Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A

Average Accuracy: 99.8% → 99.8%

Time: 5.6s

Precision: binary64

Cost: 576

Math

\[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]

↓

\[1 + x \cdot \left(-0.253 + x \cdot -0.12\right) \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))

↓

(FPCore (x) :precision binary64 (+ 1.0 (* x (+ -0.253 (* x -0.12)))))

C

double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

↓

double code(double x) {
	return 1.0 + (x * (-0.253 + (x * -0.12)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * (0.253d0 + (x * 0.12d0)))
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 + (x * ((-0.253d0) + (x * (-0.12d0))))
end function

Java

public static double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

↓

public static double code(double x) {
	return 1.0 + (x * (-0.253 + (x * -0.12)));
}

Python

def code(x):
	return 1.0 - (x * (0.253 + (x * 0.12)))

↓

def code(x):
	return 1.0 + (x * (-0.253 + (x * -0.12)))

Julia

function code(x)
	return Float64(1.0 - Float64(x * Float64(0.253 + Float64(x * 0.12))))
end

↓

function code(x)
	return Float64(1.0 + Float64(x * Float64(-0.253 + Float64(x * -0.12))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 - (x * (0.253 + (x * 0.12)));
end

↓

function tmp = code(x)
	tmp = 1.0 + (x * (-0.253 + (x * -0.12)));
end

Wolfram

code[x_] := N[(1.0 - N[(x * N[(0.253 + N[(x * 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(1.0 + N[(x * N[(-0.253 + N[(x * -0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]

2. Final simplification 99.8%

   \[\leadsto 1 + x \cdot \left(-0.253 + x \cdot -0.12\right) \]

Alternatives

Alternative 1
Accuracy	96.8%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -4.2 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot -0.12\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Accuracy	96.9%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -4.2:\\ \;\;\;\;\left(x \cdot x\right) \cdot -0.12\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot -0.12\right)\\ \end{array} \]

Alternative 3
Accuracy	97.6%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -4.2:\\ \;\;\;\;\left(x \cdot x\right) \cdot -0.12\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;1 + x \cdot -0.253\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot -0.12\right)\\ \end{array} \]

Alternative 4
Accuracy	96.8%
Cost	448

\[1 + \left(x \cdot x\right) \cdot -0.12 \]

Alternative 5
Accuracy	65.0%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023137 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))