Average Error: 0.4 → 0.1
Time: 20.1s
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 r34528477 = 60.0;
        double r34528478 = x;
        double r34528479 = y;
        double r34528480 = r34528478 - r34528479;
        double r34528481 = r34528477 * r34528480;
        double r34528482 = z;
        double r34528483 = t;
        double r34528484 = r34528482 - r34528483;
        double r34528485 = r34528481 / r34528484;
        double r34528486 = a;
        double r34528487 = 120.0;
        double r34528488 = r34528486 * r34528487;
        double r34528489 = r34528485 + r34528488;
        return r34528489;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r34528490 = a;
        double r34528491 = 120.0;
        double r34528492 = 60.0;
        double r34528493 = x;
        double r34528494 = y;
        double r34528495 = r34528493 - r34528494;
        double r34528496 = z;
        double r34528497 = t;
        double r34528498 = r34528496 - r34528497;
        double r34528499 = r34528495 / r34528498;
        double r34528500 = r34528492 * r34528499;
        double r34528501 = fma(r34528490, r34528491, r34528500);
        return r34528501;
}

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 *-un-lft-identity0.4

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

  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 2019171 +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)))