Average Error: 0.1 → 0.0
Time: 8.9s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)
double f(double x, double y, double z) {
        double r639380 = 4.0;
        double r639381 = x;
        double r639382 = y;
        double r639383 = r639381 - r639382;
        double r639384 = z;
        double r639385 = 0.5;
        double r639386 = r639384 * r639385;
        double r639387 = r639383 - r639386;
        double r639388 = r639380 * r639387;
        double r639389 = r639388 / r639384;
        return r639389;
}
↓
double f(double x, double y, double z) {
        double r639390 = 4.0;
        double r639391 = x;
        double r639392 = z;
        double r639393 = r639391 / r639392;
        double r639394 = y;
        double r639395 = r639394 / r639392;
        double r639396 = r639393 - r639395;
        double r639397 = 0.5;
        double r639398 = r639396 - r639397;
        double r639399 = r639390 * r639398;
        return r639399;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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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. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(\frac{x - y}{z} - \frac{0.5}{1}\right)}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto 4 \cdot \left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - \frac{0.5}{1}\right)\]

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(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))