Average Error: 0.1 → 0.0
Time: 10.2s
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 r496516 = 4.0;
        double r496517 = x;
        double r496518 = y;
        double r496519 = r496517 - r496518;
        double r496520 = z;
        double r496521 = 0.5;
        double r496522 = r496520 * r496521;
        double r496523 = r496519 - r496522;
        double r496524 = r496516 * r496523;
        double r496525 = r496524 / r496520;
        return r496525;
}
↓
double f(double x, double y, double z) {
        double r496526 = 4.0;
        double r496527 = x;
        double r496528 = y;
        double r496529 = r496527 - r496528;
        double r496530 = z;
        double r496531 = r496529 / r496530;
        double r496532 = 0.5;
        double r496533 = r496531 - r496532;
        double r496534 = r496526 * r496533;
        return r496534;
}

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. 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 2019306 +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))