Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 4.4s

Alternatives: 6

Speedup: 1.0×

• 33.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

C

double code(double x) {
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (0.954929658551372d0 * x) - (0.12900613773279798d0 * ((x * x) * x))
end function

Java

public static double code(double x) {
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
}

Python

def code(x):
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x))

Julia

function code(x)
	return Float64(Float64(0.954929658551372 * x) - Float64(0.12900613773279798 * Float64(Float64(x * x) * x)))
end

MATLAB

function tmp = code(x)
	tmp = (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
end

Wolfram

code[x_] := N[(N[(0.954929658551372 * x), $MachinePrecision] - N[(0.12900613773279798 * N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

C

double code(double x) {
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (0.954929658551372d0 * x) - (0.12900613773279798d0 * ((x * x) * x))
end function

Java

public static double code(double x) {
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
}

Python

def code(x):
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x))

Julia

function code(x)
	return Float64(Float64(0.954929658551372 * x) - Float64(0.12900613773279798 * Float64(Float64(x * x) * x)))
end

MATLAB

function tmp = code(x)
	tmp = (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
end

Wolfram

code[x_] := N[(N[(0.954929658551372 * x), $MachinePrecision] - N[(0.12900613773279798 * N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \mathsf{fma}\left({x_m}^{1.5}, {x_m}^{1.5} \cdot -0.12900613773279798, x_m \cdot 0.954929658551372\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m)
 :precision binary64
 (*
  x_s
  (fma
   (pow x_m 1.5)
   (* (pow x_m 1.5) -0.12900613773279798)
   (* x_m 0.954929658551372))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	return x_s * fma(pow(x_m, 1.5), (pow(x_m, 1.5) * -0.12900613773279798), (x_m * 0.954929658551372));
}

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	return Float64(x_s * fma((x_m ^ 1.5), Float64((x_m ^ 1.5) * -0.12900613773279798), Float64(x_m * 0.954929658551372)))
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := N[(x$95$s * N[(N[Power[x$95$m, 1.5], $MachinePrecision] * N[(N[Power[x$95$m, 1.5], $MachinePrecision] * -0.12900613773279798), $MachinePrecision] + N[(x$95$m * 0.954929658551372), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
2. Step-by-step derivation

   1. cancel-sign-sub-inv 99.5%

      \[\leadsto \color{blue}{0.954929658551372 \cdot x + \left(-0.12900613773279798\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)} \]

   2. metadata-eval 99.5%

      \[\leadsto 0.954929658551372 \cdot x + \color{blue}{-0.12900613773279798} \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

   3. *-commutative 99.5%

      \[\leadsto 0.954929658551372 \cdot x + \color{blue}{\left(\left(x \cdot x\right) \cdot x\right) \cdot -0.12900613773279798} \]

   4. +-commutative 99.5%

      \[\leadsto \color{blue}{\left(\left(x \cdot x\right) \cdot x\right) \cdot -0.12900613773279798 + 0.954929658551372 \cdot x} \]

   5. add-sqr-sqrt 72.6%

      \[\leadsto \color{blue}{\left(\sqrt{\left(x \cdot x\right) \cdot x} \cdot \sqrt{\left(x \cdot x\right) \cdot x}\right)} \cdot -0.12900613773279798 + 0.954929658551372 \cdot x \]

   6. associate-*l* 72.6%

      \[\leadsto \color{blue}{\sqrt{\left(x \cdot x\right) \cdot x} \cdot \left(\sqrt{\left(x \cdot x\right) \cdot x} \cdot -0.12900613773279798\right)} + 0.954929658551372 \cdot x \]

   7. fma-def 72.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\left(x \cdot x\right) \cdot x}, \sqrt{\left(x \cdot x\right) \cdot x} \cdot -0.12900613773279798, 0.954929658551372 \cdot x\right)} \]

   8. pow3 72.6%

      \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{{x}^{3}}}, \sqrt{\left(x \cdot x\right) \cdot x} \cdot -0.12900613773279798, 0.954929658551372 \cdot x\right) \]

   9. sqrt-pow1 54.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{x}^{\left(\frac{3}{2}\right)}}, \sqrt{\left(x \cdot x\right) \cdot x} \cdot -0.12900613773279798, 0.954929658551372 \cdot x\right) \]

   10. metadata-eval 54.3%

       \[\leadsto \mathsf{fma}\left({x}^{\color{blue}{1.5}}, \sqrt{\left(x \cdot x\right) \cdot x} \cdot -0.12900613773279798, 0.954929658551372 \cdot x\right) \]

   11. pow3 54.3%

       \[\leadsto \mathsf{fma}\left({x}^{1.5}, \sqrt{\color{blue}{{x}^{3}}} \cdot -0.12900613773279798, 0.954929658551372 \cdot x\right) \]

   12. sqrt-pow1 54.6%

       \[\leadsto \mathsf{fma}\left({x}^{1.5}, \color{blue}{{x}^{\left(\frac{3}{2}\right)}} \cdot -0.12900613773279798, 0.954929658551372 \cdot x\right) \]

   13. metadata-eval 54.6%

       \[\leadsto \mathsf{fma}\left({x}^{1.5}, {x}^{\color{blue}{1.5}} \cdot -0.12900613773279798, 0.954929658551372 \cdot x\right) \]

   14. *-commutative 54.6%

       \[\leadsto \mathsf{fma}\left({x}^{1.5}, {x}^{1.5} \cdot -0.12900613773279798, \color{blue}{x \cdot 0.954929658551372}\right) \]

3. Applied egg-rr 54.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left({x}^{1.5}, {x}^{1.5} \cdot -0.12900613773279798, x \cdot 0.954929658551372\right)} \]

4. Final simplification 54.6%

   \[\leadsto \mathsf{fma}\left({x}^{1.5}, {x}^{1.5} \cdot -0.12900613773279798, x \cdot 0.954929658551372\right) \]

Alternative 2: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \mathsf{fma}\left(-0.12900613773279798 \cdot {x_m}^{2}, x_m, x_m \cdot 0.954929658551372\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m)
 :precision binary64
 (*
  x_s
  (fma (* -0.12900613773279798 (pow x_m 2.0)) x_m (* x_m 0.954929658551372))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	return x_s * fma((-0.12900613773279798 * pow(x_m, 2.0)), x_m, (x_m * 0.954929658551372));
}

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	return Float64(x_s * fma(Float64(-0.12900613773279798 * (x_m ^ 2.0)), x_m, Float64(x_m * 0.954929658551372)))
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := N[(x$95$s * N[(N[(-0.12900613773279798 * N[Power[x$95$m, 2.0], $MachinePrecision]), $MachinePrecision] * x$95$m + N[(x$95$m * 0.954929658551372), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
2. Step-by-step derivation

   1. cancel-sign-sub-inv 99.5%

      \[\leadsto \color{blue}{0.954929658551372 \cdot x + \left(-0.12900613773279798\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)} \]

   2. metadata-eval 99.5%

      \[\leadsto 0.954929658551372 \cdot x + \color{blue}{-0.12900613773279798} \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

   3. *-commutative 99.5%

      \[\leadsto 0.954929658551372 \cdot x + \color{blue}{\left(\left(x \cdot x\right) \cdot x\right) \cdot -0.12900613773279798} \]

   4. +-commutative 99.5%

      \[\leadsto \color{blue}{\left(\left(x \cdot x\right) \cdot x\right) \cdot -0.12900613773279798 + 0.954929658551372 \cdot x} \]

   5. *-commutative 99.5%

      \[\leadsto \color{blue}{-0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)} + 0.954929658551372 \cdot x \]

   6. associate-*r* 99.8%

      \[\leadsto \color{blue}{\left(-0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x} + 0.954929658551372 \cdot x \]

   7. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.12900613773279798 \cdot \left(x \cdot x\right), x, 0.954929658551372 \cdot x\right)} \]

   8. pow2 99.8%

      \[\leadsto \mathsf{fma}\left(-0.12900613773279798 \cdot \color{blue}{{x}^{2}}, x, 0.954929658551372 \cdot x\right) \]

   9. *-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(-0.12900613773279798 \cdot {x}^{2}, x, \color{blue}{x \cdot 0.954929658551372}\right) \]

3. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-0.12900613773279798 \cdot {x}^{2}, x, x \cdot 0.954929658551372\right)} \]

4. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(-0.12900613773279798 \cdot {x}^{2}, x, x \cdot 0.954929658551372\right) \]

Alternative 3: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \left(x_m \cdot \left(0.954929658551372 - {x_m}^{2} \cdot 0.12900613773279798\right)\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m)
 :precision binary64
 (* x_s (* x_m (- 0.954929658551372 (* (pow x_m 2.0) 0.12900613773279798)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	return x_s * (x_m * (0.954929658551372 - (pow(x_m, 2.0) * 0.12900613773279798)));
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    code = x_s * (x_m * (0.954929658551372d0 - ((x_m ** 2.0d0) * 0.12900613773279798d0)))
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m) {
	return x_s * (x_m * (0.954929658551372 - (Math.pow(x_m, 2.0) * 0.12900613773279798)));
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m):
	return x_s * (x_m * (0.954929658551372 - (math.pow(x_m, 2.0) * 0.12900613773279798)))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	return Float64(x_s * Float64(x_m * Float64(0.954929658551372 - Float64((x_m ^ 2.0) * 0.12900613773279798))))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m)
	tmp = x_s * (x_m * (0.954929658551372 - ((x_m ^ 2.0) * 0.12900613773279798)));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := N[(x$95$s * N[(x$95$m * N[(0.954929658551372 - N[(N[Power[x$95$m, 2.0], $MachinePrecision] * 0.12900613773279798), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
2. Step-by-step derivation

   1. associate-*r* 99.8%

      \[\leadsto 0.954929658551372 \cdot x - \color{blue}{\left(0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x} \]

   2. distribute-rgt-out-- 99.8%

      \[\leadsto \color{blue}{x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)} \]

   3. pow2 99.8%

      \[\leadsto x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \color{blue}{{x}^{2}}\right) \]

3. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot {x}^{2}\right)} \]

4. Final simplification 99.8%

   \[\leadsto x \cdot \left(0.954929658551372 - {x}^{2} \cdot 0.12900613773279798\right) \]

Alternative 4: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \left(x_m \cdot \mathsf{fma}\left(x_m \cdot -0.12900613773279798, x_m, 0.954929658551372\right)\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m)
 :precision binary64
 (* x_s (* x_m (fma (* x_m -0.12900613773279798) x_m 0.954929658551372))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	return x_s * (x_m * fma((x_m * -0.12900613773279798), x_m, 0.954929658551372));
}

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	return Float64(x_s * Float64(x_m * fma(Float64(x_m * -0.12900613773279798), x_m, 0.954929658551372)))
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := N[(x$95$s * N[(x$95$m * N[(N[(x$95$m * -0.12900613773279798), $MachinePrecision] * x$95$m + 0.954929658551372), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
2. Step-by-step derivation

   1. associate-*r* 99.8%

      \[\leadsto 0.954929658551372 \cdot x - \color{blue}{\left(0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x} \]

   2. distribute-rgt-out-- 99.8%

      \[\leadsto \color{blue}{x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)} \]

   3. pow2 99.8%

      \[\leadsto x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \color{blue}{{x}^{2}}\right) \]

3. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot {x}^{2}\right)} \]
4. Step-by-step derivation

   1. sub-neg 99.8%

      \[\leadsto x \cdot \color{blue}{\left(0.954929658551372 + \left(-0.12900613773279798 \cdot {x}^{2}\right)\right)} \]

   2. +-commutative 99.8%

      \[\leadsto x \cdot \color{blue}{\left(\left(-0.12900613773279798 \cdot {x}^{2}\right) + 0.954929658551372\right)} \]

   3. distribute-lft-neg-in 99.8%

      \[\leadsto x \cdot \left(\color{blue}{\left(-0.12900613773279798\right) \cdot {x}^{2}} + 0.954929658551372\right) \]

   4. metadata-eval 99.8%

      \[\leadsto x \cdot \left(\color{blue}{-0.12900613773279798} \cdot {x}^{2} + 0.954929658551372\right) \]

   5. unpow2 99.8%

      \[\leadsto x \cdot \left(-0.12900613773279798 \cdot \color{blue}{\left(x \cdot x\right)} + 0.954929658551372\right) \]

   6. associate-*r* 99.8%

      \[\leadsto x \cdot \left(\color{blue}{\left(-0.12900613773279798 \cdot x\right) \cdot x} + 0.954929658551372\right) \]

   7. *-commutative 99.8%

      \[\leadsto x \cdot \left(\color{blue}{\left(x \cdot -0.12900613773279798\right)} \cdot x + 0.954929658551372\right) \]

   8. fma-def 99.8%

      \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(x \cdot -0.12900613773279798, x, 0.954929658551372\right)} \]

5. Applied egg-rr 99.8%

   \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(x \cdot -0.12900613773279798, x, 0.954929658551372\right)} \]

6. Final simplification 99.8%

   \[\leadsto x \cdot \mathsf{fma}\left(x \cdot -0.12900613773279798, x, 0.954929658551372\right) \]

Alternative 5: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \left(x_m \cdot 0.954929658551372 - 0.12900613773279798 \cdot \left(x_m \cdot \left(x_m \cdot x_m\right)\right)\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m)
 :precision binary64
 (*
  x_s
  (- (* x_m 0.954929658551372) (* 0.12900613773279798 (* x_m (* x_m x_m))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	return x_s * ((x_m * 0.954929658551372) - (0.12900613773279798 * (x_m * (x_m * x_m))));
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    code = x_s * ((x_m * 0.954929658551372d0) - (0.12900613773279798d0 * (x_m * (x_m * x_m))))
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m) {
	return x_s * ((x_m * 0.954929658551372) - (0.12900613773279798 * (x_m * (x_m * x_m))));
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m):
	return x_s * ((x_m * 0.954929658551372) - (0.12900613773279798 * (x_m * (x_m * x_m))))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	return Float64(x_s * Float64(Float64(x_m * 0.954929658551372) - Float64(0.12900613773279798 * Float64(x_m * Float64(x_m * x_m)))))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m)
	tmp = x_s * ((x_m * 0.954929658551372) - (0.12900613773279798 * (x_m * (x_m * x_m))));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := N[(x$95$s * N[(N[(x$95$m * 0.954929658551372), $MachinePrecision] - N[(0.12900613773279798 * N[(x$95$m * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

2. Final simplification 99.5%

   \[\leadsto x \cdot 0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot \left(x \cdot x\right)\right) \]

Alternative 6: 49.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \left(x_m \cdot 0.954929658551372\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m) :precision binary64 (* x_s (* x_m 0.954929658551372)))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	return x_s * (x_m * 0.954929658551372);
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    code = x_s * (x_m * 0.954929658551372d0)
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m) {
	return x_s * (x_m * 0.954929658551372);
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m):
	return x_s * (x_m * 0.954929658551372)

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m)
	return Float64(x_s * Float64(x_m * 0.954929658551372))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m)
	tmp = x_s * (x_m * 0.954929658551372);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := N[(x$95$s * N[(x$95$m * 0.954929658551372), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

2. Taylor expanded in x around 0 57.0%

   \[\leadsto \color{blue}{0.954929658551372 \cdot x} \]
3. Step-by-step derivation

   1. *-commutative 57.0%

      \[\leadsto \color{blue}{x \cdot 0.954929658551372} \]

4. Simplified 57.0%

   \[\leadsto \color{blue}{x \cdot 0.954929658551372} \]

5. Final simplification 57.0%

   \[\leadsto x \cdot 0.954929658551372 \]

Reproduce

herbie shell --seed 2023315 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))