Average Error: 0.1 → 0.0
Time: 11.9s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4\]
\frac{4 \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
double f(double x, double y, double z) {
        double r142913556 = 4.0;
        double r142913557 = x;
        double r142913558 = y;
        double r142913559 = r142913557 - r142913558;
        double r142913560 = z;
        double r142913561 = 0.5;
        double r142913562 = r142913560 * r142913561;
        double r142913563 = r142913559 - r142913562;
        double r142913564 = r142913556 * r142913563;
        double r142913565 = r142913564 / r142913560;
        return r142913565;
}
↓
double f(double x, double y, double z) {
        double r142913566 = x;
        double r142913567 = z;
        double r142913568 = r142913566 / r142913567;
        double r142913569 = y;
        double r142913570 = r142913569 / r142913567;
        double r142913571 = r142913568 - r142913570;
        double r142913572 = 0.5;
        double r142913573 = r142913571 - r142913572;
        double r142913574 = 4.0;
        double r142913575 = r142913573 * r142913574;
        return r142913575;
}

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. Using strategy rm

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 
(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))