Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E

Average Error: 0.1 → 0.1

Time: 6.3s

Precision: binary64

Cost: 6848

Math

\[\left(1 - x\right) + y \cdot \sqrt{x} \]

↓

\[\left(1 - x\right) + y \cdot \sqrt{x} \]

FPCore

(FPCore (x y) :precision binary64 (+ (- 1.0 x) (* y (sqrt x))))

↓

(FPCore (x y) :precision binary64 (+ (- 1.0 x) (* y (sqrt x))))

C

double code(double x, double y) {
	return (1.0 - x) + (y * sqrt(x));
}

↓

double code(double x, double y) {
	return (1.0 - x) + (y * sqrt(x));
}

Fortran

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

↓

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

Java

public static double code(double x, double y) {
	return (1.0 - x) + (y * Math.sqrt(x));
}

↓

public static double code(double x, double y) {
	return (1.0 - x) + (y * Math.sqrt(x));
}

Python

def code(x, y):
	return (1.0 - x) + (y * math.sqrt(x))

↓

def code(x, y):
	return (1.0 - x) + (y * math.sqrt(x))

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) + Float64(y * sqrt(x)))
end

↓

function code(x, y)
	return Float64(Float64(1.0 - x) + Float64(y * sqrt(x)))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) + (y * sqrt(x));
end

↓

function tmp = code(x, y)
	tmp = (1.0 - x) + (y * sqrt(x));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] + N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] + N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.1

   \[\left(1 - x\right) + y \cdot \sqrt{x} \]

2. Final simplification 0.1

   \[\leadsto \left(1 - x\right) + y \cdot \sqrt{x} \]

Alternatives

Alternative 1
Error	5.4
Cost	7120

\[\begin{array}{l} t_0 := y \cdot \sqrt{x}\\ \mathbf{if}\;y \leq -1.1909481088986603 \cdot 10^{+103}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.0129847952114264 \cdot 10^{+45}:\\ \;\;\;\;1 - x\\ \mathbf{elif}\;y \leq 2.0565636600531313 \cdot 10^{+64}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.384083704531881 \cdot 10^{+101}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	5.4
Cost	7120

\[\begin{array}{l} t_0 := y \cdot \sqrt{x}\\ \mathbf{if}\;y \leq -1.1909481088986603 \cdot 10^{+103}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.0129847952114264 \cdot 10^{+45}:\\ \;\;\;\;1 - x\\ \mathbf{elif}\;y \leq 2.0565636600531313 \cdot 10^{+64}:\\ \;\;\;\;\sqrt{y \cdot \left(x \cdot y\right)}\\ \mathbf{elif}\;y \leq 2.384083704531881 \cdot 10^{+101}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	22.2
Cost	260

\[\begin{array}{l} \mathbf{if}\;x \leq 0.05125377519440065:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4
Error	21.5
Cost	192

\[1 - x \]

Alternative 5
Error	42.5
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022291 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E"
  :precision binary64
  (+ (- 1.0 x) (* y (sqrt x))))