Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 13.3s

Alternatives: 4

Speedup: 1.2×

• 33.5% 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, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(x * N[(0.954929658551372 + N[(N[(x * x), $MachinePrecision] * -0.12900613773279798), $MachinePrecision]), $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. Step-by-step derivation

   1. fmm-def 99.8%

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

   2. *-commutative 99.8%

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

   3. distribute-rgt-neg-in 99.8%

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

   4. unpow3 99.8%

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

   5. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around 0 99.8%

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

   1. *-commutative 99.8%

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

7. Simplified 99.8%

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

   1. unpow2 99.8%

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

9. Applied egg-rr 99.8%

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

Alternative 2: 99.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(x * N[(0.954929658551372 + N[(x * N[(x * -0.12900613773279798), $MachinePrecision]), $MachinePrecision]), $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. Step-by-step derivation

   1. fmm-def 99.8%

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

   2. *-commutative 99.8%

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

   3. distribute-rgt-neg-in 99.8%

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

   4. unpow3 99.8%

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

   5. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around 0 99.8%

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

   1. *-commutative 99.8%

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

7. Simplified 99.8%

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

   1. add-cbrt-cube 89.7%

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

   2. pow1/3 39.0%

      \[\leadsto x \cdot \left(0.954929658551372 + \color{blue}{{\left(\left(\left({x}^{2} \cdot -0.12900613773279798\right) \cdot \left({x}^{2} \cdot -0.12900613773279798\right)\right) \cdot \left({x}^{2} \cdot -0.12900613773279798\right)\right)}^{0.3333333333333333}}\right) \]

   3. pow3 39.0%

      \[\leadsto x \cdot \left(0.954929658551372 + {\color{blue}{\left({\left({x}^{2} \cdot -0.12900613773279798\right)}^{3}\right)}}^{0.3333333333333333}\right) \]

   4. unpow-prod-down 39.0%

      \[\leadsto x \cdot \left(0.954929658551372 + {\color{blue}{\left({\left({x}^{2}\right)}^{3} \cdot {-0.12900613773279798}^{3}\right)}}^{0.3333333333333333}\right) \]

   5. unpow2 39.0%

      \[\leadsto x \cdot \left(0.954929658551372 + {\left({\color{blue}{\left(x \cdot x\right)}}^{3} \cdot {-0.12900613773279798}^{3}\right)}^{0.3333333333333333}\right) \]

   6. pow-prod-down 39.0%

      \[\leadsto x \cdot \left(0.954929658551372 + {\left(\color{blue}{\left({x}^{3} \cdot {x}^{3}\right)} \cdot {-0.12900613773279798}^{3}\right)}^{0.3333333333333333}\right) \]

   7. pow-prod-up 39.0%

      \[\leadsto x \cdot \left(0.954929658551372 + {\left(\color{blue}{{x}^{\left(3 + 3\right)}} \cdot {-0.12900613773279798}^{3}\right)}^{0.3333333333333333}\right) \]

   8. metadata-eval 39.0%

      \[\leadsto x \cdot \left(0.954929658551372 + {\left({x}^{\color{blue}{6}} \cdot {-0.12900613773279798}^{3}\right)}^{0.3333333333333333}\right) \]

   9. metadata-eval 39.0%

      \[\leadsto x \cdot \left(0.954929658551372 + {\left({x}^{6} \cdot \color{blue}{-0.0021469954286136776}\right)}^{0.3333333333333333}\right) \]

9. Applied egg-rr 39.0%

   \[\leadsto x \cdot \left(0.954929658551372 + \color{blue}{{\left({x}^{6} \cdot -0.0021469954286136776\right)}^{0.3333333333333333}}\right) \]
10. Step-by-step derivation

    1. unpow1/3 89.7%

       \[\leadsto x \cdot \left(0.954929658551372 + \color{blue}{\sqrt[3]{{x}^{6} \cdot -0.0021469954286136776}}\right) \]

11. Simplified 89.7%

    \[\leadsto x \cdot \left(0.954929658551372 + \color{blue}{\sqrt[3]{{x}^{6} \cdot -0.0021469954286136776}}\right) \]
12. Step-by-step derivation

    1. metadata-eval 89.7%

       \[\leadsto x \cdot \left(0.954929658551372 + \sqrt[3]{{x}^{\color{blue}{\left(3 + 3\right)}} \cdot -0.0021469954286136776}\right) \]

    2. pow-prod-up 89.7%

       \[\leadsto x \cdot \left(0.954929658551372 + \sqrt[3]{\color{blue}{\left({x}^{3} \cdot {x}^{3}\right)} \cdot -0.0021469954286136776}\right) \]

    3. pow-prod-down 89.7%

       \[\leadsto x \cdot \left(0.954929658551372 + \sqrt[3]{\color{blue}{{\left(x \cdot x\right)}^{3}} \cdot -0.0021469954286136776}\right) \]

    4. pow2 89.7%

       \[\leadsto x \cdot \left(0.954929658551372 + \sqrt[3]{{\color{blue}{\left({x}^{2}\right)}}^{3} \cdot -0.0021469954286136776}\right) \]

    5. metadata-eval 89.7%

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

    6. unpow-prod-down 89.7%

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

    7. pow2 89.7%

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

    8. pow3 89.7%

       \[\leadsto x \cdot \left(0.954929658551372 + \sqrt[3]{\color{blue}{\left(\left(\left(x \cdot x\right) \cdot -0.12900613773279798\right) \cdot \left(\left(x \cdot x\right) \cdot -0.12900613773279798\right)\right) \cdot \left(\left(x \cdot x\right) \cdot -0.12900613773279798\right)}}\right) \]

    9. cbrt-prod 93.3%

       \[\leadsto x \cdot \left(0.954929658551372 + \color{blue}{\sqrt[3]{\left(\left(x \cdot x\right) \cdot -0.12900613773279798\right) \cdot \left(\left(x \cdot x\right) \cdot -0.12900613773279798\right)} \cdot \sqrt[3]{\left(x \cdot x\right) \cdot -0.12900613773279798}}\right) \]

    10. cbrt-unprod 99.5%

        \[\leadsto x \cdot \left(0.954929658551372 + \color{blue}{\left(\sqrt[3]{\left(x \cdot x\right) \cdot -0.12900613773279798} \cdot \sqrt[3]{\left(x \cdot x\right) \cdot -0.12900613773279798}\right)} \cdot \sqrt[3]{\left(x \cdot x\right) \cdot -0.12900613773279798}\right) \]

    11. rem-3cbrt-lft 99.8%

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

    12. associate-*l* 99.8%

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

    13. *-commutative 99.8%

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

13. Applied egg-rr 99.8%

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

14. Final simplification 99.8%

    \[\leadsto x \cdot \left(0.954929658551372 + x \cdot \left(x \cdot -0.12900613773279798\right)\right) \]
15. Add Preprocessing

Alternative 3: 51.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.7:\\ \;\;\;\;x \cdot 0.954929658551372\\ \mathbf{else}:\\ \;\;\;\;x \cdot -0.954929658551372\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.7) (* x 0.954929658551372) (* x -0.954929658551372)))

C

double code(double x) {
	double tmp;
	if (x <= 2.7) {
		tmp = x * 0.954929658551372;
	} else {
		tmp = x * -0.954929658551372;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 2.7d0) then
        tmp = x * 0.954929658551372d0
    else
        tmp = x * (-0.954929658551372d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.7) {
		tmp = x * 0.954929658551372;
	} else {
		tmp = x * -0.954929658551372;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.7:
		tmp = x * 0.954929658551372
	else:
		tmp = x * -0.954929658551372
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.7)
		tmp = Float64(x * 0.954929658551372);
	else
		tmp = Float64(x * -0.954929658551372);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.7)
		tmp = x * 0.954929658551372;
	else
		tmp = x * -0.954929658551372;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.7], N[(x * 0.954929658551372), $MachinePrecision], N[(x * -0.954929658551372), $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. Step-by-step derivation

      1. fmm-def 99.8%

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

      2. *-commutative 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. unpow3 99.8%

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

      5. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 64.8%

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

      1. *-commutative 64.8%

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

   7. Simplified 64.8%

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

   if 2.7000000000000002 < x

   1. Initial program 99.6%

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

      1. fmm-def 99.6%

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

      2. *-commutative 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. unpow3 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 0.5%

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

      1. *-commutative 0.5%

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

   7. Simplified 0.5%

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

      1. *-commutative 0.5%

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

      2. add-sqr-sqrt 0.5%

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

      3. sqrt-unprod 0.5%

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

      4. *-commutative 0.5%

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

      5. *-commutative 0.5%

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

      6. swap-sqr 0.5%

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

      7. unpow2 0.5%

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

      8. metadata-eval 0.5%

         \[\leadsto \sqrt{{x}^{2} \cdot \color{blue}{0.9118906527810399}} \]

   9. Applied egg-rr 0.5%

      \[\leadsto \color{blue}{\sqrt{{x}^{2} \cdot 0.9118906527810399}} \]

   10. Taylor expanded in x around -inf 6.4%

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

       1. *-commutative 6.4%

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

   12. Simplified 6.4%

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

Alternative 4: 5.0% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return x * -0.954929658551372

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. fmm-def 99.8%

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

   2. *-commutative 99.8%

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

   3. distribute-rgt-neg-in 99.8%

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

   4. unpow3 99.8%

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

   5. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around 0 47.0%

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

   1. *-commutative 47.0%

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

7. Simplified 47.0%

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

   1. *-commutative 47.0%

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

   2. add-sqr-sqrt 22.4%

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

   3. sqrt-unprod 24.7%

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

   4. *-commutative 24.7%

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

   5. *-commutative 24.7%

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

   6. swap-sqr 24.7%

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

   7. unpow2 24.7%

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

   8. metadata-eval 24.7%

      \[\leadsto \sqrt{{x}^{2} \cdot \color{blue}{0.9118906527810399}} \]

9. Applied egg-rr 24.7%

   \[\leadsto \color{blue}{\sqrt{{x}^{2} \cdot 0.9118906527810399}} \]

10. Taylor expanded in x around -inf 5.4%

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

    1. *-commutative 5.4%

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

12. Simplified 5.4%

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

Reproduce

herbie shell --seed 2024150 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))