Average Error: 0.1 → 0.0
Time: 10.1s
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 r636441 = 4.0;
        double r636442 = x;
        double r636443 = y;
        double r636444 = r636442 - r636443;
        double r636445 = z;
        double r636446 = 0.5;
        double r636447 = r636445 * r636446;
        double r636448 = r636444 - r636447;
        double r636449 = r636441 * r636448;
        double r636450 = r636449 / r636445;
        return r636450;
}
↓
double f(double x, double y, double z) {
        double r636451 = 4.0;
        double r636452 = x;
        double r636453 = y;
        double r636454 = r636452 - r636453;
        double r636455 = z;
        double r636456 = r636454 / r636455;
        double r636457 = 0.5;
        double r636458 = r636456 - r636457;
        double r636459 = r636451 * r636458;
        return r636459;
}

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 
(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))