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

Average Error: 0.4 → 0.1

Time: 4.9s

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 r858614 = 60.0;
        double r858615 = x;
        double r858616 = y;
        double r858617 = r858615 - r858616;
        double r858618 = r858614 * r858617;
        double r858619 = z;
        double r858620 = t;
        double r858621 = r858619 - r858620;
        double r858622 = r858618 / r858621;
        double r858623 = a;
        double r858624 = 120.0;
        double r858625 = r858623 * r858624;
        double r858626 = r858622 + r858625;
        return r858626;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r858627 = 120.0;
        double r858628 = a;
        double r858629 = 60.0;
        double r858630 = z;
        double r858631 = t;
        double r858632 = r858630 - r858631;
        double r858633 = x;
        double r858634 = y;
        double r858635 = r858633 - r858634;
        double r858636 = r858632 / r858635;
        double r858637 = r858629 / r858636;
        double r858638 = fma(r858627, r858628, r858637);
        return r858638;
}

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 2020056 +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)))