Average Error: 0.1 → 0.0
Time: 1.5s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \frac{x - y}{z} + \left(-2\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \frac{x - y}{z} + \left(-2\right)
double f(double x, double y, double z) {
        double r924946 = 4.0;
        double r924947 = x;
        double r924948 = y;
        double r924949 = r924947 - r924948;
        double r924950 = z;
        double r924951 = 0.5;
        double r924952 = r924950 * r924951;
        double r924953 = r924949 - r924952;
        double r924954 = r924946 * r924953;
        double r924955 = r924954 / r924950;
        return r924955;
}
↓
double f(double x, double y, double z) {
        double r924956 = 4.0;
        double r924957 = x;
        double r924958 = y;
        double r924959 = r924957 - r924958;
        double r924960 = z;
        double r924961 = r924959 / r924960;
        double r924962 = r924956 * r924961;
        double r924963 = 2.0;
        double r924964 = -r924963;
        double r924965 = r924962 + r924964;
        return r924965;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020034 
(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))