Average Error: 9.5 → 0.1
Time: 10.3s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{x + 1} \cdot \left(\frac{x}{y} + 1\right)\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{x + 1} \cdot \left(\frac{x}{y} + 1\right)
double f(double x, double y) {
        double r818592 = x;
        double r818593 = y;
        double r818594 = r818592 / r818593;
        double r818595 = 1.0;
        double r818596 = r818594 + r818595;
        double r818597 = r818592 * r818596;
        double r818598 = r818592 + r818595;
        double r818599 = r818597 / r818598;
        return r818599;
}
↓
double f(double x, double y) {
        double r818600 = x;
        double r818601 = 1.0;
        double r818602 = r818600 + r818601;
        double r818603 = r818600 / r818602;
        double r818604 = y;
        double r818605 = r818600 / r818604;
        double r818606 = r818605 + r818601;
        double r818607 = r818603 * r818606;
        return r818607;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.5
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.5

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{x}{\frac{x + 1}{\frac{x}{y} + 1}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"
  :precision binary64

  :herbie-target
  (* (/ x 1) (/ (+ (/ x y) 1) (+ x 1)))

  (/ (* x (+ (/ x y) 1)) (+ x 1)))