Rosa's Benchmark

Average Error: 0.2 → 0.2

Time: 6.9s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = (0.954929658551372d0 + ((x * x) * (-0.12900613773279798d0))) * x
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 (0.954929658551372 + ((x * x) * -0.12900613773279798)) * x;
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

function tmp = code(x)
	tmp = (0.954929658551372 + ((x * x) * -0.12900613773279798)) * x;
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[(N[(0.954929658551372 + N[(N[(x * x), $MachinePrecision] * -0.12900613773279798), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]

Derivation

1. Initial program 0.2

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

2. Applied egg-rr 0.2

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

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	0.2
Cost	576

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

Alternative 2
Error	16.0
Cost	192

\[x \cdot 0.954929658551372 \]

Reproduce

herbie shell --seed 2023096 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))