Average Error: 0.1 → 0.0
Time: 11.7s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2
double f(double x, double y, double z) {
        double r44090630 = 4.0;
        double r44090631 = x;
        double r44090632 = y;
        double r44090633 = r44090631 - r44090632;
        double r44090634 = z;
        double r44090635 = 0.5;
        double r44090636 = r44090634 * r44090635;
        double r44090637 = r44090633 - r44090636;
        double r44090638 = r44090630 * r44090637;
        double r44090639 = r44090638 / r44090634;
        return r44090639;
}
↓
double f(double x, double y, double z) {
        double r44090640 = 4.0;
        double r44090641 = x;
        double r44090642 = z;
        double r44090643 = r44090641 / r44090642;
        double r44090644 = y;
        double r44090645 = r44090644 / r44090642;
        double r44090646 = r44090643 - r44090645;
        double r44090647 = r44090640 * r44090646;
        double r44090648 = 2.0;
        double r44090649 = r44090647 - r44090648;
        return r44090649;
}

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. 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

    \[\leadsto \color{blue}{4 \cdot \frac{x - y}{z} - 2}\]
  4. Using strategy rm

  5. Applied div-sub0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(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))