Average Error: 0.4 → 0.1
Time: 19.0s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(a, 120, \frac{60}{\frac{z - t}{x - y}}\right)
double f(double x, double y, double z, double t, double a) {
        double r1223445 = 60.0;
        double r1223446 = x;
        double r1223447 = y;
        double r1223448 = r1223446 - r1223447;
        double r1223449 = r1223445 * r1223448;
        double r1223450 = z;
        double r1223451 = t;
        double r1223452 = r1223450 - r1223451;
        double r1223453 = r1223449 / r1223452;
        double r1223454 = a;
        double r1223455 = 120.0;
        double r1223456 = r1223454 * r1223455;
        double r1223457 = r1223453 + r1223456;
        return r1223457;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1223458 = a;
        double r1223459 = 120.0;
        double r1223460 = 60.0;
        double r1223461 = z;
        double r1223462 = t;
        double r1223463 = r1223461 - r1223462;
        double r1223464 = x;
        double r1223465 = y;
        double r1223466 = r1223464 - r1223465;
        double r1223467 = r1223463 / r1223466;
        double r1223468 = r1223460 / r1223467;
        double r1223469 = fma(r1223458, r1223459, r1223468);
        return r1223469;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.4
Target0.1
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

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

  4. Applied associate-/l*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 +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)))