Average Error: 0.5 → 0.1
Time: 6.5s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, 60 \cdot \frac{x - y}{z - t}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, 60 \cdot \frac{x - y}{z - t}\right)
double f(double x, double y, double z, double t, double a) {
        double r1155447 = 60.0;
        double r1155448 = x;
        double r1155449 = y;
        double r1155450 = r1155448 - r1155449;
        double r1155451 = r1155447 * r1155450;
        double r1155452 = z;
        double r1155453 = t;
        double r1155454 = r1155452 - r1155453;
        double r1155455 = r1155451 / r1155454;
        double r1155456 = a;
        double r1155457 = 120.0;
        double r1155458 = r1155456 * r1155457;
        double r1155459 = r1155455 + r1155458;
        return r1155459;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1155460 = 120.0;
        double r1155461 = a;
        double r1155462 = 60.0;
        double r1155463 = x;
        double r1155464 = y;
        double r1155465 = r1155463 - r1155464;
        double r1155466 = z;
        double r1155467 = t;
        double r1155468 = r1155466 - r1155467;
        double r1155469 = r1155465 / r1155468;
        double r1155470 = r1155462 * r1155469;
        double r1155471 = fma(r1155460, r1155461, r1155470);
        return r1155471;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.5
Target0.2
Herbie0.1
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.5

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

  2. Simplified0.5

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

  4. Applied *-un-lft-identity0.5

    \[\leadsto \mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{\color{blue}{1 \cdot \left(z - t\right)}}\right)\]

  5. Applied times-frac0.1

    \[\leadsto \mathsf{fma}\left(120, a, \color{blue}{\frac{60}{1} \cdot \frac{x - y}{z - t}}\right)\]

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 +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)))