Average Error: 0.1 → 0.0
Time: 11.8s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2
double f(double x, double y, double z) {
        double r494549 = 4.0;
        double r494550 = x;
        double r494551 = y;
        double r494552 = r494550 - r494551;
        double r494553 = z;
        double r494554 = 0.5;
        double r494555 = r494553 * r494554;
        double r494556 = r494552 - r494555;
        double r494557 = r494549 * r494556;
        double r494558 = r494557 / r494553;
        return r494558;
}
↓
double f(double x, double y, double z) {
        double r494559 = 4.0;
        double r494560 = x;
        double r494561 = z;
        double r494562 = r494560 / r494561;
        double r494563 = y;
        double r494564 = r494563 / r494561;
        double r494565 = r494562 - r494564;
        double r494566 = r494559 * r494565;
        double r494567 = 2.0;
        double r494568 = r494566 - r494567;
        return r494568;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

    \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x}{z} - \left(4 \cdot \frac{y}{z} + 2\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - y}{z} - 2}\]
  4. Using strategy rm

  5. Applied div-sub0.0

    \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 2\]

  6. Final simplification0.0

    \[\leadsto 4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2\]

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))