Average Error: 0.2 → 0.0
Time: 20.6s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x - y}{z} - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x - y}{z} - 0.5\right)
double f(double x, double y, double z) {
        double r607019 = 4.0;
        double r607020 = x;
        double r607021 = y;
        double r607022 = r607020 - r607021;
        double r607023 = z;
        double r607024 = 0.5;
        double r607025 = r607023 * r607024;
        double r607026 = r607022 - r607025;
        double r607027 = r607019 * r607026;
        double r607028 = r607027 / r607023;
        return r607028;
}
↓
double f(double x, double y, double z) {
        double r607029 = 4.0;
        double r607030 = x;
        double r607031 = y;
        double r607032 = r607030 - r607031;
        double r607033 = z;
        double r607034 = r607032 / r607033;
        double r607035 = 0.5;
        double r607036 = r607034 - r607035;
        double r607037 = r607029 * r607036;
        return r607037;
}

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

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

Derivation

  1. Initial program 0.2

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(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))