Average Error: 0.3 → 0.2
Time: 45.8s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot z\]
↓
\[x + \left(z \cdot \left(y - x\right)\right) \cdot 6.0\]
x + \left(\left(y - x\right) \cdot 6.0\right) \cdot z
↓
x + \left(z \cdot \left(y - x\right)\right) \cdot 6.0
double f(double x, double y, double z) {
        double r40082477 = x;
        double r40082478 = y;
        double r40082479 = r40082478 - r40082477;
        double r40082480 = 6.0;
        double r40082481 = r40082479 * r40082480;
        double r40082482 = z;
        double r40082483 = r40082481 * r40082482;
        double r40082484 = r40082477 + r40082483;
        return r40082484;
}
↓
double f(double x, double y, double z) {
        double r40082485 = x;
        double r40082486 = z;
        double r40082487 = y;
        double r40082488 = r40082487 - r40082485;
        double r40082489 = r40082486 * r40082488;
        double r40082490 = 6.0;
        double r40082491 = r40082489 * r40082490;
        double r40082492 = r40082485 + r40082491;
        return r40082492;
}

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

Original0.3
Target0.2
Herbie0.2
\[x - \left(6.0 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.3

    \[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot z\]

  2. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(x + 6.0 \cdot \left(z \cdot y\right)\right) - 6.0 \cdot \left(x \cdot z\right)}\]

  3. Simplified0.2

    \[\leadsto \color{blue}{6.0 \cdot \left(z \cdot \left(y - x\right)\right) + x}\]

  4. Final simplification0.2

    \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot 6.0\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))