Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 9.6s

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_] := N[(N[Power[x, 2.0], $MachinePrecision] * N[(x * -0.12900613773279798), $MachinePrecision] + N[(x * 0.954929658551372), $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. cancel-sign-sub-inv 99.8%

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

   2. metadata-eval 99.8%

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

   3. *-commutative 99.8%

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

   4. +-commutative 99.8%

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

   5. associate-*l* 99.9%

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

   6. fma-def 99.9%

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

   7. pow2 99.9%

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

3. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left({x}^{2}, x \cdot -0.12900613773279798, x \cdot 0.954929658551372\right) \]

Alternative 2: 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 99.8%

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

   1. associate-*r* 99.9%

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

   2. distribute-rgt-out-- 99.8%

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

   3. pow2 99.8%

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

3. Applied egg-rr 99.8%

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

   1. sub-neg 99.8%

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

   2. +-commutative 99.8%

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

   3. distribute-lft-neg-in 99.8%

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

   4. metadata-eval 99.8%

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

   5. unpow2 99.8%

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

   6. associate-*r* 99.8%

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

   7. *-commutative 99.8%

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

   8. fma-def 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(N[(x * 0.954929658551372), $MachinePrecision] - N[(0.12900613773279798 * N[(x * N[(x * x), $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. Final simplification 99.8%

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

Alternative 4: 51.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.8:\\ \;\;\;\;x \cdot 0.954929658551372\\ \mathbf{else}:\\ \;\;\;\;x \cdot -0.954929658551372\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.8) (* x 0.954929658551372) (* x -0.954929658551372)))

C

double code(double x) {
	double tmp;
	if (x <= 2.8) {
		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 <= 2.8d0) 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 <= 2.8) {
		tmp = x * 0.954929658551372;
	} else {
		tmp = x * -0.954929658551372;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.8:
		tmp = x * 0.954929658551372
	else:
		tmp = x * -0.954929658551372
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.8)
		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 <= 2.8)
		tmp = x * 0.954929658551372;
	else
		tmp = x * -0.954929658551372;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.8], N[(x * 0.954929658551372), $MachinePrecision], N[(x * -0.954929658551372), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.7999999999999998

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 65.0%

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

      1. *-commutative 65.0%

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

   4. Simplified 65.0%

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

   if 2.7999999999999998 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 0.5%

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

      1. *-commutative 0.5%

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

   4. Simplified 0.5%

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

      1. pow1 0.5%

         \[\leadsto \color{blue}{{x}^{1}} \cdot 0.954929658551372 \]

      2. metadata-eval 0.5%

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

      3. sqrt-pow1 0.4%

         \[\leadsto \color{blue}{\sqrt{{x}^{2}}} \cdot 0.954929658551372 \]

      4. metadata-eval 0.4%

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

      5. sqrt-prod 0.4%

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

   6. Applied egg-rr 0.4%

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

   7. Taylor expanded in x around -inf 6.1%

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

      1. *-commutative 6.1%

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

   9. Simplified 6.1%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.8:\\ \;\;\;\;x \cdot 0.954929658551372\\ \mathbf{else}:\\ \;\;\;\;x \cdot -0.954929658551372\\ \end{array} \]

Alternative 5: 5.1% 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. Taylor expanded in x around 0 47.8%

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

   1. *-commutative 47.8%

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

4. Simplified 47.8%

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

   1. pow1 47.8%

      \[\leadsto \color{blue}{{x}^{1}} \cdot 0.954929658551372 \]

   2. metadata-eval 47.8%

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

   3. sqrt-pow1 24.8%

      \[\leadsto \color{blue}{\sqrt{{x}^{2}}} \cdot 0.954929658551372 \]

   4. metadata-eval 24.8%

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

   5. sqrt-prod 24.7%

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

6. Applied egg-rr 24.7%

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

7. Taylor expanded in x around -inf 5.4%

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

   1. *-commutative 5.4%

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

9. Simplified 5.4%

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

10. Final simplification 5.4%

    \[\leadsto x \cdot -0.954929658551372 \]

Reproduce

herbie shell --seed 2023334 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))