Average Error: 0.4 → 0.1
Time: 9.5s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, \frac{60}{\frac{z - t}{x - y}}\right)\]
\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)
double f(double x, double y, double z, double t, double a) {
        double r921511 = 60.0;
        double r921512 = x;
        double r921513 = y;
        double r921514 = r921512 - r921513;
        double r921515 = r921511 * r921514;
        double r921516 = z;
        double r921517 = t;
        double r921518 = r921516 - r921517;
        double r921519 = r921515 / r921518;
        double r921520 = a;
        double r921521 = 120.0;
        double r921522 = r921520 * r921521;
        double r921523 = r921519 + r921522;
        return r921523;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r921524 = 120.0;
        double r921525 = a;
        double r921526 = 60.0;
        double r921527 = z;
        double r921528 = t;
        double r921529 = r921527 - r921528;
        double r921530 = x;
        double r921531 = y;
        double r921532 = r921530 - r921531;
        double r921533 = r921529 / r921532;
        double r921534 = r921526 / r921533;
        double r921535 = fma(r921524, r921525, r921534);
        return r921535;
}

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

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 +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)))