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

Average Error: 0.4 → 0.1

Time: 21.3s

Precision: 64

Math

\[\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0\]

↓

\[\mathsf{fma}\left(\frac{60.0}{z - t}, x - y, 120.0 \cdot a\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r35494636 = 60.0;
        double r35494637 = x;
        double r35494638 = y;
        double r35494639 = r35494637 - r35494638;
        double r35494640 = r35494636 * r35494639;
        double r35494641 = z;
        double r35494642 = t;
        double r35494643 = r35494641 - r35494642;
        double r35494644 = r35494640 / r35494643;
        double r35494645 = a;
        double r35494646 = 120.0;
        double r35494647 = r35494645 * r35494646;
        double r35494648 = r35494644 + r35494647;
        return r35494648;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r35494649 = 60.0;
        double r35494650 = z;
        double r35494651 = t;
        double r35494652 = r35494650 - r35494651;
        double r35494653 = r35494649 / r35494652;
        double r35494654 = x;
        double r35494655 = y;
        double r35494656 = r35494654 - r35494655;
        double r35494657 = 120.0;
        double r35494658 = a;
        double r35494659 = r35494657 * r35494658;
        double r35494660 = fma(r35494653, r35494656, r35494659);
        return r35494660;
}

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

\[\frac{60.0}{\frac{z - t}{x - y}} + a \cdot 120.0\]

Derivation

1. Initial program 0.4

   \[\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0\]

2. Simplified 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{60.0}{z - t}, x - y, a \cdot 120.0\right)}\]

3. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(\frac{60.0}{z - t}, x - y, 120.0 \cdot a\right)\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"

  :herbie-target
  (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))