Average Error: 0.2 → 0.3
Time: 21.2s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \frac{1}{\frac{\sqrt{x}}{y}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \frac{1}{\frac{\sqrt{x}}{y}}
double f(double x, double y) {
        double r339111 = 1.0;
        double r339112 = x;
        double r339113 = 9.0;
        double r339114 = r339112 * r339113;
        double r339115 = r339111 / r339114;
        double r339116 = r339111 - r339115;
        double r339117 = y;
        double r339118 = 3.0;
        double r339119 = sqrt(r339112);
        double r339120 = r339118 * r339119;
        double r339121 = r339117 / r339120;
        double r339122 = r339116 - r339121;
        return r339122;
}
↓
double f(double x, double y) {
        double r339123 = 1.0;
        double r339124 = x;
        double r339125 = r339123 / r339124;
        double r339126 = 9.0;
        double r339127 = r339125 / r339126;
        double r339128 = r339123 - r339127;
        double r339129 = 1.0;
        double r339130 = 3.0;
        double r339131 = r339129 / r339130;
        double r339132 = sqrt(r339124);
        double r339133 = y;
        double r339134 = r339132 / r339133;
        double r339135 = r339129 / r339134;
        double r339136 = r339131 * r339135;
        double r339137 = r339128 - r339136;
        return r339137;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
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. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \left(1 - \color{blue}{\frac{\frac{1}{x}}{9}}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.2

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

  6. Applied times-frac0.2

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - \color{blue}{\frac{1}{3} \cdot \frac{y}{\sqrt{x}}}\]
  7. Using strategy rm

  8. Applied clear-num0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (- (- 1 (/ (/ 1 x) 9)) (/ y (* 3 (sqrt x))))

  (- (- 1 (/ 1 (* x 9))) (/ y (* 3 (sqrt x)))))