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

Average Error: 0.5 → 0.1

Time: 3.8s

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 r874305 = 60.0;
        double r874306 = x;
        double r874307 = y;
        double r874308 = r874306 - r874307;
        double r874309 = r874305 * r874308;
        double r874310 = z;
        double r874311 = t;
        double r874312 = r874310 - r874311;
        double r874313 = r874309 / r874312;
        double r874314 = a;
        double r874315 = 120.0;
        double r874316 = r874314 * r874315;
        double r874317 = r874313 + r874316;
        return r874317;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r874318 = 120.0;
        double r874319 = a;
        double r874320 = 60.0;
        double r874321 = z;
        double r874322 = t;
        double r874323 = r874321 - r874322;
        double r874324 = x;
        double r874325 = y;
        double r874326 = r874324 - r874325;
        double r874327 = r874323 / r874326;
        double r874328 = r874320 / r874327;
        double r874329 = fma(r874318, r874319, r874328);
        return r874329;
}

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 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 2020065 +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)))