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

Average Error: 0.1 → 0.1

Time: 1.5min

Precision: binary64

Cost: 6848

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 0.1

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

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	3.5
Cost	6984

\[\begin{array}{l} t_0 := 1 + y \cdot \sqrt{x}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+61}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	5.6
Cost	6856

\[\begin{array}{l} t_0 := y \cdot \sqrt{x}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+63}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.1
Cost	6848

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

Alternative 4
Error	22.0
Cost	260

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

Alternative 5
Error	21.4
Cost	192

\[1 - x \]

Alternative 6
Error	42.4
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E"
  :precision binary64
  (+ (- 1.0 x) (* y (sqrt x))))