000000000000479616346638067625463008880615234375e-49) * x))) ELSE t_1 ENDIF IN
			LET tmp = IF (t_0 <= (-2e16)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < -2e16 or 1.5e53 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 42.0%

      \[\leadsto {z}^{2} \cdot \mathsf{fma}\left(0.0007936500793651, \frac{1}{x}, \frac{y}{x}\right) \]

   6. Applied rewrites 42.0%

      \[\leadsto \frac{0.0007936500793651 + y}{x} \cdot \left(z \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 42.3%

      \[\leadsto \frac{\left(0.0007936500793651 + y\right) \cdot \left(z \cdot z\right)}{x} \]
   9. Step-by-step derivation

   10. Applied rewrites 44.7%

       \[\leadsto \left(0.0007936500793651 + y\right) \cdot \left(z \cdot \frac{z}{x}\right) \]

   if -2e16 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 1.5e53

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 94.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{1}{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)}} \]

   4. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{1}{\frac{1000000000000000}{83333333333333} \cdot x} \]
   5. Step-by-step derivation

   6. Applied rewrites 57.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{1}{12.000000000000048 \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 87.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z\\ t_1 := \left(0.0007936500793651 + y\right) \cdot \left(z \cdot \frac{z}{x}\right)\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 1.5 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right) + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z))
       (t_1 (* (+ 0.0007936500793651 y) (* z (/ z x)))))
  (if (<= t_0 -2e+16)
    t_1
    (if (<= t_0 1.5e+53)
      (+
       (fma (log x) (- x 0.5) (- 0.91893853320467 x))
       (/ 0.083333333333333 x))
      t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = (0.0007936500793651 + y) * (z * (z / x));
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 1.5e+53) {
		tmp = fma(log(x), (x - 0.5), (0.91893853320467 - x)) + (0.083333333333333 / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z)
	t_1 = Float64(Float64(0.0007936500793651 + y) * Float64(z * Float64(z / x)))
	tmp = 0.0
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 1.5e+53)
		tmp = Float64(fma(log(x), Float64(x - 0.5), Float64(0.91893853320467 - x)) + Float64(0.083333333333333 / x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.0007936500793651 + y), $MachinePrecision] * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+16], t$95$1, If[LessEqual[t$95$0, 1.5e+53], N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision] + N[(0.91893853320467 - x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

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 = ((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) IN
		LET t_1 = (((793650079365100014940070938251892584958113729953765869140625e-63) + y) * (z * (z / x))) IN
			LET tmp_1 = IF (t_0 <= (149999999999999998983142301154244196469256266291609600)) THEN ((((ln(x)) * (x - (5e-1))) + ((918938533204670005005709754186682403087615966796875e-51) - x)) + ((8333333333333299564049667651488562114536762237548828125e-56) / x)) ELSE t_1 ENDIF IN
			LET tmp = IF (t_0 <= (-2e16)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < -2e16 or 1.5e53 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 42.0%

      \[\leadsto {z}^{2} \cdot \mathsf{fma}\left(0.0007936500793651, \frac{1}{x}, \frac{y}{x}\right) \]

   6. Applied rewrites 42.0%

      \[\leadsto \frac{0.0007936500793651 + y}{x} \cdot \left(z \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 42.3%

      \[\leadsto \frac{\left(0.0007936500793651 + y\right) \cdot \left(z \cdot z\right)}{x} \]
   9. Step-by-step derivation

   10. Applied rewrites 44.7%

       \[\leadsto \left(0.0007936500793651 + y\right) \cdot \left(z \cdot \frac{z}{x}\right) \]

   if -2e16 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 1.5e53

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\frac{83333333333333}{1000000000000000}}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.3%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 57.4%

      \[\leadsto \mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right) + \frac{0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 87.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z\\ t_1 := \left(0.0007936500793651 + y\right) \cdot \left(z \cdot \frac{z}{x}\right)\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 1.5 \cdot 10^{+53}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log x, x - 0.5, \frac{0.083333333333333}{x}\right) + 0.91893853320467\right) - x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z))
       (t_1 (* (+ 0.0007936500793651 y) (* z (/ z x)))))
  (if (<= t_0 -2e+16)
    t_1
    (if (<= t_0 1.5e+53)
      (-
       (+
        (fma (log x) (- x 0.5) (/ 0.083333333333333 x))
        0.91893853320467)
       x)
      t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = (0.0007936500793651 + y) * (z * (z / x));
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 1.5e+53) {
		tmp = (fma(log(x), (x - 0.5), (0.083333333333333 / x)) + 0.91893853320467) - x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z)
	t_1 = Float64(Float64(0.0007936500793651 + y) * Float64(z * Float64(z / x)))
	tmp = 0.0
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 1.5e+53)
		tmp = Float64(Float64(fma(log(x), Float64(x - 0.5), Float64(0.083333333333333 / x)) + 0.91893853320467) - x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.0007936500793651 + y), $MachinePrecision] * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+16], t$95$1, If[LessEqual[t$95$0, 1.5e+53], N[(N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision] + 0.91893853320467), $MachinePrecision] - x), $MachinePrecision], t$95$1]]]]

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 = ((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) IN
		LET t_1 = (((793650079365100014940070938251892584958113729953765869140625e-63) + y) * (z * (z / x))) IN
			LET tmp_1 = IF (t_0 <= (149999999999999998983142301154244196469256266291609600)) THEN (((((ln(x)) * (x - (5e-1))) + ((8333333333333299564049667651488562114536762237548828125e-56) / x)) + (918938533204670005005709754186682403087615966796875e-51)) - x) ELSE t_1 ENDIF IN
			LET tmp = IF (t_0 <= (-2e16)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < -2e16 or 1.5e53 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 42.0%

      \[\leadsto {z}^{2} \cdot \mathsf{fma}\left(0.0007936500793651, \frac{1}{x}, \frac{y}{x}\right) \]

   6. Applied rewrites 42.0%

      \[\leadsto \frac{0.0007936500793651 + y}{x} \cdot \left(z \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 42.3%

      \[\leadsto \frac{\left(0.0007936500793651 + y\right) \cdot \left(z \cdot z\right)}{x} \]
   9. Step-by-step derivation

   10. Applied rewrites 44.7%

       \[\leadsto \left(0.0007936500793651 + y\right) \cdot \left(z \cdot \frac{z}{x}\right) \]

   if -2e16 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 1.5e53

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0

      \[\leadsto \left(\frac{91893853320467}{100000000000000} + \left(\frac{83333333333333}{1000000000000000} \cdot \frac{1}{x} + \log x \cdot \left(x - \frac{1}{2}\right)\right)\right) - x \]
   3. Step-by-step derivation

   4. Applied rewrites 57.3%

      \[\leadsto \left(0.91893853320467 + \mathsf{fma}\left(0.083333333333333, \frac{1}{x}, \log x \cdot \left(x - 0.5\right)\right)\right) - x \]

   6. Applied rewrites 57.3%

      \[\leadsto \left(\mathsf{fma}\left(\log x, x - 0.5, \frac{0.083333333333333}{x}\right) + 0.91893853320467\right) - x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 84.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 1.4148135358670568 \cdot 10^{+45}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\left(1 - \log x\right) \cdot y}{y} \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x 1.4148135358670568e+45)
  (/
   (fma
    (fma (+ 0.0007936500793651 y) z -0.0027777777777778)
    z
    0.083333333333333)
   x)
  (- (* (/ (* (- 1.0 (log x)) y) y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.4148135358670568e+45) {
		tmp = fma(fma((0.0007936500793651 + y), z, -0.0027777777777778), z, 0.083333333333333) / x;
	} else {
		tmp = -((((1.0 - log(x)) * y) / y) * x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.4148135358670568e+45)
		tmp = Float64(fma(fma(Float64(0.0007936500793651 + y), z, -0.0027777777777778), z, 0.083333333333333) / x);
	else
		tmp = Float64(-Float64(Float64(Float64(Float64(1.0 - log(x)) * y) / y) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.4148135358670568e+45], N[(N[(N[(N[(0.0007936500793651 + y), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision], (-N[(N[(N[(N[(1.0 - N[Log[x], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] / y), $MachinePrecision] * x), $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 <= (1414813535867056792625653556705392199183892480)) THEN (((((((793650079365100014940070938251892584958113729953765869140625e-63) + y) * z) + (-2777777777777800001512975569539776188321411609649658203125e-60)) * z) + (8333333333333299564049667651488562114536762237548828125e-56)) / x) ELSE (- (((((1) - (ln(x))) * y) / y) * x)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 1.4148135358670568e45

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   8. Applied rewrites 63.6%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   if 1.4148135358670568e45 < x

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in y around inf

      \[\leadsto y \cdot \left(\left(\frac{\frac{83333333333333}{1000000000000000}}{x \cdot y} + \left(\frac{91893853320467}{100000000000000} \cdot \frac{1}{y} + \left(\frac{z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot z - \frac{13888888888889}{5000000000000000}\right)}{x \cdot y} + \left(\frac{\log x \cdot \left(x - \frac{1}{2}\right)}{y} + \frac{{z}^{2}}{x}\right)\right)\right)\right) - \frac{x}{y}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 63.1%

      \[\leadsto y \cdot \left(\left(\frac{0.083333333333333}{x \cdot y} + \mathsf{fma}\left(0.91893853320467, \frac{1}{y}, \frac{z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x \cdot y} + \left(\frac{\log x \cdot \left(x - 0.5\right)}{y} + \frac{{z}^{2}}{x}\right)\right)\right) - \frac{x}{y}\right) \]

   5. Taylor expanded in x around -inf

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

   7. Applied rewrites 34.7%

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

   9. Applied rewrites 34.7%

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

   11. Applied rewrites 34.8%

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

Alternative 12: 84.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 1.4148135358670568 \cdot 10^{+45}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(1 - \log x\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x 1.4148135358670568e+45)
  (/
   (fma
    (fma (+ 0.0007936500793651 y) z -0.0027777777777778)
    z
    0.083333333333333)
   x)
  (* -1.0 (* x (- 1.0 (log x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.4148135358670568e+45) {
		tmp = fma(fma((0.0007936500793651 + y), z, -0.0027777777777778), z, 0.083333333333333) / x;
	} else {
		tmp = -1.0 * (x * (1.0 - log(x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.4148135358670568e+45)
		tmp = Float64(fma(fma(Float64(0.0007936500793651 + y), z, -0.0027777777777778), z, 0.083333333333333) / x);
	else
		tmp = Float64(-1.0 * Float64(x * Float64(1.0 - log(x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.4148135358670568e+45], N[(N[(N[(N[(0.0007936500793651 + y), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision], N[(-1.0 * N[(x * N[(1.0 - N[Log[x], $MachinePrecision]), $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 <= (1414813535867056792625653556705392199183892480)) THEN (((((((793650079365100014940070938251892584958113729953765869140625e-63) + y) * z) + (-2777777777777800001512975569539776188321411609649658203125e-60)) * z) + (8333333333333299564049667651488562114536762237548828125e-56)) / x) ELSE ((-1) * (x * ((1) - (ln(x))))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 1.4148135358670568e45

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   8. Applied rewrites 63.6%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0007936500793651 + y, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   if 1.4148135358670568e45 < x

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in y around inf

      \[\leadsto y \cdot \left(\left(\frac{\frac{83333333333333}{1000000000000000}}{x \cdot y} + \left(\frac{91893853320467}{100000000000000} \cdot \frac{1}{y} + \left(\frac{z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot z - \frac{13888888888889}{5000000000000000}\right)}{x \cdot y} + \left(\frac{\log x \cdot \left(x - \frac{1}{2}\right)}{y} + \frac{{z}^{2}}{x}\right)\right)\right)\right) - \frac{x}{y}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 63.1%

      \[\leadsto y \cdot \left(\left(\frac{0.083333333333333}{x \cdot y} + \mathsf{fma}\left(0.91893853320467, \frac{1}{y}, \frac{z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x \cdot y} + \left(\frac{\log x \cdot \left(x - 0.5\right)}{y} + \frac{{z}^{2}}{x}\right)\right)\right) - \frac{x}{y}\right) \]

   5. Taylor expanded in x around -inf

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

   7. Applied rewrites 34.7%

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

   9. Applied rewrites 28.4%

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

   10. Taylor expanded in x around 0

       \[\leadsto -1 \cdot \left(x \cdot \left(1 - \log x\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 34.8%

       \[\leadsto -1 \cdot \left(x \cdot \left(1 - \log x\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 71.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 8.10976389826166 \cdot 10^{-108}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{elif}\;x \leq 1.4148135358670568 \cdot 10^{+45}:\\ \;\;\;\;\left(0.0007936500793651 + y\right) \cdot \left(z \cdot \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(1 - \log x\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x 8.10976389826166e-108)
  (/
   (fma
    (fma 0.0007936500793651 z -0.0027777777777778)
    z
    0.083333333333333)
   x)
  (if (<= x 1.4148135358670568e+45)
    (* (+ 0.0007936500793651 y) (* z (/ z x)))
    (* -1.0 (* x (- 1.0 (log x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 8.10976389826166e-108) {
		tmp = fma(fma(0.0007936500793651, z, -0.0027777777777778), z, 0.083333333333333) / x;
	} else if (x <= 1.4148135358670568e+45) {
		tmp = (0.0007936500793651 + y) * (z * (z / x));
	} else {
		tmp = -1.0 * (x * (1.0 - log(x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 8.10976389826166e-108)
		tmp = Float64(fma(fma(0.0007936500793651, z, -0.0027777777777778), z, 0.083333333333333) / x);
	elseif (x <= 1.4148135358670568e+45)
		tmp = Float64(Float64(0.0007936500793651 + y) * Float64(z * Float64(z / x)));
	else
		tmp = Float64(-1.0 * Float64(x * Float64(1.0 - log(x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 8.10976389826166e-108], N[(N[(N[(0.0007936500793651 * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 1.4148135358670568e+45], N[(N[(0.0007936500793651 + y), $MachinePrecision] * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(x * N[(1.0 - N[Log[x], $MachinePrecision]), $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_1 = IF (x <= (1414813535867056792625653556705392199183892480)) THEN (((793650079365100014940070938251892584958113729953765869140625e-63) + y) * (z * (z / x))) ELSE ((-1) * (x * ((1) - (ln(x))))) ENDIF IN
	LET tmp = IF (x <= (8109763898261660412946910755716538958125293812642230663278428361947358144455511608344208635421273341575704082857342453732978575428784592471495045829813239624306520375042532561379870168004990773597135235046705894650266191884615767028297935073940944297610973500768649646630592542351223528385162353515625e-408)) THEN ((((((793650079365100014940070938251892584958113729953765869140625e-63) * z) + (-2777777777777800001512975569539776188321411609649658203125e-60)) * z) + (8333333333333299564049667651488562114536762237548828125e-56)) / x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if x < 8.1097638982616604e-108

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   7. Taylor expanded in y around 0

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \frac{7936500793651}{10000000000000000} - 0.0027777777777778\right)}{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 47.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot 0.0007936500793651 - 0.0027777777777778\right)}{x} \]

   11. Applied rewrites 47.6%

       \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x} \]

   if 8.1097638982616604e-108 < x < 1.4148135358670568e45

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 42.0%

      \[\leadsto {z}^{2} \cdot \mathsf{fma}\left(0.0007936500793651, \frac{1}{x}, \frac{y}{x}\right) \]

   6. Applied rewrites 42.0%

      \[\leadsto \frac{0.0007936500793651 + y}{x} \cdot \left(z \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 42.3%

      \[\leadsto \frac{\left(0.0007936500793651 + y\right) \cdot \left(z \cdot z\right)}{x} \]
   9. Step-by-step derivation

   10. Applied rewrites 44.7%

       \[\leadsto \left(0.0007936500793651 + y\right) \cdot \left(z \cdot \frac{z}{x}\right) \]

   if 1.4148135358670568e45 < x

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in y around inf

      \[\leadsto y \cdot \left(\left(\frac{\frac{83333333333333}{1000000000000000}}{x \cdot y} + \left(\frac{91893853320467}{100000000000000} \cdot \frac{1}{y} + \left(\frac{z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot z - \frac{13888888888889}{5000000000000000}\right)}{x \cdot y} + \left(\frac{\log x \cdot \left(x - \frac{1}{2}\right)}{y} + \frac{{z}^{2}}{x}\right)\right)\right)\right) - \frac{x}{y}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 63.1%

      \[\leadsto y \cdot \left(\left(\frac{0.083333333333333}{x \cdot y} + \mathsf{fma}\left(0.91893853320467, \frac{1}{y}, \frac{z \cdot \left(0.0007936500793651 \cdot z - 0.0027777777777778\right)}{x \cdot y} + \left(\frac{\log x \cdot \left(x - 0.5\right)}{y} + \frac{{z}^{2}}{x}\right)\right)\right) - \frac{x}{y}\right) \]

   5. Taylor expanded in x around -inf

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

   7. Applied rewrites 34.7%

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

   9. Applied rewrites 28.4%

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

   10. Taylor expanded in x around 0

       \[\leadsto -1 \cdot \left(x \cdot \left(1 - \log x\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 34.8%

       \[\leadsto -1 \cdot \left(x \cdot \left(1 - \log x\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 65.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z\\ t_1 := \left(0.0007936500793651 + y\right) \cdot \left(z \cdot \frac{z}{x}\right)\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{x \cdot \frac{1}{0.083333333333333}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z))
       (t_1 (* (+ 0.0007936500793651 y) (* z (/ z x)))))
  (if (<= t_0 -2e+16)
    t_1
    (if (<= t_0 5e-15) (/ 1.0 (* x (/ 1.0 0.083333333333333))) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = (0.0007936500793651 + y) * (z * (z / x));
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 5e-15) {
		tmp = 1.0 / (x * (1.0 / 0.083333333333333));
	} else {
		tmp = t_1;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z
    t_1 = (0.0007936500793651d0 + y) * (z * (z / x))
    if (t_0 <= (-2d+16)) then
        tmp = t_1
    else if (t_0 <= 5d-15) then
        tmp = 1.0d0 / (x * (1.0d0 / 0.083333333333333d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = (0.0007936500793651 + y) * (z * (z / x));
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 5e-15) {
		tmp = 1.0 / (x * (1.0 / 0.083333333333333));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z
	t_1 = (0.0007936500793651 + y) * (z * (z / x))
	tmp = 0
	if t_0 <= -2e+16:
		tmp = t_1
	elif t_0 <= 5e-15:
		tmp = 1.0 / (x * (1.0 / 0.083333333333333))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z)
	t_1 = Float64(Float64(0.0007936500793651 + y) * Float64(z * Float64(z / x)))
	tmp = 0.0
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 5e-15)
		tmp = Float64(1.0 / Float64(x * Float64(1.0 / 0.083333333333333)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	t_1 = (0.0007936500793651 + y) * (z * (z / x));
	tmp = 0.0;
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 5e-15)
		tmp = 1.0 / (x * (1.0 / 0.083333333333333));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.0007936500793651 + y), $MachinePrecision] * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+16], t$95$1, If[LessEqual[t$95$0, 5e-15], N[(1.0 / N[(x * N[(1.0 / 0.083333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

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 = ((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) IN
		LET t_1 = (((793650079365100014940070938251892584958113729953765869140625e-63) + y) * (z * (z / x))) IN
			LET tmp_1 = IF (t_0 <= (49999999999999999940965467727994934856716453645819608908595910179428756237030029296875e-100)) THEN ((1) / (x * ((1) / (8333333333333299564049667651488562114536762237548828125e-56)))) ELSE t_1 ENDIF IN
			LET tmp = IF (t_0 <= (-2e16)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < -2e16 or 5e-15 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 42.0%

      \[\leadsto {z}^{2} \cdot \mathsf{fma}\left(0.0007936500793651, \frac{1}{x}, \frac{y}{x}\right) \]

   6. Applied rewrites 42.0%

      \[\leadsto \frac{0.0007936500793651 + y}{x} \cdot \left(z \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 42.3%

      \[\leadsto \frac{\left(0.0007936500793651 + y\right) \cdot \left(z \cdot z\right)}{x} \]
   9. Step-by-step derivation

   10. Applied rewrites 44.7%

       \[\leadsto \left(0.0007936500793651 + y\right) \cdot \left(z \cdot \frac{z}{x}\right) \]

   if -2e16 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 5e-15

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.8%

      \[\leadsto \frac{1}{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 23.8%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333}} \]

   11. Applied rewrites 23.9%

       \[\leadsto \frac{1}{x \cdot \frac{1}{0.083333333333333}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 64.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{z \cdot \left(0.0007936500793651 + y\right)}{x} \cdot z\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{x \cdot \frac{1}{0.083333333333333}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(0.0007936500793651 + y\right) \cdot z\right) \cdot z}{x}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)))
  (if (<= t_0 -2e+16)
    (* (/ (* z (+ 0.0007936500793651 y)) x) z)
    (if (<= t_0 5e-15)
      (/ 1.0 (* x (/ 1.0 0.083333333333333)))
      (/ (* (* (+ 0.0007936500793651 y) z) z) x)))))

C

double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = ((z * (0.0007936500793651 + y)) / x) * z;
	} else if (t_0 <= 5e-15) {
		tmp = 1.0 / (x * (1.0 / 0.083333333333333));
	} else {
		tmp = (((0.0007936500793651 + y) * z) * z) / 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) :: t_0
    real(8) :: tmp
    t_0 = (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z
    if (t_0 <= (-2d+16)) then
        tmp = ((z * (0.0007936500793651d0 + y)) / x) * z
    else if (t_0 <= 5d-15) then
        tmp = 1.0d0 / (x * (1.0d0 / 0.083333333333333d0))
    else
        tmp = (((0.0007936500793651d0 + y) * z) * z) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = ((z * (0.0007936500793651 + y)) / x) * z;
	} else if (t_0 <= 5e-15) {
		tmp = 1.0 / (x * (1.0 / 0.083333333333333));
	} else {
		tmp = (((0.0007936500793651 + y) * z) * z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z
	tmp = 0
	if t_0 <= -2e+16:
		tmp = ((z * (0.0007936500793651 + y)) / x) * z
	elif t_0 <= 5e-15:
		tmp = 1.0 / (x * (1.0 / 0.083333333333333))
	else:
		tmp = (((0.0007936500793651 + y) * z) * z) / x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z)
	tmp = 0.0
	if (t_0 <= -2e+16)
		tmp = Float64(Float64(Float64(z * Float64(0.0007936500793651 + y)) / x) * z);
	elseif (t_0 <= 5e-15)
		tmp = Float64(1.0 / Float64(x * Float64(1.0 / 0.083333333333333)));
	else
		tmp = Float64(Float64(Float64(Float64(0.0007936500793651 + y) * z) * z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	tmp = 0.0;
	if (t_0 <= -2e+16)
		tmp = ((z * (0.0007936500793651 + y)) / x) * z;
	elseif (t_0 <= 5e-15)
		tmp = 1.0 / (x * (1.0 / 0.083333333333333));
	else
		tmp = (((0.0007936500793651 + y) * z) * z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+16], N[(N[(N[(z * N[(0.0007936500793651 + y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$0, 5e-15], N[(1.0 / N[(x * N[(1.0 / 0.083333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0007936500793651 + y), $MachinePrecision] * z), $MachinePrecision] * z), $MachinePrecision] / x), $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 = ((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) IN
		LET tmp_1 = IF (t_0 <= (49999999999999999940965467727994934856716453645819608908595910179428756237030029296875e-100)) THEN ((1) / (x * ((1) / (8333333333333299564049667651488562114536762237548828125e-56)))) ELSE (((((793650079365100014940070938251892584958113729953765869140625e-63) + y) * z) * z) / x) ENDIF IN
		LET tmp = IF (t_0 <= (-2e16)) THEN (((z * ((793650079365100014940070938251892584958113729953765869140625e-63) + y)) / x) * z) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < -2e16

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 42.0%

      \[\leadsto {z}^{2} \cdot \mathsf{fma}\left(0.0007936500793651, \frac{1}{x}, \frac{y}{x}\right) \]

   6. Applied rewrites 42.0%

      \[\leadsto \frac{0.0007936500793651 + y}{x} \cdot \left(z \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 43.8%

      \[\leadsto \left(\frac{0.0007936500793651 + y}{x} \cdot z\right) \cdot z \]

   9. Taylor expanded in x around 0

      \[\leadsto \frac{z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right)}{x} \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 44.0%

       \[\leadsto \frac{z \cdot \left(0.0007936500793651 + y\right)}{x} \cdot z \]

   if -2e16 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 5e-15

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.8%

      \[\leadsto \frac{1}{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 23.8%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333}} \]

   11. Applied rewrites 23.9%

       \[\leadsto \frac{1}{x \cdot \frac{1}{0.083333333333333}} \]

   if 5e-15 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 42.0%

      \[\leadsto {z}^{2} \cdot \mathsf{fma}\left(0.0007936500793651, \frac{1}{x}, \frac{y}{x}\right) \]

   6. Applied rewrites 42.0%

      \[\leadsto \frac{0.0007936500793651 + y}{x} \cdot \left(z \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 42.3%

      \[\leadsto \frac{\left(0.0007936500793651 + y\right) \cdot \left(z \cdot z\right)}{x} \]
   9. Step-by-step derivation

   10. Applied rewrites 42.3%

       \[\leadsto \frac{\left(\left(0.0007936500793651 + y\right) \cdot z\right) \cdot z}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 62.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z\\ t_1 := \frac{z \cdot \left(0.0007936500793651 + y\right)}{x} \cdot z\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{x \cdot \frac{1}{0.083333333333333}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z))
       (t_1 (* (/ (* z (+ 0.0007936500793651 y)) x) z)))
  (if (<= t_0 -2e+16)
    t_1
    (if (<= t_0 5e-15) (/ 1.0 (* x (/ 1.0 0.083333333333333))) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = ((z * (0.0007936500793651 + y)) / x) * z;
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 5e-15) {
		tmp = 1.0 / (x * (1.0 / 0.083333333333333));
	} else {
		tmp = t_1;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z
    t_1 = ((z * (0.0007936500793651d0 + y)) / x) * z
    if (t_0 <= (-2d+16)) then
        tmp = t_1
    else if (t_0 <= 5d-15) then
        tmp = 1.0d0 / (x * (1.0d0 / 0.083333333333333d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = ((z * (0.0007936500793651 + y)) / x) * z;
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 5e-15) {
		tmp = 1.0 / (x * (1.0 / 0.083333333333333));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z
	t_1 = ((z * (0.0007936500793651 + y)) / x) * z
	tmp = 0
	if t_0 <= -2e+16:
		tmp = t_1
	elif t_0 <= 5e-15:
		tmp = 1.0 / (x * (1.0 / 0.083333333333333))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z)
	t_1 = Float64(Float64(Float64(z * Float64(0.0007936500793651 + y)) / x) * z)
	tmp = 0.0
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 5e-15)
		tmp = Float64(1.0 / Float64(x * Float64(1.0 / 0.083333333333333)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	t_1 = ((z * (0.0007936500793651 + y)) / x) * z;
	tmp = 0.0;
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 5e-15)
		tmp = 1.0 / (x * (1.0 / 0.083333333333333));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(z * N[(0.0007936500793651 + y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+16], t$95$1, If[LessEqual[t$95$0, 5e-15], N[(1.0 / N[(x * N[(1.0 / 0.083333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

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 = ((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) IN
		LET t_1 = (((z * ((793650079365100014940070938251892584958113729953765869140625e-63) + y)) / x) * z) IN
			LET tmp_1 = IF (t_0 <= (49999999999999999940965467727994934856716453645819608908595910179428756237030029296875e-100)) THEN ((1) / (x * ((1) / (8333333333333299564049667651488562114536762237548828125e-56)))) ELSE t_1 ENDIF IN
			LET tmp = IF (t_0 <= (-2e16)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < -2e16 or 5e-15 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 42.0%

      \[\leadsto {z}^{2} \cdot \mathsf{fma}\left(0.0007936500793651, \frac{1}{x}, \frac{y}{x}\right) \]

   6. Applied rewrites 42.0%

      \[\leadsto \frac{0.0007936500793651 + y}{x} \cdot \left(z \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 43.8%

      \[\leadsto \left(\frac{0.0007936500793651 + y}{x} \cdot z\right) \cdot z \]

   9. Taylor expanded in x around 0

      \[\leadsto \frac{z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right)}{x} \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 44.0%

       \[\leadsto \frac{z \cdot \left(0.0007936500793651 + y\right)}{x} \cdot z \]

   if -2e16 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 5e-15

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.8%

      \[\leadsto \frac{1}{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 23.8%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333}} \]

   11. Applied rewrites 23.9%

       \[\leadsto \frac{1}{x \cdot \frac{1}{0.083333333333333}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 56.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z\\ t_1 := \frac{y \cdot z}{x} \cdot z\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 4000:\\ \;\;\;\;\frac{1}{x \cdot \frac{1}{0.083333333333333}}\\ \mathbf{elif}\;t\_0 \leq 10^{+213}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{0}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z))
       (t_1 (* (/ (* y z) x) z)))
  (if (<= t_0 -2e+16)
    t_1
    (if (<= t_0 4000.0)
      (/ 1.0 (* x (/ 1.0 0.083333333333333)))
      (if (<= t_0 1e+213) t_1 (/ 0.083333333333333 0.0))))))

C

double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = ((y * z) / x) * z;
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 4000.0) {
		tmp = 1.0 / (x * (1.0 / 0.083333333333333));
	} else if (t_0 <= 1e+213) {
		tmp = t_1;
	} else {
		tmp = 0.083333333333333 / 0.0;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z
    t_1 = ((y * z) / x) * z
    if (t_0 <= (-2d+16)) then
        tmp = t_1
    else if (t_0 <= 4000.0d0) then
        tmp = 1.0d0 / (x * (1.0d0 / 0.083333333333333d0))
    else if (t_0 <= 1d+213) then
        tmp = t_1
    else
        tmp = 0.083333333333333d0 / 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = ((y * z) / x) * z;
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 4000.0) {
		tmp = 1.0 / (x * (1.0 / 0.083333333333333));
	} else if (t_0 <= 1e+213) {
		tmp = t_1;
	} else {
		tmp = 0.083333333333333 / 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z
	t_1 = ((y * z) / x) * z
	tmp = 0
	if t_0 <= -2e+16:
		tmp = t_1
	elif t_0 <= 4000.0:
		tmp = 1.0 / (x * (1.0 / 0.083333333333333))
	elif t_0 <= 1e+213:
		tmp = t_1
	else:
		tmp = 0.083333333333333 / 0.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z)
	t_1 = Float64(Float64(Float64(y * z) / x) * z)
	tmp = 0.0
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 4000.0)
		tmp = Float64(1.0 / Float64(x * Float64(1.0 / 0.083333333333333)));
	elseif (t_0 <= 1e+213)
		tmp = t_1;
	else
		tmp = Float64(0.083333333333333 / 0.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	t_1 = ((y * z) / x) * z;
	tmp = 0.0;
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 4000.0)
		tmp = 1.0 / (x * (1.0 / 0.083333333333333));
	elseif (t_0 <= 1e+213)
		tmp = t_1;
	else
		tmp = 0.083333333333333 / 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+16], t$95$1, If[LessEqual[t$95$0, 4000.0], N[(1.0 / N[(x * N[(1.0 / 0.083333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+213], t$95$1, N[(0.083333333333333 / 0.0), $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 = ((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) IN
		LET t_1 = (((y * z) / x) * z) IN
			LET tmp_2 = IF (t_0 <= (999999999999999984345037526797422397233524775199337052919583787413130412889023223627065756931830180808571031008919677160084252852199641809946030023447952696435527124027376600704816231425231719002378564135125254144)) THEN t_1 ELSE ((8333333333333299564049667651488562114536762237548828125e-56) / (0)) ENDIF IN
			LET tmp_1 = IF (t_0 <= (4000)) THEN ((1) / (x * ((1) / (8333333333333299564049667651488562114536762237548828125e-56)))) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_0 <= (-2e16)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < -2e16 or 4e3 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 9.9999999999999998e212

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 42.0%

      \[\leadsto {z}^{2} \cdot \mathsf{fma}\left(0.0007936500793651, \frac{1}{x}, \frac{y}{x}\right) \]

   6. Applied rewrites 42.0%

      \[\leadsto \frac{0.0007936500793651 + y}{x} \cdot \left(z \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 43.8%

      \[\leadsto \left(\frac{0.0007936500793651 + y}{x} \cdot z\right) \cdot z \]

   9. Taylor expanded in y around inf

      \[\leadsto \frac{y \cdot z}{x} \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 29.1%

       \[\leadsto \frac{y \cdot z}{x} \cdot z \]

   if -2e16 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 4e3

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.8%

      \[\leadsto \frac{1}{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 23.8%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333}} \]

   11. Applied rewrites 23.9%

       \[\leadsto \frac{1}{x \cdot \frac{1}{0.083333333333333}} \]

   if 9.9999999999999998e212 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   7. Taylor expanded in undef-var around zero

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]
   8. Step-by-step derivation

   9. Applied rewrites 35.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]

   10. Taylor expanded in z around 0

       \[\leadsto \frac{\frac{83333333333333}{1000000000000000}}{0} \]
   11. Step-by-step derivation

   12. Applied rewrites 26.3%

       \[\leadsto \frac{0.083333333333333}{0} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 56.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z\\ t_1 := \frac{y \cdot z}{x} \cdot z\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 4000:\\ \;\;\;\;\frac{1}{\frac{x}{0.083333333333333}}\\ \mathbf{elif}\;t\_0 \leq 10^{+213}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{0}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z))
       (t_1 (* (/ (* y z) x) z)))
  (if (<= t_0 -2e+16)
    t_1
    (if (<= t_0 4000.0)
      (/ 1.0 (/ x 0.083333333333333))
      (if (<= t_0 1e+213) t_1 (/ 0.083333333333333 0.0))))))

C

double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = ((y * z) / x) * z;
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 4000.0) {
		tmp = 1.0 / (x / 0.083333333333333);
	} else if (t_0 <= 1e+213) {
		tmp = t_1;
	} else {
		tmp = 0.083333333333333 / 0.0;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z
    t_1 = ((y * z) / x) * z
    if (t_0 <= (-2d+16)) then
        tmp = t_1
    else if (t_0 <= 4000.0d0) then
        tmp = 1.0d0 / (x / 0.083333333333333d0)
    else if (t_0 <= 1d+213) then
        tmp = t_1
    else
        tmp = 0.083333333333333d0 / 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double t_1 = ((y * z) / x) * z;
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 4000.0) {
		tmp = 1.0 / (x / 0.083333333333333);
	} else if (t_0 <= 1e+213) {
		tmp = t_1;
	} else {
		tmp = 0.083333333333333 / 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z
	t_1 = ((y * z) / x) * z
	tmp = 0
	if t_0 <= -2e+16:
		tmp = t_1
	elif t_0 <= 4000.0:
		tmp = 1.0 / (x / 0.083333333333333)
	elif t_0 <= 1e+213:
		tmp = t_1
	else:
		tmp = 0.083333333333333 / 0.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z)
	t_1 = Float64(Float64(Float64(y * z) / x) * z)
	tmp = 0.0
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 4000.0)
		tmp = Float64(1.0 / Float64(x / 0.083333333333333));
	elseif (t_0 <= 1e+213)
		tmp = t_1;
	else
		tmp = Float64(0.083333333333333 / 0.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	t_1 = ((y * z) / x) * z;
	tmp = 0.0;
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 4000.0)
		tmp = 1.0 / (x / 0.083333333333333);
	elseif (t_0 <= 1e+213)
		tmp = t_1;
	else
		tmp = 0.083333333333333 / 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+16], t$95$1, If[LessEqual[t$95$0, 4000.0], N[(1.0 / N[(x / 0.083333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+213], t$95$1, N[(0.083333333333333 / 0.0), $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 = ((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) IN
		LET t_1 = (((y * z) / x) * z) IN
			LET tmp_2 = IF (t_0 <= (999999999999999984345037526797422397233524775199337052919583787413130412889023223627065756931830180808571031008919677160084252852199641809946030023447952696435527124027376600704816231425231719002378564135125254144)) THEN t_1 ELSE ((8333333333333299564049667651488562114536762237548828125e-56) / (0)) ENDIF IN
			LET tmp_1 = IF (t_0 <= (4000)) THEN ((1) / (x / (8333333333333299564049667651488562114536762237548828125e-56))) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_0 <= (-2e16)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < -2e16 or 4e3 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 9.9999999999999998e212

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around inf

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 42.0%

      \[\leadsto {z}^{2} \cdot \mathsf{fma}\left(0.0007936500793651, \frac{1}{x}, \frac{y}{x}\right) \]

   6. Applied rewrites 42.0%

      \[\leadsto \frac{0.0007936500793651 + y}{x} \cdot \left(z \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 43.8%

      \[\leadsto \left(\frac{0.0007936500793651 + y}{x} \cdot z\right) \cdot z \]

   9. Taylor expanded in y around inf

      \[\leadsto \frac{y \cdot z}{x} \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 29.1%

       \[\leadsto \frac{y \cdot z}{x} \cdot z \]

   if -2e16 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 4e3

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.8%

      \[\leadsto \frac{1}{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 23.8%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333}} \]

   if 9.9999999999999998e212 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   7. Taylor expanded in undef-var around zero

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]
   8. Step-by-step derivation

   9. Applied rewrites 35.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]

   10. Taylor expanded in z around 0

       \[\leadsto \frac{\frac{83333333333333}{1000000000000000}}{0} \]
   11. Step-by-step derivation

   12. Applied rewrites 26.3%

       \[\leadsto \frac{0.083333333333333}{0} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+168}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot -0.0027777777777778}{0}\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{1}{\frac{x}{0.083333333333333}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{0}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)))
  (if (<= t_0 -2e+168)
    (/ (+ 0.083333333333333 (* z -0.0027777777777778)) 0.0)
    (if (<= t_0 2e-36)
      (/ 1.0 (/ x 0.083333333333333))
      (/ 0.083333333333333 0.0)))))

C

double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double tmp;
	if (t_0 <= -2e+168) {
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / 0.0;
	} else if (t_0 <= 2e-36) {
		tmp = 1.0 / (x / 0.083333333333333);
	} else {
		tmp = 0.083333333333333 / 0.0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z
    if (t_0 <= (-2d+168)) then
        tmp = (0.083333333333333d0 + (z * (-0.0027777777777778d0))) / 0.0d0
    else if (t_0 <= 2d-36) then
        tmp = 1.0d0 / (x / 0.083333333333333d0)
    else
        tmp = 0.083333333333333d0 / 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	double tmp;
	if (t_0 <= -2e+168) {
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / 0.0;
	} else if (t_0 <= 2e-36) {
		tmp = 1.0 / (x / 0.083333333333333);
	} else {
		tmp = 0.083333333333333 / 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z
	tmp = 0
	if t_0 <= -2e+168:
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / 0.0
	elif t_0 <= 2e-36:
		tmp = 1.0 / (x / 0.083333333333333)
	else:
		tmp = 0.083333333333333 / 0.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z)
	tmp = 0.0
	if (t_0 <= -2e+168)
		tmp = Float64(Float64(0.083333333333333 + Float64(z * -0.0027777777777778)) / 0.0);
	elseif (t_0 <= 2e-36)
		tmp = Float64(1.0 / Float64(x / 0.083333333333333));
	else
		tmp = Float64(0.083333333333333 / 0.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((y + 0.0007936500793651) * z) - 0.0027777777777778) * z;
	tmp = 0.0;
	if (t_0 <= -2e+168)
		tmp = (0.083333333333333 + (z * -0.0027777777777778)) / 0.0;
	elseif (t_0 <= 2e-36)
		tmp = 1.0 / (x / 0.083333333333333);
	else
		tmp = 0.083333333333333 / 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+168], N[(N[(0.083333333333333 + N[(z * -0.0027777777777778), $MachinePrecision]), $MachinePrecision] / 0.0), $MachinePrecision], If[LessEqual[t$95$0, 2e-36], N[(1.0 / N[(x / 0.083333333333333), $MachinePrecision]), $MachinePrecision], N[(0.083333333333333 / 0.0), $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 = ((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) IN
		LET tmp_1 = IF (t_0 <= (199999999999999988207685488455497830081834903144751854848685577351213967183330845199919898109476579239895954742678441107273101806640625e-170)) THEN ((1) / (x / (8333333333333299564049667651488562114536762237548828125e-56))) ELSE ((8333333333333299564049667651488562114536762237548828125e-56) / (0)) ENDIF IN
		LET tmp = IF (t_0 <= (-1999999999999999867720989669485949124743900432860663037223385644615401293399207295251384865191691894341829109199397042951078761626889625586558917010807457234988770000896)) THEN (((8333333333333299564049667651488562114536762237548828125e-56) + (z * (-2777777777777800001512975569539776188321411609649658203125e-60))) / (0)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < -1.9999999999999999e168

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   7. Taylor expanded in undef-var around zero

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]
   8. Step-by-step derivation

   9. Applied rewrites 35.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]

   10. Taylor expanded in z around 0

       \[\leadsto \frac{0.083333333333333 + z \cdot \frac{-13888888888889}{5000000000000000}}{0} \]
   11. Step-by-step derivation

   12. Applied rewrites 19.4%

       \[\leadsto \frac{0.083333333333333 + z \cdot -0.0027777777777778}{0} \]

   if -1.9999999999999999e168 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 1.9999999999999999e-36

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.8%

      \[\leadsto \frac{1}{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 23.8%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333}} \]

   if 1.9999999999999999e-36 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   7. Taylor expanded in undef-var around zero

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]
   8. Step-by-step derivation

   9. Applied rewrites 35.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]

   10. Taylor expanded in z around 0

       \[\leadsto \frac{\frac{83333333333333}{1000000000000000}}{0} \]
   11. Step-by-step derivation

   12. Applied rewrites 26.3%

       \[\leadsto \frac{0.083333333333333}{0} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 46.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-0.0027777777777778, z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{0}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<=
     (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
     2e-36)
  (/ (fma -0.0027777777777778 z 0.083333333333333) x)
  (/ 0.083333333333333 0.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) <= 2e-36) {
		tmp = fma(-0.0027777777777778, z, 0.083333333333333) / x;
	} else {
		tmp = 0.083333333333333 / 0.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) <= 2e-36)
		tmp = Float64(fma(-0.0027777777777778, z, 0.083333333333333) / x);
	else
		tmp = Float64(0.083333333333333 / 0.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision], 2e-36], N[(N[(-0.0027777777777778 * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision], N[(0.083333333333333 / 0.0), $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 (((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) <= (199999999999999988207685488455497830081834903144751854848685577351213967183330845199919898109476579239895954742678441107273101806640625e-170)) THEN ((((-2777777777777800001512975569539776188321411609649658203125e-60) * z) + (8333333333333299564049667651488562114536762237548828125e-56)) / x) ELSE ((8333333333333299564049667651488562114536762237548828125e-56) / (0)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 1.9999999999999999e-36

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{0.083333333333333 + z \cdot \frac{-13888888888889}{5000000000000000}}{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 29.9%

      \[\leadsto \frac{0.083333333333333 + z \cdot -0.0027777777777778}{x} \]

   11. Applied rewrites 29.9%

       \[\leadsto \frac{\mathsf{fma}\left(-0.0027777777777778, z, 0.083333333333333\right)}{x} \]

   if 1.9999999999999999e-36 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   7. Taylor expanded in undef-var around zero

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]
   8. Step-by-step derivation

   9. Applied rewrites 35.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]

   10. Taylor expanded in z around 0

       \[\leadsto \frac{\frac{83333333333333}{1000000000000000}}{0} \]
   11. Step-by-step derivation

   12. Applied rewrites 26.3%

       \[\leadsto \frac{0.083333333333333}{0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 44.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z \leq 2.0770422066643692 \cdot 10^{-35}:\\ \;\;\;\;\frac{1}{\frac{x}{0.083333333333333}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{0}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<=
     (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
     2.0770422066643692e-35)
  (/ 1.0 (/ x 0.083333333333333))
  (/ 0.083333333333333 0.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) <= 2.0770422066643692e-35) {
		tmp = 1.0 / (x / 0.083333333333333);
	} else {
		tmp = 0.083333333333333 / 0.0;
	}
	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 (((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) <= 2.0770422066643692d-35) then
        tmp = 1.0d0 / (x / 0.083333333333333d0)
    else
        tmp = 0.083333333333333d0 / 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) <= 2.0770422066643692e-35) {
		tmp = 1.0 / (x / 0.083333333333333);
	} else {
		tmp = 0.083333333333333 / 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) <= 2.0770422066643692e-35:
		tmp = 1.0 / (x / 0.083333333333333)
	else:
		tmp = 0.083333333333333 / 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) <= 2.0770422066643692e-35)
		tmp = Float64(1.0 / Float64(x / 0.083333333333333));
	else
		tmp = Float64(0.083333333333333 / 0.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) <= 2.0770422066643692e-35)
		tmp = 1.0 / (x / 0.083333333333333);
	else
		tmp = 0.083333333333333 / 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision], 2.0770422066643692e-35], N[(1.0 / N[(x / 0.083333333333333), $MachinePrecision]), $MachinePrecision], N[(0.083333333333333 / 0.0), $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 (((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) <= (207704220666436917585371079448996920778888835289299955399166092320823273170231741241895345555235063983445797930471599102020263671875e-166)) THEN ((1) / (x / (8333333333333299564049667651488562114536762237548828125e-56))) ELSE ((8333333333333299564049667651488562114536762237548828125e-56) / (0)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 2.0770422066643692e-35

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.8%

      \[\leadsto \frac{1}{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{1}{\frac{x}{\frac{83333333333333}{1000000000000000}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 23.8%

      \[\leadsto \frac{1}{\frac{x}{0.083333333333333}} \]

   if 2.0770422066643692e-35 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   7. Taylor expanded in undef-var around zero

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]
   8. Step-by-step derivation

   9. Applied rewrites 35.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]

   10. Taylor expanded in z around 0

       \[\leadsto \frac{\frac{83333333333333}{1000000000000000}}{0} \]
   11. Step-by-step derivation

   12. Applied rewrites 26.3%

       \[\leadsto \frac{0.083333333333333}{0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 44.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z \leq 2.0770422066643692 \cdot 10^{-35}:\\ \;\;\;\;\frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.083333333333333}{0}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<=
     (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
     2.0770422066643692e-35)
  (/ 0.083333333333333 x)
  (/ 0.083333333333333 0.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) <= 2.0770422066643692e-35) {
		tmp = 0.083333333333333 / x;
	} else {
		tmp = 0.083333333333333 / 0.0;
	}
	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 (((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) <= 2.0770422066643692d-35) then
        tmp = 0.083333333333333d0 / x
    else
        tmp = 0.083333333333333d0 / 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) <= 2.0770422066643692e-35) {
		tmp = 0.083333333333333 / x;
	} else {
		tmp = 0.083333333333333 / 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) <= 2.0770422066643692e-35:
		tmp = 0.083333333333333 / x
	else:
		tmp = 0.083333333333333 / 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) <= 2.0770422066643692e-35)
		tmp = Float64(0.083333333333333 / x);
	else
		tmp = Float64(0.083333333333333 / 0.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) <= 2.0770422066643692e-35)
		tmp = 0.083333333333333 / x;
	else
		tmp = 0.083333333333333 / 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision], 2.0770422066643692e-35], N[(0.083333333333333 / x), $MachinePrecision], N[(0.083333333333333 / 0.0), $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 (((((y + (793650079365100014940070938251892584958113729953765869140625e-63)) * z) - (2777777777777800001512975569539776188321411609649658203125e-60)) * z) <= (207704220666436917585371079448996920778888835289299955399166092320823273170231741241895345555235063983445797930471599102020263671875e-166)) THEN ((8333333333333299564049667651488562114536762237548828125e-56) / x) ELSE ((8333333333333299564049667651488562114536762237548828125e-56) / (0)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) < 2.0770422066643692e-35

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000}}{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 23.8%

      \[\leadsto \frac{0.083333333333333}{x} \]

   if 2.0770422066643692e-35 < (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z)

   1. Initial program 94.3%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

   3. Applied rewrites 78.9%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   7. Taylor expanded in undef-var around zero

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]
   8. Step-by-step derivation

   9. Applied rewrites 35.6%

      \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{0} \]

   10. Taylor expanded in z around 0

       \[\leadsto \frac{\frac{83333333333333}{1000000000000000}}{0} \]
   11. Step-by-step derivation

   12. Applied rewrites 26.3%

       \[\leadsto \frac{0.083333333333333}{0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 23.8% accurate, 7.9× speedup

Math

\[\frac{0.083333333333333}{x} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (/ 0.083333333333333 x))

C

double code(double x, double y, double z) {
	return 0.083333333333333 / x;
}

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 = 0.083333333333333d0 / x
end function

Java

public static double code(double x, double y, double z) {
	return 0.083333333333333 / x;
}

Python

def code(x, y, z):
	return 0.083333333333333 / x

Julia

function code(x, y, z)
	return Float64(0.083333333333333 / x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.083333333333333 / x;
end

Wolfram

code[x_, y_, z_] := N[(0.083333333333333 / x), $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 =
	(8333333333333299564049667651488562114536762237548828125e-56) / x
END code

Derivation

1. Initial program 94.3%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Step-by-step derivation

3. Applied rewrites 78.9%

   \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - x\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0007936500793651 + y, -0.0027777777777778\right), z, 0.083333333333333\right)\right)}{x} \]

4. Taylor expanded in x around 0

   \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]
5. Step-by-step derivation

6. Applied rewrites 63.6%

   \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

7. Taylor expanded in z around 0

   \[\leadsto \frac{\frac{83333333333333}{1000000000000000}}{x} \]
8. Step-by-step derivation

9. Applied rewrites 23.8%

   \[\leadsto \frac{0.083333333333333}{x} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)))