Average Error: 0.2 → 0.3
Time: 3.8s
Precision: binary64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
↓
\[\left(1 + 0.1111111111111111 \cdot \frac{-1}{x}\right) - \frac{y}{{\left(\frac{x}{0.1111111111111111}\right)}^{0.5}} \]
(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))
↓
(FPCore (x y)
 :precision binary64
 (-
  (+ 1.0 (* 0.1111111111111111 (/ -1.0 x)))
  (/ y (pow (/ x 0.1111111111111111) 0.5))))
double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
}
↓
double code(double x, double y) {
	return (1.0 + (0.1111111111111111 * (-1.0 / x))) - (y / pow((x / 0.1111111111111111), 0.5));
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (1.0d0 / (x * 9.0d0))) - (y / (3.0d0 * sqrt(x)))
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 + (0.1111111111111111d0 * ((-1.0d0) / x))) - (y / ((x / 0.1111111111111111d0) ** 0.5d0))
end function

public static double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * Math.sqrt(x)));
}
↓
public static double code(double x, double y) {
	return (1.0 + (0.1111111111111111 * (-1.0 / x))) - (y / Math.pow((x / 0.1111111111111111), 0.5));
}

def code(x, y):
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * math.sqrt(x)))
↓
def code(x, y):
	return (1.0 + (0.1111111111111111 * (-1.0 / x))) - (y / math.pow((x / 0.1111111111111111), 0.5))

function code(x, y)
	return Float64(Float64(1.0 - Float64(1.0 / Float64(x * 9.0))) - Float64(y / Float64(3.0 * sqrt(x))))
end
↓
function code(x, y)
	return Float64(Float64(1.0 + Float64(0.1111111111111111 * Float64(-1.0 / x))) - Float64(y / (Float64(x / 0.1111111111111111) ^ 0.5)))
end

function tmp = code(x, y)
	tmp = (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
end
↓
function tmp = code(x, y)
	tmp = (1.0 + (0.1111111111111111 * (-1.0 / x))) - (y / ((x / 0.1111111111111111) ^ 0.5));
end

code[x_, y_] := N[(N[(1.0 - N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(N[(1.0 + N[(0.1111111111111111 * N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[Power[N[(x / 0.1111111111111111), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 + 0.1111111111111111 \cdot \frac{-1}{x}\right) - \frac{y}{{\left(\frac{x}{0.1111111111111111}\right)}^{0.5}}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.3
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]

Derivation

  1. Initial program 0.2

    \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]

  2. Applied egg-rr0.2

    \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\color{blue}{\sqrt{x \cdot 9}}} \]

  3. Applied egg-rr0.3

    \[\leadsto \left(1 - \color{blue}{0.1111111111111111 \cdot \frac{1}{x}}\right) - \frac{y}{\sqrt{x \cdot 9}} \]

  4. Applied egg-rr0.3

    \[\leadsto \left(1 - 0.1111111111111111 \cdot \frac{1}{x}\right) - \frac{y}{\color{blue}{{\left(\frac{x}{0.1111111111111111}\right)}^{0.5}}} \]

  5. Final simplification0.3

    \[\leadsto \left(1 + 0.1111111111111111 \cdot \frac{-1}{x}\right) - \frac{y}{{\left(\frac{x}{0.1111111111111111}\right)}^{0.5}} \]

Reproduce

herbie shell --seed 2022210 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))