Average Error: 0.3 → 0.2
Time: 2.9s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[x + \left(y - x\right) \cdot \frac{6}{\frac{1}{z}}\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
x + \left(y - x\right) \cdot \frac{6}{\frac{1}{z}}
double code(double x, double y, double z) {
	return ((double) (x + ((double) (((double) (((double) (y - x)) * 6.0)) * z))));
}
↓
double code(double x, double y, double z) {
	return ((double) (x + ((double) (((double) (y - x)) * (6.0 / (1.0 / z))))));
}

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

Derivation

  1. Initial program 0.3

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

  2. Simplified0.2

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

  4. Applied flip--24.4

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

  5. Applied associate-*l/28.1

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

  6. Simplified18.1

    \[\leadsto x + \frac{\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(z \cdot \left(y + x\right)\right)\right)}}{y + x}\]
  7. Using strategy rm

  8. Applied *-un-lft-identity18.1

    \[\leadsto x + \frac{\left(y - x\right) \cdot \left(6 \cdot \left(z \cdot \left(y + x\right)\right)\right)}{\color{blue}{1 \cdot \left(y + x\right)}}\]

  9. Applied times-frac0.2

    \[\leadsto x + \color{blue}{\frac{y - x}{1} \cdot \frac{6 \cdot \left(z \cdot \left(y + x\right)\right)}{y + x}}\]

  10. Simplified0.2

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

  11. Simplified0.2

    \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\frac{6}{\frac{1}{z}}}\]

  12. Final simplification0.2

    \[\leadsto x + \left(y - x\right) \cdot \frac{6}{\frac{1}{z}}\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

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

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