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

Average Error: 0.5 → 0.1

Time: 5.3s

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 r724650 = 60.0;
        double r724651 = x;
        double r724652 = y;
        double r724653 = r724651 - r724652;
        double r724654 = r724650 * r724653;
        double r724655 = z;
        double r724656 = t;
        double r724657 = r724655 - r724656;
        double r724658 = r724654 / r724657;
        double r724659 = a;
        double r724660 = 120.0;
        double r724661 = r724659 * r724660;
        double r724662 = r724658 + r724661;
        return r724662;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r724663 = 120.0;
        double r724664 = a;
        double r724665 = 60.0;
        double r724666 = z;
        double r724667 = t;
        double r724668 = r724666 - r724667;
        double r724669 = x;
        double r724670 = y;
        double r724671 = r724669 - r724670;
        double r724672 = r724668 / r724671;
        double r724673 = r724665 / r724672;
        double r724674 = fma(r724663, r724664, r724673);
        return r724674;
}

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 2020024 +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)))