Average Error: 0.1 → 0.0
Time: 8.2s
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 r1405083 = 4.0;
        double r1405084 = x;
        double r1405085 = y;
        double r1405086 = r1405084 - r1405085;
        double r1405087 = z;
        double r1405088 = 0.5;
        double r1405089 = r1405087 * r1405088;
        double r1405090 = r1405086 - r1405089;
        double r1405091 = r1405083 * r1405090;
        double r1405092 = r1405091 / r1405087;
        return r1405092;
}
↓
double f(double x, double y, double z) {
        double r1405093 = 4.0;
        double r1405094 = x;
        double r1405095 = y;
        double r1405096 = r1405094 - r1405095;
        double r1405097 = z;
        double r1405098 = r1405096 / r1405097;
        double r1405099 = 0.5;
        double r1405100 = r1405098 - r1405099;
        double r1405101 = r1405093 * r1405100;
        return r1405101;
}

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 2020047 
(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))