Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 6.6s

Alternatives: 6

Speedup: 1.4×

• 32.8% 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, 0.2× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m)
 :precision binary64
 (*
  x_s
  (fma
   (* x_m (* (pow x_m 1.5) -0.12900613773279798))
   (sqrt x_m)
   (* 0.954929658551372 x_m))))

C

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

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m)
	return Float64(x_s * fma(Float64(x_m * Float64((x_m ^ 1.5) * -0.12900613773279798)), sqrt(x_m), Float64(0.954929658551372 * 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 * N[(N[Power[x$95$m, 1.5], $MachinePrecision] * -0.12900613773279798), $MachinePrecision]), $MachinePrecision] * N[Sqrt[x$95$m], $MachinePrecision] + N[(0.954929658551372 * x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

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

   1. lift--.f64 N/A

      \[\leadsto \color{blue}{\frac{238732414637843}{250000000000000} \cdot x - \frac{6450306886639899}{50000000000000000} \cdot \left(\left(x \cdot x\right) \cdot x\right)} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{238732414637843}{250000000000000} \cdot x - \color{blue}{\frac{6450306886639899}{50000000000000000} \cdot \left(\left(x \cdot x\right) \cdot x\right)} \]

   3. fp-cancel-sub-sign-inv N/A

      \[\leadsto \color{blue}{\frac{238732414637843}{250000000000000} \cdot x + \left(\mathsf{neg}\left(\frac{6450306886639899}{50000000000000000}\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)} \]

   4. lift-*.f64 N/A

      \[\leadsto \color{blue}{\frac{238732414637843}{250000000000000} \cdot x} + \left(\mathsf{neg}\left(\frac{6450306886639899}{50000000000000000}\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

   5. rem-square-sqrt N/A

      \[\leadsto \frac{238732414637843}{250000000000000} \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} + \left(\mathsf{neg}\left(\frac{6450306886639899}{50000000000000000}\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

   6. sqrt-prod N/A

      \[\leadsto \frac{238732414637843}{250000000000000} \cdot \color{blue}{\sqrt{x \cdot x}} + \left(\mathsf{neg}\left(\frac{6450306886639899}{50000000000000000}\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

   7. sqr-neg-rev N/A

      \[\leadsto \frac{238732414637843}{250000000000000} \cdot \sqrt{\color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(x\right)\right)}} + \left(\mathsf{neg}\left(\frac{6450306886639899}{50000000000000000}\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

   8. pow2 N/A

      \[\leadsto \frac{238732414637843}{250000000000000} \cdot \sqrt{\color{blue}{{\left(\mathsf{neg}\left(x\right)\right)}^{2}}} + \left(\mathsf{neg}\left(\frac{6450306886639899}{50000000000000000}\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

   9. sqrt-pow1 N/A

      \[\leadsto \frac{238732414637843}{250000000000000} \cdot \color{blue}{{\left(\mathsf{neg}\left(x\right)\right)}^{\left(\frac{2}{2}\right)}} + \left(\mathsf{neg}\left(\frac{6450306886639899}{50000000000000000}\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

   10. metadata-eval N/A

       \[\leadsto \frac{238732414637843}{250000000000000} \cdot {\left(\mathsf{neg}\left(x\right)\right)}^{\color{blue}{1}} + \left(\mathsf{neg}\left(\frac{6450306886639899}{50000000000000000}\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

   11. unpow1 N/A

       \[\leadsto \frac{238732414637843}{250000000000000} \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(\frac{6450306886639899}{50000000000000000}\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

   12. distribute-rgt-neg-in N/A

       \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000} \cdot x\right)\right)} + \left(\mathsf{neg}\left(\frac{6450306886639899}{50000000000000000}\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

   13. lift-*.f64 N/A

       \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\frac{238732414637843}{250000000000000} \cdot x}\right)\right) + \left(\mathsf{neg}\left(\frac{6450306886639899}{50000000000000000}\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right) \]

   14. distribute-lft-neg-in N/A

       \[\leadsto \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000} \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{6450306886639899}{50000000000000000} \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)\right)} \]

   15. lift-*.f64 N/A

       \[\leadsto \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000} \cdot x\right)\right) + \left(\mathsf{neg}\left(\color{blue}{\frac{6450306886639899}{50000000000000000} \cdot \left(\left(x \cdot x\right) \cdot x\right)}\right)\right) \]

   16. distribute-neg-in N/A

       \[\leadsto \color{blue}{\mathsf{neg}\left(\left(\frac{238732414637843}{250000000000000} \cdot x + \frac{6450306886639899}{50000000000000000} \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)\right)} \]

   17. lift-*.f64 N/A

       \[\leadsto \mathsf{neg}\left(\left(\color{blue}{\frac{238732414637843}{250000000000000} \cdot x} + \frac{6450306886639899}{50000000000000000} \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)\right) \]

   18. lift-*.f64 N/A

       \[\leadsto \mathsf{neg}\left(\left(\frac{238732414637843}{250000000000000} \cdot x + \color{blue}{\frac{6450306886639899}{50000000000000000} \cdot \left(\left(x \cdot x\right) \cdot x\right)}\right)\right) \]

   19. lift-*.f64 N/A

       \[\leadsto \mathsf{neg}\left(\left(\frac{238732414637843}{250000000000000} \cdot x + \frac{6450306886639899}{50000000000000000} \cdot \color{blue}{\left(\left(x \cdot x\right) \cdot x\right)}\right)\right) \]

   20. associate-*r* N/A

       \[\leadsto \mathsf{neg}\left(\left(\frac{238732414637843}{250000000000000} \cdot x + \color{blue}{\left(\frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right) \cdot x}\right)\right) \]

   21. distribute-rgt-out N/A

       \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \left(\frac{238732414637843}{250000000000000} + \frac{6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right)}\right) \]

4. Applied rewrites 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 0.954929658551372, -0.12900613773279798 \cdot {x}^{3}\right)} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, \color{blue}{\frac{-6450306886639899}{50000000000000000} \cdot {x}^{3}}\right) \]

   2. lift-pow.f64 N/A

      \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, \frac{-6450306886639899}{50000000000000000} \cdot \color{blue}{{x}^{3}}\right) \]

   3. pow3 N/A

      \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, \frac{-6450306886639899}{50000000000000000} \cdot \color{blue}{\left(\left(x \cdot x\right) \cdot x\right)}\right) \]

   4. lift-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, \frac{-6450306886639899}{50000000000000000} \cdot \left(\color{blue}{\left(x \cdot x\right)} \cdot x\right)\right) \]

   5. associate-*r* N/A

      \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, \color{blue}{\left(\frac{-6450306886639899}{50000000000000000} \cdot \left(x \cdot x\right)\right) \cdot x}\right) \]

   6. lift-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, \left(\frac{-6450306886639899}{50000000000000000} \cdot \color{blue}{\left(x \cdot x\right)}\right) \cdot x\right) \]

   7. associate-*l* N/A

      \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, \color{blue}{\left(\left(\frac{-6450306886639899}{50000000000000000} \cdot x\right) \cdot x\right)} \cdot x\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, \left(\color{blue}{\left(\frac{-6450306886639899}{50000000000000000} \cdot x\right)} \cdot x\right) \cdot x\right) \]

   9. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, \color{blue}{\left(x \cdot \left(\frac{-6450306886639899}{50000000000000000} \cdot x\right)\right)} \cdot x\right) \]

   10. associate-*r* N/A

       \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, \color{blue}{x \cdot \left(\left(\frac{-6450306886639899}{50000000000000000} \cdot x\right) \cdot x\right)}\right) \]

   11. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, x \cdot \color{blue}{\left(x \cdot \left(\frac{-6450306886639899}{50000000000000000} \cdot x\right)\right)}\right) \]

   12. associate-*r* N/A

       \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, \color{blue}{\left(x \cdot x\right) \cdot \left(\frac{-6450306886639899}{50000000000000000} \cdot x\right)}\right) \]

   13. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(x, \frac{238732414637843}{250000000000000}, \color{blue}{\left(x \cdot x\right)} \cdot \left(\frac{-6450306886639899}{50000000000000000} \cdot x\right)\right) \]

   14. lower-*.f64 99.8

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

6. Applied rewrites 99.8%

   \[\leadsto \mathsf{fma}\left(x, 0.954929658551372, \color{blue}{\left(x \cdot x\right) \cdot \left(-0.12900613773279798 \cdot x\right)}\right) \]
7. Step-by-step derivation

   1. lift-fma.f64 N/A

      \[\leadsto \color{blue}{x \cdot \frac{238732414637843}{250000000000000} + \left(x \cdot x\right) \cdot \left(\frac{-6450306886639899}{50000000000000000} \cdot x\right)} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot \left(\frac{-6450306886639899}{50000000000000000} \cdot x\right) + x \cdot \frac{238732414637843}{250000000000000}} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot \left(\frac{-6450306886639899}{50000000000000000} \cdot x\right)} + x \cdot \frac{238732414637843}{250000000000000} \]

   4. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot x\right)} \cdot \left(\frac{-6450306886639899}{50000000000000000} \cdot x\right) + x \cdot \frac{238732414637843}{250000000000000} \]

   5. associate-*l* N/A

      \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(\frac{-6450306886639899}{50000000000000000} \cdot x\right)\right)} + x \cdot \frac{238732414637843}{250000000000000} \]

   6. lift-*.f64 N/A

      \[\leadsto x \cdot \left(x \cdot \color{blue}{\left(\frac{-6450306886639899}{50000000000000000} \cdot x\right)}\right) + x \cdot \frac{238732414637843}{250000000000000} \]

   7. associate-*r* N/A

      \[\leadsto x \cdot \color{blue}{\left(\left(x \cdot \frac{-6450306886639899}{50000000000000000}\right) \cdot x\right)} + x \cdot \frac{238732414637843}{250000000000000} \]

   8. *-commutative N/A

      \[\leadsto x \cdot \left(\color{blue}{\left(\frac{-6450306886639899}{50000000000000000} \cdot x\right)} \cdot x\right) + x \cdot \frac{238732414637843}{250000000000000} \]

   9. rem-square-sqrt N/A

      \[\leadsto x \cdot \left(\left(\frac{-6450306886639899}{50000000000000000} \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}\right) \cdot x\right) + x \cdot \frac{238732414637843}{250000000000000} \]

   10. lift-sqrt.f64 N/A

       \[\leadsto x \cdot \left(\left(\frac{-6450306886639899}{50000000000000000} \cdot \left(\color{blue}{\sqrt{x}} \cdot \sqrt{x}\right)\right) \cdot x\right) + x \cdot \frac{238732414637843}{250000000000000} \]

   11. lift-sqrt.f64 N/A

       \[\leadsto x \cdot \left(\left(\frac{-6450306886639899}{50000000000000000} \cdot \left(\sqrt{x} \cdot \color{blue}{\sqrt{x}}\right)\right) \cdot x\right) + x \cdot \frac{238732414637843}{250000000000000} \]

   12. associate-*l* N/A

       \[\leadsto x \cdot \left(\color{blue}{\left(\left(\frac{-6450306886639899}{50000000000000000} \cdot \sqrt{x}\right) \cdot \sqrt{x}\right)} \cdot x\right) + x \cdot \frac{238732414637843}{250000000000000} \]

   13. lift-*.f64 N/A

       \[\leadsto x \cdot \left(\left(\color{blue}{\left(\frac{-6450306886639899}{50000000000000000} \cdot \sqrt{x}\right)} \cdot \sqrt{x}\right) \cdot x\right) + x \cdot \frac{238732414637843}{250000000000000} \]

   14. lift-*.f64 N/A

       \[\leadsto x \cdot \left(\color{blue}{\left(\left(\frac{-6450306886639899}{50000000000000000} \cdot \sqrt{x}\right) \cdot \sqrt{x}\right)} \cdot x\right) + x \cdot \frac{238732414637843}{250000000000000} \]

8. Applied rewrites 49.1%

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

Alternative 2: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;0.954929658551372 \cdot x\_m - 0.12900613773279798 \cdot \left(\left(x\_m \cdot x\_m\right) \cdot x\_m\right) \leq -5 \cdot 10^{+21}:\\ \;\;\;\;\left(\left(-0.12900613773279798 \cdot x\_m\right) \cdot x\_m\right) \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;0.954929658551372 \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m)
 :precision binary64
 (*
  x_s
  (if (<=
       (-
        (* 0.954929658551372 x_m)
        (* 0.12900613773279798 (* (* x_m x_m) x_m)))
       -5e+21)
    (* (* (* -0.12900613773279798 x_m) x_m) x_m)
    (* 0.954929658551372 x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double tmp;
	if (((0.954929658551372 * x_m) - (0.12900613773279798 * ((x_m * x_m) * x_m))) <= -5e+21) {
		tmp = ((-0.12900613773279798 * x_m) * x_m) * x_m;
	} else {
		tmp = 0.954929658551372 * x_m;
	}
	return x_s * tmp;
}

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
    real(8) :: tmp
    if (((0.954929658551372d0 * x_m) - (0.12900613773279798d0 * ((x_m * x_m) * x_m))) <= (-5d+21)) then
        tmp = (((-0.12900613773279798d0) * x_m) * x_m) * x_m
    else
        tmp = 0.954929658551372d0 * x_m
    end if
    code = x_s * tmp
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) {
	double tmp;
	if (((0.954929658551372 * x_m) - (0.12900613773279798 * ((x_m * x_m) * x_m))) <= -5e+21) {
		tmp = ((-0.12900613773279798 * x_m) * x_m) * x_m;
	} else {
		tmp = 0.954929658551372 * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m):
	tmp = 0
	if ((0.954929658551372 * x_m) - (0.12900613773279798 * ((x_m * x_m) * x_m))) <= -5e+21:
		tmp = ((-0.12900613773279798 * x_m) * x_m) * x_m
	else:
		tmp = 0.954929658551372 * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m)
	tmp = 0.0
	if (Float64(Float64(0.954929658551372 * x_m) - Float64(0.12900613773279798 * Float64(Float64(x_m * x_m) * x_m))) <= -5e+21)
		tmp = Float64(Float64(Float64(-0.12900613773279798 * x_m) * x_m) * x_m);
	else
		tmp = Float64(0.954929658551372 * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m)
	tmp = 0.0;
	if (((0.954929658551372 * x_m) - (0.12900613773279798 * ((x_m * x_m) * x_m))) <= -5e+21)
		tmp = ((-0.12900613773279798 * x_m) * x_m) * x_m;
	else
		tmp = 0.954929658551372 * x_m;
	end
	tmp_2 = x_s * tmp;
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 * If[LessEqual[N[(N[(0.954929658551372 * x$95$m), $MachinePrecision] - N[(0.12900613773279798 * N[(N[(x$95$m * x$95$m), $MachinePrecision] * x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e+21], N[(N[(N[(-0.12900613773279798 * x$95$m), $MachinePrecision] * x$95$m), $MachinePrecision] * x$95$m), $MachinePrecision], N[(0.954929658551372 * x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 #s(literal 238732414637843/250000000000000 binary64) x) (*.f64 #s(literal 6450306886639899/50000000000000000 binary64) (*.f64 (*.f64 x x) x))) < -5e21

   1. Initial program 98.5%

      \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(\frac{238732414637843}{250000000000000} + \frac{-6450306886639899}{50000000000000000} \cdot {x}^{2}\right)} \]

   5. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.12900613773279798 \cdot x, x, 0.954929658551372\right) \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.6%

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

   8. Taylor expanded in x around -inf

      \[\leadsto \left(\frac{6450306886639899}{50000000000000000} \cdot \left({x}^{2} \cdot {\left(\sqrt{-1}\right)}^{2}\right)\right) \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 99.6%

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

   if -5e21 < (-.f64 (*.f64 #s(literal 238732414637843/250000000000000 binary64) x) (*.f64 #s(literal 6450306886639899/50000000000000000 binary64) (*.f64 (*.f64 x x) x)))

   1. Initial program 99.8%

      \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{238732414637843}{250000000000000} \cdot x} \]
   4. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \frac{238732414637843}{250000000000000} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

      2. distribute-rgt-neg-out N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{238732414637843}{250000000000000} \cdot \left(\mathsf{neg}\left(x\right)\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{238732414637843}{250000000000000}}\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(x \cdot \frac{238732414637843}{250000000000000}\right)\right)}\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot x}\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \left(\mathsf{neg}\left(x\right)\right)} \]

      8. metadata-eval N/A

         \[\leadsto \color{blue}{\frac{-238732414637843}{250000000000000}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \color{blue}{\left(\frac{-238732414637843}{250000000000000} \cdot 1\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)} \cdot 1\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      11. lft-mult-inverse N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \color{blue}{\left(\frac{1}{{x}^{2}} \cdot {x}^{2}\right)}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      12. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right) \cdot {x}^{2}\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)\right)} \cdot {x}^{2}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      15. associate-*l/ N/A

          \[\leadsto \color{blue}{\frac{1 \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)}{{x}^{2}}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}}}{{x}^{2}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      17. *-lft-identity N/A

          \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)}}{{x}^{2}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      18. associate-*l/ N/A

          \[\leadsto \color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(\frac{1}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)\right) \cdot {x}^{2}\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      20. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right)} \cdot {x}^{2}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      21. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right) \cdot {x}^{2}\right) \cdot x\right)} \]

   5. Applied rewrites 63.3%

      \[\leadsto \color{blue}{0.954929658551372 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \leq -5 \cdot 10^{+21}:\\ \;\;\;\;\left(\left(-0.12900613773279798 \cdot x\right) \cdot x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.954929658551372 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;0.954929658551372 \cdot x\_m - 0.12900613773279798 \cdot \left(\left(x\_m \cdot x\_m\right) \cdot x\_m\right) \leq -5 \cdot 10^{+21}:\\ \;\;\;\;\left(\left(x\_m \cdot x\_m\right) \cdot -0.12900613773279798\right) \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;0.954929658551372 \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m)
 :precision binary64
 (*
  x_s
  (if (<=
       (-
        (* 0.954929658551372 x_m)
        (* 0.12900613773279798 (* (* x_m x_m) x_m)))
       -5e+21)
    (* (* (* x_m x_m) -0.12900613773279798) x_m)
    (* 0.954929658551372 x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double tmp;
	if (((0.954929658551372 * x_m) - (0.12900613773279798 * ((x_m * x_m) * x_m))) <= -5e+21) {
		tmp = ((x_m * x_m) * -0.12900613773279798) * x_m;
	} else {
		tmp = 0.954929658551372 * x_m;
	}
	return x_s * tmp;
}

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
    real(8) :: tmp
    if (((0.954929658551372d0 * x_m) - (0.12900613773279798d0 * ((x_m * x_m) * x_m))) <= (-5d+21)) then
        tmp = ((x_m * x_m) * (-0.12900613773279798d0)) * x_m
    else
        tmp = 0.954929658551372d0 * x_m
    end if
    code = x_s * tmp
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) {
	double tmp;
	if (((0.954929658551372 * x_m) - (0.12900613773279798 * ((x_m * x_m) * x_m))) <= -5e+21) {
		tmp = ((x_m * x_m) * -0.12900613773279798) * x_m;
	} else {
		tmp = 0.954929658551372 * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m):
	tmp = 0
	if ((0.954929658551372 * x_m) - (0.12900613773279798 * ((x_m * x_m) * x_m))) <= -5e+21:
		tmp = ((x_m * x_m) * -0.12900613773279798) * x_m
	else:
		tmp = 0.954929658551372 * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m)
	tmp = 0.0
	if (Float64(Float64(0.954929658551372 * x_m) - Float64(0.12900613773279798 * Float64(Float64(x_m * x_m) * x_m))) <= -5e+21)
		tmp = Float64(Float64(Float64(x_m * x_m) * -0.12900613773279798) * x_m);
	else
		tmp = Float64(0.954929658551372 * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m)
	tmp = 0.0;
	if (((0.954929658551372 * x_m) - (0.12900613773279798 * ((x_m * x_m) * x_m))) <= -5e+21)
		tmp = ((x_m * x_m) * -0.12900613773279798) * x_m;
	else
		tmp = 0.954929658551372 * x_m;
	end
	tmp_2 = x_s * tmp;
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 * If[LessEqual[N[(N[(0.954929658551372 * x$95$m), $MachinePrecision] - N[(0.12900613773279798 * N[(N[(x$95$m * x$95$m), $MachinePrecision] * x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e+21], N[(N[(N[(x$95$m * x$95$m), $MachinePrecision] * -0.12900613773279798), $MachinePrecision] * x$95$m), $MachinePrecision], N[(0.954929658551372 * x$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 #s(literal 238732414637843/250000000000000 binary64) x) (*.f64 #s(literal 6450306886639899/50000000000000000 binary64) (*.f64 (*.f64 x x) x))) < -5e21

   1. Initial program 98.5%

      \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(\frac{238732414637843}{250000000000000} + \frac{-6450306886639899}{50000000000000000} \cdot {x}^{2}\right)} \]

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(\frac{-6450306886639899}{50000000000000000} \cdot {x}^{2}\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 99.6%

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

   if -5e21 < (-.f64 (*.f64 #s(literal 238732414637843/250000000000000 binary64) x) (*.f64 #s(literal 6450306886639899/50000000000000000 binary64) (*.f64 (*.f64 x x) x)))

   1. Initial program 99.8%

      \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{238732414637843}{250000000000000} \cdot x} \]
   4. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \frac{238732414637843}{250000000000000} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

      2. distribute-rgt-neg-out N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{238732414637843}{250000000000000} \cdot \left(\mathsf{neg}\left(x\right)\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{238732414637843}{250000000000000}}\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(x \cdot \frac{238732414637843}{250000000000000}\right)\right)}\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot x}\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \left(\mathsf{neg}\left(x\right)\right)} \]

      8. metadata-eval N/A

         \[\leadsto \color{blue}{\frac{-238732414637843}{250000000000000}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \color{blue}{\left(\frac{-238732414637843}{250000000000000} \cdot 1\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)} \cdot 1\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      11. lft-mult-inverse N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \color{blue}{\left(\frac{1}{{x}^{2}} \cdot {x}^{2}\right)}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      12. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right) \cdot {x}^{2}\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)\right)} \cdot {x}^{2}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      15. associate-*l/ N/A

          \[\leadsto \color{blue}{\frac{1 \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)}{{x}^{2}}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}}}{{x}^{2}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      17. *-lft-identity N/A

          \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)}}{{x}^{2}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      18. associate-*l/ N/A

          \[\leadsto \color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(\frac{1}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)\right) \cdot {x}^{2}\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      20. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right)} \cdot {x}^{2}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      21. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right) \cdot {x}^{2}\right) \cdot x\right)} \]

   5. Applied rewrites 63.3%

      \[\leadsto \color{blue}{0.954929658551372 \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.8% accurate, 1.4× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m)
 :precision binary64
 (* x_s (* (fma (* -0.12900613773279798 x_m) x_m 0.954929658551372) x_m)))

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 * x_m), x_m, 0.954929658551372) * x_m);
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m)
	return Float64(x_s * Float64(fma(Float64(-0.12900613773279798 * x_m), x_m, 0.954929658551372) * 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[(N[(-0.12900613773279798 * x$95$m), $MachinePrecision] * x$95$m + 0.954929658551372), $MachinePrecision] * x$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{x \cdot \left(\frac{238732414637843}{250000000000000} + \frac{-6450306886639899}{50000000000000000} \cdot {x}^{2}\right)} \]

5. Applied rewrites 99.8%

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

Alternative 5: 52.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 2.7:\\ \;\;\;\;0.954929658551372 \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot -0.954929658551372\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m)
 :precision binary64
 (*
  x_s
  (if (<= x_m 2.7) (* 0.954929658551372 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) {
	double tmp;
	if (x_m <= 2.7) {
		tmp = 0.954929658551372 * x_m;
	} else {
		tmp = x_m * -0.954929658551372;
	}
	return x_s * tmp;
}

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
    real(8) :: tmp
    if (x_m <= 2.7d0) then
        tmp = 0.954929658551372d0 * x_m
    else
        tmp = x_m * (-0.954929658551372d0)
    end if
    code = x_s * tmp
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) {
	double tmp;
	if (x_m <= 2.7) {
		tmp = 0.954929658551372 * x_m;
	} else {
		tmp = x_m * -0.954929658551372;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m):
	tmp = 0
	if x_m <= 2.7:
		tmp = 0.954929658551372 * x_m
	else:
		tmp = x_m * -0.954929658551372
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m)
	tmp = 0.0
	if (x_m <= 2.7)
		tmp = Float64(0.954929658551372 * x_m);
	else
		tmp = Float64(x_m * -0.954929658551372);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m)
	tmp = 0.0;
	if (x_m <= 2.7)
		tmp = 0.954929658551372 * x_m;
	else
		tmp = x_m * -0.954929658551372;
	end
	tmp_2 = x_s * tmp;
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 * If[LessEqual[x$95$m, 2.7], N[(0.954929658551372 * x$95$m), $MachinePrecision], N[(x$95$m * -0.954929658551372), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 2.7000000000000002

   1. Initial program 99.8%

      \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{238732414637843}{250000000000000} \cdot x} \]
   4. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \frac{238732414637843}{250000000000000} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

      2. distribute-rgt-neg-out N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{238732414637843}{250000000000000} \cdot \left(\mathsf{neg}\left(x\right)\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{238732414637843}{250000000000000}}\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(x \cdot \frac{238732414637843}{250000000000000}\right)\right)}\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot x}\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \left(\mathsf{neg}\left(x\right)\right)} \]

      8. metadata-eval N/A

         \[\leadsto \color{blue}{\frac{-238732414637843}{250000000000000}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \color{blue}{\left(\frac{-238732414637843}{250000000000000} \cdot 1\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)} \cdot 1\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      11. lft-mult-inverse N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \color{blue}{\left(\frac{1}{{x}^{2}} \cdot {x}^{2}\right)}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      12. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right) \cdot {x}^{2}\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)\right)} \cdot {x}^{2}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      15. associate-*l/ N/A

          \[\leadsto \color{blue}{\frac{1 \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)}{{x}^{2}}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}}}{{x}^{2}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      17. *-lft-identity N/A

          \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)}}{{x}^{2}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      18. associate-*l/ N/A

          \[\leadsto \color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(\frac{1}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)\right) \cdot {x}^{2}\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      20. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right)} \cdot {x}^{2}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      21. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right) \cdot {x}^{2}\right) \cdot x\right)} \]

   5. Applied rewrites 64.3%

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

   if 2.7000000000000002 < x

   1. Initial program 98.5%

      \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{238732414637843}{250000000000000} \cdot x} \]
   4. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \frac{238732414637843}{250000000000000} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

      2. distribute-rgt-neg-out N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{238732414637843}{250000000000000} \cdot \left(\mathsf{neg}\left(x\right)\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{238732414637843}{250000000000000}}\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(x \cdot \frac{238732414637843}{250000000000000}\right)\right)}\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot x}\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \left(\mathsf{neg}\left(x\right)\right)} \]

      8. metadata-eval N/A

         \[\leadsto \color{blue}{\frac{-238732414637843}{250000000000000}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \color{blue}{\left(\frac{-238732414637843}{250000000000000} \cdot 1\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)} \cdot 1\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      11. lft-mult-inverse N/A

          \[\leadsto \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \color{blue}{\left(\frac{1}{{x}^{2}} \cdot {x}^{2}\right)}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      12. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right) \cdot {x}^{2}\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)\right)} \cdot {x}^{2}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      15. associate-*l/ N/A

          \[\leadsto \color{blue}{\frac{1 \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)}{{x}^{2}}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      16. *-lft-identity N/A

          \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}}}{{x}^{2}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      17. *-lft-identity N/A

          \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)}}{{x}^{2}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      18. associate-*l/ N/A

          \[\leadsto \color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(\frac{1}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)\right) \cdot {x}^{2}\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      20. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right)} \cdot {x}^{2}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

      21. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right) \cdot {x}^{2}\right) \cdot x\right)} \]

   5. Applied rewrites 0.5%

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

   7. Applied rewrites 6.3%

      \[\leadsto x \cdot \color{blue}{-0.954929658551372} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 49.9% accurate, 4.0× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m) :precision binary64 (* x_s (* 0.954929658551372 x_m)))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	return x_s * (0.954929658551372 * 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 * (0.954929658551372d0 * 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 * (0.954929658551372 * x_m);
}

Python

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

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m)
	return Float64(x_s * Float64(0.954929658551372 * 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 * (0.954929658551372 * 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[(0.954929658551372 * x$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{238732414637843}{250000000000000} \cdot x} \]
4. Step-by-step derivation

   1. remove-double-neg N/A

      \[\leadsto \frac{238732414637843}{250000000000000} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

   2. distribute-rgt-neg-out N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{238732414637843}{250000000000000} \cdot \left(\mathsf{neg}\left(x\right)\right)\right)} \]

   3. *-commutative N/A

      \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \frac{238732414637843}{250000000000000}}\right) \]

   4. distribute-lft-neg-out N/A

      \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(x \cdot \frac{238732414637843}{250000000000000}\right)\right)}\right) \]

   5. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot x}\right) \]

   7. distribute-rgt-neg-out N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \left(\mathsf{neg}\left(x\right)\right)} \]

   8. metadata-eval N/A

      \[\leadsto \color{blue}{\frac{-238732414637843}{250000000000000}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \color{blue}{\left(\frac{-238732414637843}{250000000000000} \cdot 1\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)} \cdot 1\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   11. lft-mult-inverse N/A

       \[\leadsto \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \color{blue}{\left(\frac{1}{{x}^{2}} \cdot {x}^{2}\right)}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   12. associate-*l* N/A

       \[\leadsto \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right) \cdot {x}^{2}\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   13. *-commutative N/A

       \[\leadsto \left(\color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)\right)} \cdot {x}^{2}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   14. associate-*l* N/A

       \[\leadsto \color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   15. associate-*l/ N/A

       \[\leadsto \color{blue}{\frac{1 \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)}{{x}^{2}}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   16. *-lft-identity N/A

       \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}}}{{x}^{2}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   17. *-lft-identity N/A

       \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)}}{{x}^{2}} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   18. associate-*l/ N/A

       \[\leadsto \color{blue}{\left(\frac{1}{{x}^{2}} \cdot \left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot {x}^{2}\right)\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   19. associate-*l* N/A

       \[\leadsto \color{blue}{\left(\left(\frac{1}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right)\right) \cdot {x}^{2}\right)} \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   20. *-commutative N/A

       \[\leadsto \left(\color{blue}{\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right)} \cdot {x}^{2}\right) \cdot \left(\mathsf{neg}\left(x\right)\right) \]

   21. distribute-rgt-neg-in N/A

       \[\leadsto \color{blue}{\mathsf{neg}\left(\left(\left(\left(\mathsf{neg}\left(\frac{238732414637843}{250000000000000}\right)\right) \cdot \frac{1}{{x}^{2}}\right) \cdot {x}^{2}\right) \cdot x\right)} \]

5. Applied rewrites 47.3%

   \[\leadsto \color{blue}{0.954929658551372 \cdot x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024338 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))