Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 6.4s

Alternatives: 2

Speedup: 1.2×

• 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, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. cancel-sign-sub-inv 99.5%

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

   2. +-commutative 99.5%

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

   3. *-commutative 99.5%

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

   4. fma-def 99.5%

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

   5. unpow3 99.5%

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

   6. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. unpow3 99.5%

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

   2. fma-udef 99.5%

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

   3. *-commutative 99.5%

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

   4. associate-*l* 99.8%

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

   5. *-commutative 99.8%

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

   6. distribute-lft-out 99.8%

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

   7. pow2 99.8%

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

5. Applied egg-rr 99.8%

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

   1. add-cube-cbrt 99.6%

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

   2. pow3 99.6%

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

7. Applied egg-rr 99.6%

   \[\leadsto x \cdot \left(\color{blue}{{\left(\sqrt[3]{{x}^{2} \cdot -0.12900613773279798}\right)}^{3}} + 0.954929658551372\right) \]
8. Step-by-step derivation

   1. rem-cube-cbrt 99.8%

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

   2. *-commutative 99.8%

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

   3. unpow2 99.8%

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

   4. associate-*r* 99.8%

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

9. Applied egg-rr 99.8%

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

10. Final simplification 99.8%

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

Alternative 2: 49.9% 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 99.5%

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

   1. cancel-sign-sub-inv 99.5%

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

   2. +-commutative 99.5%

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

   3. *-commutative 99.5%

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

   4. fma-def 99.5%

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

   5. unpow3 99.5%

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

   6. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in x around 0 48.6%

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

   1. *-commutative 48.6%

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

6. Simplified 48.6%

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

7. Final simplification 48.6%

   \[\leadsto x \cdot 0.954929658551372 \]

Reproduce

herbie shell --seed 2023305 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))