Average Error: 0.2 → 0.0
Time: 10.9s
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 r961996 = 4.0;
        double r961997 = x;
        double r961998 = y;
        double r961999 = r961997 - r961998;
        double r962000 = z;
        double r962001 = 0.5;
        double r962002 = r962000 * r962001;
        double r962003 = r961999 - r962002;
        double r962004 = r961996 * r962003;
        double r962005 = r962004 / r962000;
        return r962005;
}
↓
double f(double x, double y, double z) {
        double r962006 = 4.0;
        double r962007 = x;
        double r962008 = y;
        double r962009 = r962007 - r962008;
        double r962010 = z;
        double r962011 = r962009 / r962010;
        double r962012 = 0.5;
        double r962013 = r962011 - r962012;
        double r962014 = r962006 * r962013;
        return r962014;
}

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

Original0.2
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.2

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

  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 2020042 +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))