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

Average Error: 0.4 → 0.1

Time: 14.3s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r492399 = 60.0;
        double r492400 = x;
        double r492401 = y;
        double r492402 = r492400 - r492401;
        double r492403 = r492399 * r492402;
        double r492404 = z;
        double r492405 = t;
        double r492406 = r492404 - r492405;
        double r492407 = r492403 / r492406;
        double r492408 = a;
        double r492409 = 120.0;
        double r492410 = r492408 * r492409;
        double r492411 = r492407 + r492410;
        return r492411;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r492412 = 120.0;
        double r492413 = a;
        double r492414 = 60.0;
        double r492415 = z;
        double r492416 = t;
        double r492417 = r492415 - r492416;
        double r492418 = x;
        double r492419 = y;
        double r492420 = r492418 - r492419;
        double r492421 = r492417 / r492420;
        double r492422 = r492414 / r492421;
        double r492423 = fma(r492412, r492413, r492422);
        return r492423;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	0.4
Target	0.2
Herbie	0.1

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

Derivation

1. Initial program 0.4

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

2. Simplified 0.4

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

4. Applied associate-/l* 0.1

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019325 +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)))