Average Error: 0.4 → 0.4
Time: 2.6s
Precision: binary64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
↓
\[\sqrt{9 \cdot x} \cdot \left(-1 + \left(y + \frac{-1}{x \cdot -9}\right)\right) \]
(FPCore (x y)
 :precision binary64
 (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
↓
(FPCore (x y)
 :precision binary64
 (* (sqrt (* 9.0 x)) (+ -1.0 (+ y (/ -1.0 (* x -9.0))))))
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 sqrt((9.0 * x)) * (-1.0 + (y + (-1.0 / (x * -9.0))));
}

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 = sqrt((9.0d0 * x)) * ((-1.0d0) + (y + ((-1.0d0) / (x * (-9.0d0)))))
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 Math.sqrt((9.0 * x)) * (-1.0 + (y + (-1.0 / (x * -9.0))));
}

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

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(sqrt(Float64(9.0 * x)) * Float64(-1.0 + Float64(y + Float64(-1.0 / Float64(x * -9.0)))))
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 = sqrt((9.0 * x)) * (-1.0 + (y + (-1.0 / (x * -9.0))));
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[Sqrt[N[(9.0 * x), $MachinePrecision]], $MachinePrecision] * N[(-1.0 + N[(y + N[(-1.0 / N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

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

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. Applied egg-rr0.5

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

  3. Taylor expanded in x around 0 0.4

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

  4. Applied egg-rr0.5

    \[\leadsto \sqrt{9 \cdot x} \cdot \left(\left(y + \color{blue}{{\left(\sqrt{\frac{0.1111111111111111}{x}}\right)}^{2}}\right) - 1\right) \]

  5. Applied egg-rr0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2022150 
(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)))