Average Error: 0.5 → 0.1
Time: 5.8s
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 r791217 = 60.0;
        double r791218 = x;
        double r791219 = y;
        double r791220 = r791218 - r791219;
        double r791221 = r791217 * r791220;
        double r791222 = z;
        double r791223 = t;
        double r791224 = r791222 - r791223;
        double r791225 = r791221 / r791224;
        double r791226 = a;
        double r791227 = 120.0;
        double r791228 = r791226 * r791227;
        double r791229 = r791225 + r791228;
        return r791229;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r791230 = 120.0;
        double r791231 = a;
        double r791232 = 60.0;
        double r791233 = x;
        double r791234 = y;
        double r791235 = r791233 - r791234;
        double r791236 = z;
        double r791237 = t;
        double r791238 = r791236 - r791237;
        double r791239 = r791235 / r791238;
        double r791240 = r791232 * r791239;
        double r791241 = fma(r791230, r791231, r791240);
        return r791241;
}

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 *-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 2020001 +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)))