Average Error: 0.5 → 0.1
Time: 16.0s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, \left(x - y\right) \cdot \frac{60}{z - t}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, \left(x - y\right) \cdot \frac{60}{z - t}\right)
double f(double x, double y, double z, double t, double a) {
        double r505401 = 60.0;
        double r505402 = x;
        double r505403 = y;
        double r505404 = r505402 - r505403;
        double r505405 = r505401 * r505404;
        double r505406 = z;
        double r505407 = t;
        double r505408 = r505406 - r505407;
        double r505409 = r505405 / r505408;
        double r505410 = a;
        double r505411 = 120.0;
        double r505412 = r505410 * r505411;
        double r505413 = r505409 + r505412;
        return r505413;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r505414 = 120.0;
        double r505415 = a;
        double r505416 = x;
        double r505417 = y;
        double r505418 = r505416 - r505417;
        double r505419 = 60.0;
        double r505420 = z;
        double r505421 = t;
        double r505422 = r505420 - r505421;
        double r505423 = r505419 / r505422;
        double r505424 = r505418 * r505423;
        double r505425 = fma(r505414, r505415, r505424);
        return r505425;
}

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. Simplified0.4

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

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

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

  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. Using strategy rm

  8. Applied *-un-lft-identity0.1

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

  9. Applied associate-*l*0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 +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)))