Average Error: 0.4 → 0.1
Time: 16.8s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, \left(x - y\right) \cdot \frac{60}{z - t}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, \left(x - y\right) \cdot \frac{60}{z - t}\right)
double f(double x, double y, double z, double t, double a) {
        double r530131 = 60.0;
        double r530132 = x;
        double r530133 = y;
        double r530134 = r530132 - r530133;
        double r530135 = r530131 * r530134;
        double r530136 = z;
        double r530137 = t;
        double r530138 = r530136 - r530137;
        double r530139 = r530135 / r530138;
        double r530140 = a;
        double r530141 = 120.0;
        double r530142 = r530140 * r530141;
        double r530143 = r530139 + r530142;
        return r530143;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r530144 = 120.0;
        double r530145 = a;
        double r530146 = x;
        double r530147 = y;
        double r530148 = r530146 - r530147;
        double r530149 = 60.0;
        double r530150 = z;
        double r530151 = t;
        double r530152 = r530150 - r530151;
        double r530153 = r530149 / r530152;
        double r530154 = r530148 * r530153;
        double r530155 = fma(r530144, r530145, r530154);
        return r530155;
}

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. Using strategy rm

  8. Applied *-un-lft-identity0.1

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

  9. Applied associate-*l*0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 +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)))