Rosa's Benchmark

Percentage Accurate: 99.8% → 99.8%

Time: 5.3s

Alternatives: 4

Speedup: 1.0×

• 33.0% 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

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

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 99.5%

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

   1. fma-neg 99.5%

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

   2. *-commutative 99.5%

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

   3. distribute-rgt-neg-in 99.5%

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

   4. unpow3 99.5%

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

   5. metadata-eval 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.954929658551372, x, {x}^{3} \cdot -0.12900613773279798\right)} \]
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. Final simplification 99.8%

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

Alternative 2: 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 99.5%

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

3. Final simplification 99.5%

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

Alternative 3: 50.9% 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 99.4%

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

      1. fma-neg 99.4%

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

      2. *-commutative 99.4%

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

      3. distribute-rgt-neg-in 99.4%

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

      4. unpow3 99.3%

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

      5. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 66.3%

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

      1. *-commutative 66.3%

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

   7. Simplified 66.3%

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

   if 2.7000000000000002 < x

   1. Initial program 99.9%

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

      1. fma-neg 99.9%

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

      2. *-commutative 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. unpow3 99.9%

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

      5. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 0.4%

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

      1. *-commutative 0.4%

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

   7. Simplified 0.4%

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

      1. pow1 0.4%

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

      2. metadata-eval 0.4%

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

      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%

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

   9. Applied egg-rr 0.4%

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

   10. Taylor expanded in x around -inf 6.5%

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

       1. *-commutative 6.5%

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

   12. Simplified 6.5%

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

4. Final simplification 53.7%

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

Alternative 4: 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 99.5%

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

   1. fma-neg 99.5%

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

   2. *-commutative 99.5%

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

   3. distribute-rgt-neg-in 99.5%

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

   4. unpow3 99.5%

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

   5. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around 0 52.4%

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

   1. *-commutative 52.4%

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

7. Simplified 52.4%

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

   1. pow1 52.4%

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

   2. metadata-eval 52.4%

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

   3. sqrt-pow1 33.7%

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

   4. metadata-eval 33.7%

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

   5. sqrt-prod 33.7%

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

9. Applied egg-rr 33.7%

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

10. Taylor expanded in x around -inf 4.9%

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

    1. *-commutative 4.9%

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

12. Simplified 4.9%

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

13. Final simplification 4.9%

    \[\leadsto x \cdot -0.954929658551372 \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2024072 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))