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

Average Error: 0.4 → 0.1

Time: 15.0s

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 r487184 = 60.0;
        double r487185 = x;
        double r487186 = y;
        double r487187 = r487185 - r487186;
        double r487188 = r487184 * r487187;
        double r487189 = z;
        double r487190 = t;
        double r487191 = r487189 - r487190;
        double r487192 = r487188 / r487191;
        double r487193 = a;
        double r487194 = 120.0;
        double r487195 = r487193 * r487194;
        double r487196 = r487192 + r487195;
        return r487196;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r487197 = 120.0;
        double r487198 = a;
        double r487199 = 60.0;
        double r487200 = z;
        double r487201 = t;
        double r487202 = r487200 - r487201;
        double r487203 = x;
        double r487204 = y;
        double r487205 = r487203 - r487204;
        double r487206 = r487202 / r487205;
        double r487207 = r487199 / r487206;
        double r487208 = fma(r487197, r487198, r487207);
        return r487208;
}

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)))