Average Error: 0.1 → 0.0
Time: 2.6s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) + \left(-2\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) + \left(-2\right)
double f(double x, double y, double z) {
        double r1008039 = 4.0;
        double r1008040 = x;
        double r1008041 = y;
        double r1008042 = r1008040 - r1008041;
        double r1008043 = z;
        double r1008044 = 0.5;
        double r1008045 = r1008043 * r1008044;
        double r1008046 = r1008042 - r1008045;
        double r1008047 = r1008039 * r1008046;
        double r1008048 = r1008047 / r1008043;
        return r1008048;
}
↓
double f(double x, double y, double z) {
        double r1008049 = 4.0;
        double r1008050 = x;
        double r1008051 = z;
        double r1008052 = r1008050 / r1008051;
        double r1008053 = y;
        double r1008054 = r1008053 / r1008051;
        double r1008055 = r1008052 - r1008054;
        double r1008056 = r1008049 * r1008055;
        double r1008057 = 2.0;
        double r1008058 = -r1008057;
        double r1008059 = r1008056 + r1008058;
        return r1008059;
}

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

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

  5. Applied div-sub0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020089 
(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))