Average Error: 0.1 → 0.0
Time: 12.0s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\frac{x - y}{z} - 0.5\right) \cdot 4\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\left(\frac{x - y}{z} - 0.5\right) \cdot 4
double f(double x, double y, double z) {
        double r899555 = 4.0;
        double r899556 = x;
        double r899557 = y;
        double r899558 = r899556 - r899557;
        double r899559 = z;
        double r899560 = 0.5;
        double r899561 = r899559 * r899560;
        double r899562 = r899558 - r899561;
        double r899563 = r899555 * r899562;
        double r899564 = r899563 / r899559;
        return r899564;
}
↓
double f(double x, double y, double z) {
        double r899565 = x;
        double r899566 = y;
        double r899567 = r899565 - r899566;
        double r899568 = z;
        double r899569 = r899567 / r899568;
        double r899570 = 0.5;
        double r899571 = r899569 - r899570;
        double r899572 = 4.0;
        double r899573 = r899571 * r899572;
        return r899573;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +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))