Average Error: 0.4 → 0.5
Time: 4.3s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, \frac{60}{\frac{z}{x - y} - \frac{t}{x - y}}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, \frac{60}{\frac{z}{x - y} - \frac{t}{x - y}}\right)
double f(double x, double y, double z, double t, double a) {
        double r888471 = 60.0;
        double r888472 = x;
        double r888473 = y;
        double r888474 = r888472 - r888473;
        double r888475 = r888471 * r888474;
        double r888476 = z;
        double r888477 = t;
        double r888478 = r888476 - r888477;
        double r888479 = r888475 / r888478;
        double r888480 = a;
        double r888481 = 120.0;
        double r888482 = r888480 * r888481;
        double r888483 = r888479 + r888482;
        return r888483;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r888484 = 120.0;
        double r888485 = a;
        double r888486 = 60.0;
        double r888487 = z;
        double r888488 = x;
        double r888489 = y;
        double r888490 = r888488 - r888489;
        double r888491 = r888487 / r888490;
        double r888492 = t;
        double r888493 = r888492 / r888490;
        double r888494 = r888491 - r888493;
        double r888495 = r888486 / r888494;
        double r888496 = fma(r888484, r888485, r888495);
        return r888496;
}

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
Herbie0.5
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.4

    \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

  2. Simplified0.4

    \[\leadsto \color{blue}{\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z - t}\right)}\]
  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. Using strategy rm

  6. Applied div-sub0.5

    \[\leadsto \mathsf{fma}\left(120, a, \frac{60}{\color{blue}{\frac{z}{x - y} - \frac{t}{x - y}}}\right)\]

  7. Final simplification0.5

    \[\leadsto \mathsf{fma}\left(120, a, \frac{60}{\frac{z}{x - y} - \frac{t}{x - y}}\right)\]

Reproduce

herbie shell --seed 2020060 +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)))