Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 5.7s

Alternatives: 5

Speedup: 1.4×

• 32.7% 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

\[\begin{array}{l} \\ \mathsf{fma}\left({x}^{3}, -0.12900613773279798, 0.954929658551372 \cdot x\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (fma (pow x 3.0) -0.12900613773279798 (* 0.954929658551372 x)))

C

double code(double x) {
	return fma(pow(x, 3.0), -0.12900613773279798, (0.954929658551372 * x));
}

Julia

function code(x)
	return fma((x ^ 3.0), -0.12900613773279798, Float64(0.954929658551372 * x))
end

Wolfram

code[x_] := N[(N[Power[x, 3.0], $MachinePrecision] * -0.12900613773279798 + N[(0.954929658551372 * x), $MachinePrecision]), $MachinePrecision]

Derivation

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. 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. sub-neg N/A

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

   3. +-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

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

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

   7. lower-fma.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. lift-*.f64 N/A

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

   10. pow3 N/A

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

   11. lower-pow.f64 N/A

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

   12. metadata-eval 99.9

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

   13. lift-*.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-*.f64 99.9

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

4. Applied rewrites 99.9%

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

5. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left({x}^{3}, -0.12900613773279798, 0.954929658551372 \cdot x\right) \]
6. Add Preprocessing

Alternative 2: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot x\right) \cdot x\\ \mathbf{if}\;0.954929658551372 \cdot x - t\_0 \cdot 0.12900613773279798 \leq -1:\\ \;\;\;\;t\_0 \cdot -0.12900613773279798\\ \mathbf{else}:\\ \;\;\;\;0.954929658551372 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* (* x x) x)))
   (if (<= (- (* 0.954929658551372 x) (* t_0 0.12900613773279798)) -1.0)
     (* t_0 -0.12900613773279798)
     (* 0.954929658551372 x))))

C

double code(double x) {
	double t_0 = (x * x) * x;
	double tmp;
	if (((0.954929658551372 * x) - (t_0 * 0.12900613773279798)) <= -1.0) {
		tmp = t_0 * -0.12900613773279798;
	} else {
		tmp = 0.954929658551372 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * x) * x
    if (((0.954929658551372d0 * x) - (t_0 * 0.12900613773279798d0)) <= (-1.0d0)) then
        tmp = t_0 * (-0.12900613773279798d0)
    else
        tmp = 0.954929658551372d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = (x * x) * x;
	double tmp;
	if (((0.954929658551372 * x) - (t_0 * 0.12900613773279798)) <= -1.0) {
		tmp = t_0 * -0.12900613773279798;
	} else {
		tmp = 0.954929658551372 * x;
	}
	return tmp;
}

Python

def code(x):
	t_0 = (x * x) * x
	tmp = 0
	if ((0.954929658551372 * x) - (t_0 * 0.12900613773279798)) <= -1.0:
		tmp = t_0 * -0.12900613773279798
	else:
		tmp = 0.954929658551372 * x
	return tmp

Julia

function code(x)
	t_0 = Float64(Float64(x * x) * x)
	tmp = 0.0
	if (Float64(Float64(0.954929658551372 * x) - Float64(t_0 * 0.12900613773279798)) <= -1.0)
		tmp = Float64(t_0 * -0.12900613773279798);
	else
		tmp = Float64(0.954929658551372 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = (x * x) * x;
	tmp = 0.0;
	if (((0.954929658551372 * x) - (t_0 * 0.12900613773279798)) <= -1.0)
		tmp = t_0 * -0.12900613773279798;
	else
		tmp = 0.954929658551372 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(N[(0.954929658551372 * x), $MachinePrecision] - N[(t$95$0 * 0.12900613773279798), $MachinePrecision]), $MachinePrecision], -1.0], N[(t$95$0 * -0.12900613773279798), $MachinePrecision], N[(0.954929658551372 * x), $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))) < -1

   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 inf

      \[\leadsto \color{blue}{\frac{-6450306886639899}{50000000000000000} \cdot {x}^{3}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{{x}^{3} \cdot \frac{-6450306886639899}{50000000000000000}} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{{x}^{3} \cdot \frac{-6450306886639899}{50000000000000000}} \]

      3. lower-pow.f64 98.9

         \[\leadsto \color{blue}{{x}^{3}} \cdot -0.12900613773279798 \]

   5. Applied rewrites 98.9%

      \[\leadsto \color{blue}{{x}^{3} \cdot -0.12900613773279798} \]
   6. Step-by-step derivation

   7. Applied rewrites 98.8%

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

   if -1 < (-.f64 (*.f64 #s(literal 238732414637843/250000000000000 binary64) x) (*.f64 #s(literal 6450306886639899/50000000000000000 binary64) (*.f64 (*.f64 x x) x)))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \frac{238732414637843}{250000000000000}} \]

      2. lower-*.f64 60.4

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

   5. Applied rewrites 60.4%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;0.954929658551372 \cdot x - \left(\left(x \cdot x\right) \cdot x\right) \cdot 0.12900613773279798 \leq -1:\\ \;\;\;\;\left(\left(x \cdot x\right) \cdot x\right) \cdot -0.12900613773279798\\ \mathbf{else}:\\ \;\;\;\;0.954929658551372 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;0.954929658551372 \cdot x - \left(\left(x \cdot x\right) \cdot x\right) \cdot 0.12900613773279798 \leq -1:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(-0.12900613773279798 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;0.954929658551372 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (- (* 0.954929658551372 x) (* (* (* x x) x) 0.12900613773279798))
      -1.0)
   (* (* x x) (* -0.12900613773279798 x))
   (* 0.954929658551372 x)))

C

double code(double x) {
	double tmp;
	if (((0.954929658551372 * x) - (((x * x) * x) * 0.12900613773279798)) <= -1.0) {
		tmp = (x * x) * (-0.12900613773279798 * x);
	} else {
		tmp = 0.954929658551372 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((0.954929658551372d0 * x) - (((x * x) * x) * 0.12900613773279798d0)) <= (-1.0d0)) then
        tmp = (x * x) * ((-0.12900613773279798d0) * x)
    else
        tmp = 0.954929658551372d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((0.954929658551372 * x) - (((x * x) * x) * 0.12900613773279798)) <= -1.0) {
		tmp = (x * x) * (-0.12900613773279798 * x);
	} else {
		tmp = 0.954929658551372 * x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((0.954929658551372 * x) - (((x * x) * x) * 0.12900613773279798)) <= -1.0:
		tmp = (x * x) * (-0.12900613773279798 * x)
	else:
		tmp = 0.954929658551372 * x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(0.954929658551372 * x) - Float64(Float64(Float64(x * x) * x) * 0.12900613773279798)) <= -1.0)
		tmp = Float64(Float64(x * x) * Float64(-0.12900613773279798 * x));
	else
		tmp = Float64(0.954929658551372 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((0.954929658551372 * x) - (((x * x) * x) * 0.12900613773279798)) <= -1.0)
		tmp = (x * x) * (-0.12900613773279798 * x);
	else
		tmp = 0.954929658551372 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(0.954929658551372 * x), $MachinePrecision] - N[(N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision] * 0.12900613773279798), $MachinePrecision]), $MachinePrecision], -1.0], N[(N[(x * x), $MachinePrecision] * N[(-0.12900613773279798 * x), $MachinePrecision]), $MachinePrecision], N[(0.954929658551372 * x), $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))) < -1

   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 inf

      \[\leadsto \color{blue}{\frac{-6450306886639899}{50000000000000000} \cdot {x}^{3}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{{x}^{3} \cdot \frac{-6450306886639899}{50000000000000000}} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{{x}^{3} \cdot \frac{-6450306886639899}{50000000000000000}} \]

      3. lower-pow.f64 98.9

         \[\leadsto \color{blue}{{x}^{3}} \cdot -0.12900613773279798 \]

   5. Applied rewrites 98.9%

      \[\leadsto \color{blue}{{x}^{3} \cdot -0.12900613773279798} \]
   6. Step-by-step derivation

   7. Applied rewrites 98.8%

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

   if -1 < (-.f64 (*.f64 #s(literal 238732414637843/250000000000000 binary64) x) (*.f64 #s(literal 6450306886639899/50000000000000000 binary64) (*.f64 (*.f64 x x) x)))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \frac{238732414637843}{250000000000000}} \]

      2. lower-*.f64 60.4

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

   5. Applied rewrites 60.4%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;0.954929658551372 \cdot x - \left(\left(x \cdot x\right) \cdot x\right) \cdot 0.12900613773279798 \leq -1:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(-0.12900613773279798 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;0.954929658551372 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. 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. sub-neg N/A

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

   3. +-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. associate-*r* N/A

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

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

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

   8. lift-*.f64 N/A

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

   9. distribute-rgt-out N/A

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

   10. lower-*.f64 N/A

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

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

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

   12. lift-*.f64 N/A

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

   13. associate-*r* N/A

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

   14. lower-fma.f64 N/A

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

   15. lower-*.f64 N/A

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

   16. metadata-eval 99.9

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

4. Applied rewrites 99.9%

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

5. Final simplification 99.9%

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

Alternative 5: 50.6% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ 0.954929658551372 \cdot x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return 0.954929658551372 * x

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. *-commutative N/A

      \[\leadsto \color{blue}{x \cdot \frac{238732414637843}{250000000000000}} \]

   2. lower-*.f64 45.8

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

5. Applied rewrites 45.8%

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

6. Final simplification 45.8%

   \[\leadsto 0.954929658551372 \cdot x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024270 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))