Average Error: 0.4 → 0.1
Time: 49.6s
Precision: 64
\[\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0\]
↓
\[\mathsf{fma}\left(a, 120.0, \frac{x - y}{\frac{z - t}{60.0}}\right)\]
\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0
↓
\mathsf{fma}\left(a, 120.0, \frac{x - y}{\frac{z - t}{60.0}}\right)
double f(double x, double y, double z, double t, double a) {
        double r24842445 = 60.0;
        double r24842446 = x;
        double r24842447 = y;
        double r24842448 = r24842446 - r24842447;
        double r24842449 = r24842445 * r24842448;
        double r24842450 = z;
        double r24842451 = t;
        double r24842452 = r24842450 - r24842451;
        double r24842453 = r24842449 / r24842452;
        double r24842454 = a;
        double r24842455 = 120.0;
        double r24842456 = r24842454 * r24842455;
        double r24842457 = r24842453 + r24842456;
        return r24842457;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r24842458 = a;
        double r24842459 = 120.0;
        double r24842460 = x;
        double r24842461 = y;
        double r24842462 = r24842460 - r24842461;
        double r24842463 = z;
        double r24842464 = t;
        double r24842465 = r24842463 - r24842464;
        double r24842466 = 60.0;
        double r24842467 = r24842465 / r24842466;
        double r24842468 = r24842462 / r24842467;
        double r24842469 = fma(r24842458, r24842459, r24842468);
        return r24842469;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.4
Target0.2
Herbie0.1
\[\frac{60.0}{\frac{z - t}{x - y}} + a \cdot 120.0\]

Derivation

  1. Initial program 0.4

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

  2. Simplified0.3

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

  4. Applied associate-/l*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 +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)))