Data.Colour.RGB:hslsv from colour-2.3.3, B

Average Error: 0.5 → 0.1

Time: 9.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

↓

\[\mathsf{fma}\left(120, a, \frac{60}{z - t} \cdot \left(x - y\right)\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r938604 = 60.0;
        double r938605 = x;
        double r938606 = y;
        double r938607 = r938605 - r938606;
        double r938608 = r938604 * r938607;
        double r938609 = z;
        double r938610 = t;
        double r938611 = r938609 - r938610;
        double r938612 = r938608 / r938611;
        double r938613 = a;
        double r938614 = 120.0;
        double r938615 = r938613 * r938614;
        double r938616 = r938612 + r938615;
        return r938616;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r938617 = 120.0;
        double r938618 = a;
        double r938619 = 60.0;
        double r938620 = z;
        double r938621 = t;
        double r938622 = r938620 - r938621;
        double r938623 = r938619 / r938622;
        double r938624 = x;
        double r938625 = y;
        double r938626 = r938624 - r938625;
        double r938627 = r938623 * r938626;
        double r938628 = fma(r938617, r938618, r938627);
        return r938628;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	0.5
Target	0.2
Herbie	0.1

\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

1. Initial program 0.5

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

2. Simplified 0.5

   \[\leadsto \color{blue}{\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z - t}\right)}\]
3. Using strategy rm

4. Applied *-un-lft-identity 0.5

   \[\leadsto \mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{\color{blue}{1 \cdot \left(z - t\right)}}\right)\]

5. Applied times-frac 0.1

   \[\leadsto \mathsf{fma}\left(120, a, \color{blue}{\frac{60}{1} \cdot \frac{x - y}{z - t}}\right)\]

6. Simplified 0.1

   \[\leadsto \mathsf{fma}\left(120, a, \color{blue}{60} \cdot \frac{x - y}{z - t}\right)\]
7. Using strategy rm

8. Applied pow1 0.1

   \[\leadsto \mathsf{fma}\left(120, a, 60 \cdot \color{blue}{{\left(\frac{x - y}{z - t}\right)}^{1}}\right)\]

9. Applied pow1 0.1

   \[\leadsto \mathsf{fma}\left(120, a, \color{blue}{{60}^{1}} \cdot {\left(\frac{x - y}{z - t}\right)}^{1}\right)\]

10. Applied pow-prod-down 0.1

    \[\leadsto \mathsf{fma}\left(120, a, \color{blue}{{\left(60 \cdot \frac{x - y}{z - t}\right)}^{1}}\right)\]

11. Simplified 0.1

    \[\leadsto \mathsf{fma}\left(120, a, {\color{blue}{\left(\left(x - y\right) \cdot \frac{60}{z - t}\right)}}^{1}\right)\]

12. Final simplification 0.1

    \[\leadsto \mathsf{fma}\left(120, a, \frac{60}{z - t} \cdot \left(x - y\right)\right)\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60 (/ (- z t) (- x y))) (* a 120))

  (+ (/ (* 60 (- x y)) (- z t)) (* a 120)))