Average Error: 0.4 → 0.1
Time: 19.7s
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 r32824032 = 60.0;
        double r32824033 = x;
        double r32824034 = y;
        double r32824035 = r32824033 - r32824034;
        double r32824036 = r32824032 * r32824035;
        double r32824037 = z;
        double r32824038 = t;
        double r32824039 = r32824037 - r32824038;
        double r32824040 = r32824036 / r32824039;
        double r32824041 = a;
        double r32824042 = 120.0;
        double r32824043 = r32824041 * r32824042;
        double r32824044 = r32824040 + r32824043;
        return r32824044;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r32824045 = a;
        double r32824046 = 120.0;
        double r32824047 = 60.0;
        double r32824048 = x;
        double r32824049 = y;
        double r32824050 = r32824048 - r32824049;
        double r32824051 = z;
        double r32824052 = t;
        double r32824053 = r32824051 - r32824052;
        double r32824054 = r32824050 / r32824053;
        double r32824055 = r32824047 * r32824054;
        double r32824056 = fma(r32824045, r32824046, r32824055);
        return r32824056;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)}\]
  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 2019172 +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)))