Average Error: 0.1 → 0.0
Time: 14.7s
Precision: 64
\[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4.0\]
\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4.0
double f(double x, double y, double z) {
        double r34092506 = 4.0;
        double r34092507 = x;
        double r34092508 = y;
        double r34092509 = r34092507 - r34092508;
        double r34092510 = z;
        double r34092511 = 0.5;
        double r34092512 = r34092510 * r34092511;
        double r34092513 = r34092509 - r34092512;
        double r34092514 = r34092506 * r34092513;
        double r34092515 = r34092514 / r34092510;
        return r34092515;
}
↓
double f(double x, double y, double z) {
        double r34092516 = x;
        double r34092517 = z;
        double r34092518 = r34092516 / r34092517;
        double r34092519 = y;
        double r34092520 = r34092519 / r34092517;
        double r34092521 = r34092518 - r34092520;
        double r34092522 = 0.5;
        double r34092523 = r34092521 - r34092522;
        double r34092524 = 4.0;
        double r34092525 = r34092523 * r34092524;
        return r34092525;
}

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
\[4.0 \cdot \frac{x}{z} - \left(2.0 + 4.0 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

    \[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(\frac{x - y}{z} - 0.5\right) \cdot 4.0}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto \left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 0.5\right) \cdot 4.0\]

  5. Final simplification0.0

    \[\leadsto \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4.0\]

Reproduce

herbie shell --seed 2019163 +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))