Average Error: 0.4 → 0.1
Time: 5.9s
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 r874723 = 60.0;
        double r874724 = x;
        double r874725 = y;
        double r874726 = r874724 - r874725;
        double r874727 = r874723 * r874726;
        double r874728 = z;
        double r874729 = t;
        double r874730 = r874728 - r874729;
        double r874731 = r874727 / r874730;
        double r874732 = a;
        double r874733 = 120.0;
        double r874734 = r874732 * r874733;
        double r874735 = r874731 + r874734;
        return r874735;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r874736 = 120.0;
        double r874737 = a;
        double r874738 = 60.0;
        double r874739 = x;
        double r874740 = y;
        double r874741 = r874739 - r874740;
        double r874742 = z;
        double r874743 = t;
        double r874744 = r874742 - r874743;
        double r874745 = r874741 / r874744;
        double r874746 = r874738 * r874745;
        double r874747 = fma(r874736, r874737, r874746);
        return r874747;
}

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 *-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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020064 +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)))