Average Error: 0.4 → 0.1
Time: 9.1s
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 r915387 = 60.0;
        double r915388 = x;
        double r915389 = y;
        double r915390 = r915388 - r915389;
        double r915391 = r915387 * r915390;
        double r915392 = z;
        double r915393 = t;
        double r915394 = r915392 - r915393;
        double r915395 = r915391 / r915394;
        double r915396 = a;
        double r915397 = 120.0;
        double r915398 = r915396 * r915397;
        double r915399 = r915395 + r915398;
        return r915399;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r915400 = 120.0;
        double r915401 = a;
        double r915402 = 60.0;
        double r915403 = z;
        double r915404 = t;
        double r915405 = r915403 - r915404;
        double r915406 = x;
        double r915407 = y;
        double r915408 = r915406 - r915407;
        double r915409 = r915405 / r915408;
        double r915410 = r915402 / r915409;
        double r915411 = fma(r915400, r915401, r915410);
        return r915411;
}

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)))