Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 10.0s

Alternatives: 5

Speedup: 1.0×

• 32.9% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ 0.954929658551372 \cdot x + {x}^{3} \cdot -0.12900613773279798 \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (0.954929658551372d0 * x) + ((x ** 3.0d0) * (-0.12900613773279798d0))
end function

Java

public static double code(double x) {
	return (0.954929658551372 * x) + (Math.pow(x, 3.0) * -0.12900613773279798);
}

Python

def code(x):
	return (0.954929658551372 * x) + (math.pow(x, 3.0) * -0.12900613773279798)

Julia

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

MATLAB

function tmp = code(x)
	tmp = (0.954929658551372 * x) + ((x ^ 3.0) * -0.12900613773279798);
end

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. sub-neg 99.7%

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

   2. *-commutative 99.7%

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

   3. distribute-rgt-neg-in 99.7%

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

   4. unpow3 99.8%

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

   5. metadata-eval 99.8%

      \[\leadsto 0.954929658551372 \cdot x + {x}^{3} \cdot \color{blue}{-0.12900613773279798} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{0.954929658551372 \cdot x + {x}^{3} \cdot -0.12900613773279798} \]
4. Add Preprocessing

5. Final simplification 99.8%

   \[\leadsto 0.954929658551372 \cdot x + {x}^{3} \cdot -0.12900613773279798 \]
6. Add Preprocessing

Alternative 2: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot {x}^{2}\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (* x (- 0.954929658551372 (* 0.12900613773279798 (pow x 2.0)))))

C

double code(double x) {
	return x * (0.954929658551372 - (0.12900613773279798 * pow(x, 2.0)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * (0.954929658551372d0 - (0.12900613773279798d0 * (x ** 2.0d0)))
end function

Java

public static double code(double x) {
	return x * (0.954929658551372 - (0.12900613773279798 * Math.pow(x, 2.0)));
}

Python

def code(x):
	return x * (0.954929658551372 - (0.12900613773279798 * math.pow(x, 2.0)))

Julia

function code(x)
	return Float64(x * Float64(0.954929658551372 - Float64(0.12900613773279798 * (x ^ 2.0))))
end

MATLAB

function tmp = code(x)
	tmp = x * (0.954929658551372 - (0.12900613773279798 * (x ^ 2.0)));
end

Wolfram

code[x_] := N[(x * N[(0.954929658551372 - N[(0.12900613773279798 * N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

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

   1. sub-neg 99.7%

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

   2. *-commutative 99.7%

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

   3. distribute-rgt-neg-in 99.7%

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

   4. unpow3 99.8%

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

   5. metadata-eval 99.8%

      \[\leadsto 0.954929658551372 \cdot x + {x}^{3} \cdot \color{blue}{-0.12900613773279798} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{0.954929658551372 \cdot x + {x}^{3} \cdot -0.12900613773279798} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. pow3 99.7%

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

   2. *-commutative 99.7%

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

   3. metadata-eval 99.7%

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

   4. cancel-sign-sub-inv 99.7%

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

   5. associate-*r* 99.8%

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

   6. distribute-rgt-out-- 99.8%

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

   7. pow2 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 3: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. sub-neg 99.7%

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

   2. *-commutative 99.7%

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

   3. distribute-rgt-neg-in 99.7%

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

   4. unpow3 99.8%

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

   5. metadata-eval 99.8%

      \[\leadsto 0.954929658551372 \cdot x + {x}^{3} \cdot \color{blue}{-0.12900613773279798} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{0.954929658551372 \cdot x + {x}^{3} \cdot -0.12900613773279798} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. +-commutative 99.8%

      \[\leadsto \color{blue}{{x}^{3} \cdot -0.12900613773279798 + 0.954929658551372 \cdot x} \]

   2. pow3 99.7%

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

   3. fma-define 99.7%

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

   4. pow3 99.8%

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

6. Applied egg-rr 99.8%

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

   1. *-commutative 99.8%

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

8. Simplified 99.8%

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

9. Taylor expanded in x around 0 99.8%

   \[\leadsto \color{blue}{-0.12900613773279798 \cdot {x}^{3} + 0.954929658551372 \cdot x} \]
10. Step-by-step derivation

    1. *-commutative 99.8%

       \[\leadsto \color{blue}{{x}^{3} \cdot -0.12900613773279798} + 0.954929658551372 \cdot x \]

    2. *-commutative 99.8%

       \[\leadsto {x}^{3} \cdot -0.12900613773279798 + \color{blue}{x \cdot 0.954929658551372} \]

    3. cancel-sign-sub 99.8%

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

    4. distribute-lft-neg-in 99.8%

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

    5. *-commutative 99.8%

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

    6. distribute-lft-neg-in 99.8%

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

    7. metadata-eval 99.8%

       \[\leadsto {x}^{3} \cdot -0.12900613773279798 - \color{blue}{-0.954929658551372} \cdot x \]

    8. rem-square-sqrt 0.0%

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

    9. unpow2 0.0%

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

    10. *-commutative 0.0%

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

    11. unpow3 0.0%

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

    12. unpow2 0.0%

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

    13. associate-*r* 0.0%

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

    14. distribute-rgt-out-- 0.0%

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

    15. unpow2 0.0%

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

    16. rem-square-sqrt 99.8%

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

11. Simplified 99.8%

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

    1. unpow2 99.8%

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

    2. associate-*r* 99.8%

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

    3. fma-neg 99.8%

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

    4. metadata-eval 99.8%

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

13. Applied egg-rr 99.8%

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

    1. *-commutative 99.8%

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

15. Simplified 99.8%

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

16. Final simplification 99.8%

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

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

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(x * Float64(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[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

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

3. Final simplification 99.7%

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

Alternative 5: 49.6% accurate, 3.7× 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 99.7%

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

   1. sub-neg 99.7%

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

   2. *-commutative 99.7%

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

   3. distribute-rgt-neg-in 99.7%

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

   4. unpow3 99.8%

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

   5. metadata-eval 99.8%

      \[\leadsto 0.954929658551372 \cdot x + {x}^{3} \cdot \color{blue}{-0.12900613773279798} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{0.954929658551372 \cdot x + {x}^{3} \cdot -0.12900613773279798} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 47.7%

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

   1. *-commutative 47.7%

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

7. Simplified 47.7%

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

8. Final simplification 47.7%

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

Reproduce

herbie shell --seed 2024048 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))