Average Error: 0.4 → 0.3
Time: 3.4s
Precision: binary64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
↓
\[\left(3 \cdot \left(y \cdot \sqrt{x}\right) + \sqrt{\frac{1}{x} \cdot 0.1111111111111111}\right) - 3 \cdot \sqrt{x} \]
(FPCore (x y)
 :precision binary64
 (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
↓
(FPCore (x y)
 :precision binary64
 (-
  (+ (* 3.0 (* y (sqrt x))) (sqrt (* (/ 1.0 x) 0.1111111111111111)))
  (* 3.0 (sqrt x))))
double code(double x, double y) {
	return (3.0 * sqrt(x)) * ((y + (1.0 / (x * 9.0))) - 1.0);
}
↓
double code(double x, double y) {
	return ((3.0 * (y * sqrt(x))) + sqrt(((1.0 / x) * 0.1111111111111111))) - (3.0 * sqrt(x));
}

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

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

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

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

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

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

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

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.4
Herbie0.3
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right) \]

Derivation

  1. Initial program 0.4

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

  2. Taylor expanded in y around 0 0.4

    \[\leadsto \color{blue}{\left(3 \cdot \left(y \cdot \sqrt{x}\right) + 0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\right) - 3 \cdot \sqrt{x}} \]

  3. Applied egg-rr0.3

    \[\leadsto \left(3 \cdot \left(y \cdot \sqrt{x}\right) + \color{blue}{\sqrt{\frac{1}{x} \cdot 0.1111111111111111}}\right) - 3 \cdot \sqrt{x} \]

  4. Final simplification0.3

    \[\leadsto \left(3 \cdot \left(y \cdot \sqrt{x}\right) + \sqrt{\frac{1}{x} \cdot 0.1111111111111111}\right) - 3 \cdot \sqrt{x} \]

Reproduce

herbie shell --seed 2022133 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

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

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