Average Error: 0.5 → 0.1
Time: 18.3s
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 r569821 = 60.0;
        double r569822 = x;
        double r569823 = y;
        double r569824 = r569822 - r569823;
        double r569825 = r569821 * r569824;
        double r569826 = z;
        double r569827 = t;
        double r569828 = r569826 - r569827;
        double r569829 = r569825 / r569828;
        double r569830 = a;
        double r569831 = 120.0;
        double r569832 = r569830 * r569831;
        double r569833 = r569829 + r569832;
        return r569833;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r569834 = a;
        double r569835 = 120.0;
        double r569836 = 60.0;
        double r569837 = x;
        double r569838 = y;
        double r569839 = r569837 - r569838;
        double r569840 = z;
        double r569841 = t;
        double r569842 = r569840 - r569841;
        double r569843 = r569839 / r569842;
        double r569844 = r569836 * r569843;
        double r569845 = fma(r569834, r569835, r569844);
        return r569845;
}

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)))