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

Average Error: 0.1 → 0.1

Time: 7.7s

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 0.1

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

2. Final simplification 0.1

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

Alternatives

Alternative 1
Error	1.8
Cost	584

\[\begin{array}{l} t_0 := \left(x \cdot x\right) \cdot -0.12\\ \mathbf{if}\;x \leq -326855712.47714084:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.5645384811959887:\\ \;\;\;\;1 + x \cdot -0.253\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	1.7
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(x \cdot -0.12\right)\\ \mathbf{if}\;x \leq -326855712.47714084:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.5645384811959887:\\ \;\;\;\;1 + x \cdot -0.253\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	2.1
Cost	448

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

Alternative 4
Error	20.8
Cost	320

\[1 + x \cdot -0.253 \]

Alternative 5
Error	21.8
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022308 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))