Average Error: 0.5 → 0.1
Time: 3.9s
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 r2317398 = 60.0;
        double r2317399 = x;
        double r2317400 = y;
        double r2317401 = r2317399 - r2317400;
        double r2317402 = r2317398 * r2317401;
        double r2317403 = z;
        double r2317404 = t;
        double r2317405 = r2317403 - r2317404;
        double r2317406 = r2317402 / r2317405;
        double r2317407 = a;
        double r2317408 = 120.0;
        double r2317409 = r2317407 * r2317408;
        double r2317410 = r2317406 + r2317409;
        return r2317410;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2317411 = 120.0;
        double r2317412 = a;
        double r2317413 = 60.0;
        double r2317414 = z;
        double r2317415 = t;
        double r2317416 = r2317414 - r2317415;
        double r2317417 = x;
        double r2317418 = y;
        double r2317419 = r2317417 - r2317418;
        double r2317420 = r2317416 / r2317419;
        double r2317421 = r2317413 / r2317420;
        double r2317422 = fma(r2317411, r2317412, r2317421);
        return r2317422;
}

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 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 2020018 +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)))