Average Error: 0.4 → 0.4
Time: 45.2s
Precision: binary64
Cost: 7232
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
↓
\[\sqrt{x \cdot 9} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) + -1\right) \]
(FPCore (x y)
 :precision binary64
 (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
↓
(FPCore (x y)
 :precision binary64
 (* (sqrt (* x 9.0)) (+ (+ y (/ 1.0 (* x 9.0))) -1.0)))
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((x * 9.0)) * ((y + (1.0 / (x * 9.0))) + -1.0);
}

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((x * 9.0d0)) * ((y + (1.0d0 / (x * 9.0d0))) + (-1.0d0))
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((x * 9.0)) * ((y + (1.0 / (x * 9.0))) + -1.0);
}

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

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

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

Error

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-rr0.4

    \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

  3. Simplified0.4

    \[\leadsto \color{blue}{\sqrt{x \cdot 9}} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
    Proof
    (sqrt.f64 (*.f64 x 9)): 0 points increase in error, 0 points decrease in error
    (Rewrite<= unpow1/2_binary64 (pow.f64 (*.f64 x 9) 1/2)): 0 points increase in error, 0 points decrease in error

  4. Final simplification0.4

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

Alternatives

Alternative 1
Error23.5
Cost7512
\[\begin{array}{l} t_0 := \sqrt{\frac{0.1111111111111111}{x}}\\ t_1 := -\sqrt{x \cdot 9}\\ t_2 := 3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{if}\;x \leq 6 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 2
Error23.6
Cost7512
\[\begin{array}{l} t_0 := \sqrt{\frac{0.1111111111111111}{x}}\\ t_1 := \sqrt{x} \cdot \left(y \cdot 3\right)\\ t_2 := -\sqrt{x \cdot 9}\\ \mathbf{if}\;x \leq 6 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+34}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error23.6
Cost7512
\[\begin{array}{l} t_0 := \sqrt{\frac{0.1111111111111111}{x}}\\ t_1 := \sqrt{x \cdot 9}\\ t_2 := \sqrt{x} \cdot \left(y \cdot 3\right)\\ t_3 := -t_1\\ \mathbf{if}\;x \leq 6 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+34}:\\ \;\;\;\;t_1 \cdot y\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 4
Error11.0
Cost7244
\[\begin{array}{l} t_0 := \sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{if}\;x \leq 5.6 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-97}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 - y \cdot -3\right)\\ \end{array} \]
Alternative 5
Error11.0
Cost7244
\[\begin{array}{l} t_0 := \sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{if}\;x \leq 6 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-97}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \]
Alternative 6
Error1.4
Cost7240
\[\begin{array}{l} t_0 := \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} - y \cdot -3\right)\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 7
Error1.8
Cost7240
\[\begin{array}{l} t_0 := \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} - y \cdot -3\right)\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+18}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(\frac{0.1111111111111111}{x} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 8
Error9.9
Cost7112
\[\begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+38}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot y\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+48}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \]
Alternative 9
Error0.4
Cost7104
\[\sqrt{x \cdot 9} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]
Alternative 10
Error22.4
Cost6788
\[\begin{array}{l} \mathbf{if}\;x \leq 0.7:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;-\sqrt{x \cdot 9}\\ \end{array} \]
Alternative 11
Error38.2
Cost6592
\[\sqrt{\frac{0.1111111111111111}{x}} \]

Error

Reproduce

herbie shell --seed 2022325 
(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)))