Rosa's Benchmark

Percentage Accurate: 99.7% → 99.8%

Time: 6.3s

Alternatives: 5

Speedup: 1.0×

• 32.4% 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: 99.7% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Alternative 2: 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 99.8%

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

3. Taylor expanded in x around 0 99.8%

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

   1. *-commutative 99.8%

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

5. Simplified 99.8%

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

Alternative 3: 99.7% 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 99.8%

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

3. Final simplification 99.8%

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

Alternative 4: 51.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

double code(double x) {
	double tmp;
	if (x <= 2.7) {
		tmp = 0.954929658551372 * x;
	} 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 = 0.954929658551372d0 * x
    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 = 0.954929658551372 * x;
	} else {
		tmp = x * -0.954929658551372;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := If[LessEqual[x, 2.7], N[(0.954929658551372 * x), $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. Add Preprocessing

   3. Taylor expanded in x around 0 67.2%

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

      1. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   if 2.7000000000000002 < x

   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 0.6%

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

      1. *-commutative 0.6%

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

   5. Simplified 0.6%

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

      1. pow1 0.6%

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

      2. metadata-eval 0.6%

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

      3. sqrt-pow1 0.5%

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

      4. metadata-eval 0.5%

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

      5. sqrt-prod 0.5%

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

   7. Applied egg-rr 0.5%

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

   8. Taylor expanded in x around -inf 6.6%

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

      1. *-commutative 6.6%

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

   10. Simplified 6.6%

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

4. Final simplification 52.0%

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

Alternative 5: 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. Add Preprocessing

3. Taylor expanded in x around 0 50.5%

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

   1. *-commutative 50.5%

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

5. Simplified 50.5%

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

   1. pow1 50.5%

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

   2. metadata-eval 50.5%

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

   3. sqrt-pow1 26.3%

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

   4. metadata-eval 26.3%

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

   5. sqrt-prod 26.4%

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

7. Applied egg-rr 26.4%

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

8. Taylor expanded in x around -inf 5.2%

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

   1. *-commutative 5.2%

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

10. Simplified 5.2%

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

Reproduce

herbie shell --seed 2024092 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))