Rosa's Benchmark

Average Error: 0.2 → 0.2

Time: 10.2s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* x (* 0.12900613773279798 (* x 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 * 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 * 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 * 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 * 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 * x) - Float64(x * Float64(0.12900613773279798 * Float64(x * 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 * 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 * x), $MachinePrecision] - N[(x * N[(0.12900613773279798 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.2

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

2. Simplified 0.2

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

   [Start] 0.2	\[ 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right) \]
   rational_best-simplify-2 [=>] 0.2	\[ 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \color{blue}{\left(x \cdot \left(x \cdot x\right)\right)} \]
   rational_best-simplify-44 [=>] 0.2	\[ 0.954929658551372 \cdot x - \color{blue}{x \cdot \left(0.12900613773279798 \cdot \left(x \cdot x\right)\right)} \]

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	1.2
Cost	712

\[\begin{array}{l} t_0 := -0.12900613773279798 \cdot \left(x \cdot \left(x \cdot x\right)\right)\\ \mathbf{if}\;x \leq -2.7:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.7:\\ \;\;\;\;x \cdot 0.954929658551372\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	1.2
Cost	712

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

Alternative 3
Error	0.2
Cost	576

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

Alternative 4
Error	16.8
Cost	192

\[x \cdot 0.954929658551372 \]

Reproduce

herbie shell --seed 2023094 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))