Average Error: 0.1 → 0.0
Time: 2.7s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \frac{x - y}{z} + \left(-2\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \frac{x - y}{z} + \left(-2\right)
double f(double x, double y, double z) {
        double r771094 = 4.0;
        double r771095 = x;
        double r771096 = y;
        double r771097 = r771095 - r771096;
        double r771098 = z;
        double r771099 = 0.5;
        double r771100 = r771098 * r771099;
        double r771101 = r771097 - r771100;
        double r771102 = r771094 * r771101;
        double r771103 = r771102 / r771098;
        return r771103;
}
↓
double f(double x, double y, double z) {
        double r771104 = 4.0;
        double r771105 = x;
        double r771106 = y;
        double r771107 = r771105 - r771106;
        double r771108 = z;
        double r771109 = r771107 / r771108;
        double r771110 = r771104 * r771109;
        double r771111 = 2.0;
        double r771112 = -r771111;
        double r771113 = r771110 + r771112;
        return r771113;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

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. 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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4 (/ x z)) (+ 2 (* 4 (/ y z))))

  (/ (* 4 (- (- x y) (* z 0.5))) z))