Rosa's Benchmark

Average Accuracy: 99.6% → 99.7%

Time: 9.1s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 99.6%

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

2. Applied egg-rr 99.7%

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

   [Start] 99.6	\[ 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
   associate-*r* [=>] 99.7	\[ 0.954929658551372 \cdot x - \color{blue}{\left(0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x} \]
   distribute-rgt-out-- [=>] 99.7	\[ \color{blue}{x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)} \]
   *-commutative [=>] 99.7	\[ \color{blue}{\left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x} \]
   cancel-sign-sub-inv [=>] 99.7	\[ \color{blue}{\left(0.954929658551372 + \left(-0.12900613773279798\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
   *-commutative [=>] 99.7	\[ \left(0.954929658551372 + \color{blue}{\left(x \cdot x\right) \cdot \left(-0.12900613773279798\right)}\right) \cdot x \]
   metadata-eval [=>] 99.7	\[ \left(0.954929658551372 + \left(x \cdot x\right) \cdot \color{blue}{-0.12900613773279798}\right) \cdot x \]

3. Final simplification 99.7%

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

Alternatives

Alternative 1
Accuracy	98.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -2.7 \lor \neg \left(x \leq 2.7\right):\\ \;\;\;\;x \cdot \left(\left(x \cdot x\right) \cdot -0.12900613773279798\right)\\ \mathbf{else}:\\ \;\;\;\;0.954929658551372 \cdot x\\ \end{array} \]

Alternative 2
Accuracy	73.8%
Cost	192

\[0.954929658551372 \cdot x \]

Reproduce

herbie shell --seed 2023138 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))