Average Error: 0.4 → 0.4
Time: 12.3s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1.0}{x}}{9.0}\right) - 1.0\right)\right)\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1.0}{x}}{9.0}\right) - 1.0\right)\right)
double f(double x, double y) {
        double r7170148 = 3.0;
        double r7170149 = x;
        double r7170150 = sqrt(r7170149);
        double r7170151 = r7170148 * r7170150;
        double r7170152 = y;
        double r7170153 = 1.0;
        double r7170154 = 9.0;
        double r7170155 = r7170149 * r7170154;
        double r7170156 = r7170153 / r7170155;
        double r7170157 = r7170152 + r7170156;
        double r7170158 = r7170157 - r7170153;
        double r7170159 = r7170151 * r7170158;
        return r7170159;
}
↓
double f(double x, double y) {
        double r7170160 = 3.0;
        double r7170161 = x;
        double r7170162 = sqrt(r7170161);
        double r7170163 = y;
        double r7170164 = 1.0;
        double r7170165 = r7170164 / r7170161;
        double r7170166 = 9.0;
        double r7170167 = r7170165 / r7170166;
        double r7170168 = r7170163 + r7170167;
        double r7170169 = r7170168 - r7170164;
        double r7170170 = r7170162 * r7170169;
        double r7170171 = r7170160 * r7170170;
        return r7170171;
}

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
\[3.0 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1.0}{x \cdot 9.0} - 1.0\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)}\]
  4. Using strategy rm

  5. Applied associate-/r*0.4

    \[\leadsto 3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \color{blue}{\frac{\frac{1.0}{x}}{9.0}}\right) - 1.0\right)\right)\]

  6. Final simplification0.4

    \[\leadsto 3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1.0}{x}}{9.0}\right) - 1.0\right)\right)\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :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)))