Average Error: 0.5 → 0.1
Time: 18.0s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(a, 120, 60 \cdot \frac{x - y}{z - t}\right)
double f(double x, double y, double z, double t, double a) {
        double r36006756 = 60.0;
        double r36006757 = x;
        double r36006758 = y;
        double r36006759 = r36006757 - r36006758;
        double r36006760 = r36006756 * r36006759;
        double r36006761 = z;
        double r36006762 = t;
        double r36006763 = r36006761 - r36006762;
        double r36006764 = r36006760 / r36006763;
        double r36006765 = a;
        double r36006766 = 120.0;
        double r36006767 = r36006765 * r36006766;
        double r36006768 = r36006764 + r36006767;
        return r36006768;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r36006769 = a;
        double r36006770 = 120.0;
        double r36006771 = 60.0;
        double r36006772 = x;
        double r36006773 = y;
        double r36006774 = r36006772 - r36006773;
        double r36006775 = z;
        double r36006776 = t;
        double r36006777 = r36006775 - r36006776;
        double r36006778 = r36006774 / r36006777;
        double r36006779 = r36006771 * r36006778;
        double r36006780 = fma(r36006769, r36006770, r36006779);
        return r36006780;
}

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. Simplified0.5

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

  4. Applied *-un-lft-identity0.5

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

  5. Applied times-frac0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 +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)))