Average Error: 0.5 → 0.1
Time: 19.4s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)
double f(double x, double y, double z, double t, double a) {
        double r52766360 = 60.0;
        double r52766361 = x;
        double r52766362 = y;
        double r52766363 = r52766361 - r52766362;
        double r52766364 = r52766360 * r52766363;
        double r52766365 = z;
        double r52766366 = t;
        double r52766367 = r52766365 - r52766366;
        double r52766368 = r52766364 / r52766367;
        double r52766369 = a;
        double r52766370 = 120.0;
        double r52766371 = r52766369 * r52766370;
        double r52766372 = r52766368 + r52766371;
        return r52766372;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r52766373 = a;
        double r52766374 = 120.0;
        double r52766375 = 60.0;
        double r52766376 = x;
        double r52766377 = y;
        double r52766378 = r52766376 - r52766377;
        double r52766379 = z;
        double r52766380 = t;
        double r52766381 = r52766379 - r52766380;
        double r52766382 = r52766378 / r52766381;
        double r52766383 = r52766375 * r52766382;
        double r52766384 = fma(r52766373, r52766374, r52766383);
        return r52766384;
}

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

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

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

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

  5. Applied times-frac0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 +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)))