Average Error: 0.2 → 0.2
Time: 2.7s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[\left(y - x\right) \cdot \left(6 \cdot z\right) + x\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
\left(y - x\right) \cdot \left(6 \cdot z\right) + x
double f(double x, double y, double z) {
        double r837207 = x;
        double r837208 = y;
        double r837209 = r837208 - r837207;
        double r837210 = 6.0;
        double r837211 = r837209 * r837210;
        double r837212 = z;
        double r837213 = r837211 * r837212;
        double r837214 = r837207 + r837213;
        return r837214;
}
↓
double f(double x, double y, double z) {
        double r837215 = y;
        double r837216 = x;
        double r837217 = r837215 - r837216;
        double r837218 = 6.0;
        double r837219 = z;
        double r837220 = r837218 * r837219;
        double r837221 = r837217 * r837220;
        double r837222 = r837221 + r837216;
        return r837222;
}

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
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.2

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)}\]
  3. Using strategy rm

  4. Applied fma-udef0.2

    \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x}\]

  5. Final simplification0.2

    \[\leadsto \left(y - x\right) \cdot \left(6 \cdot z\right) + x\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6 z) (- x y)))

  (+ x (* (* (- y x) 6) z)))