Average Error: 0.5 → 0.1
Time: 6.1s
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 r887680 = 60.0;
        double r887681 = x;
        double r887682 = y;
        double r887683 = r887681 - r887682;
        double r887684 = r887680 * r887683;
        double r887685 = z;
        double r887686 = t;
        double r887687 = r887685 - r887686;
        double r887688 = r887684 / r887687;
        double r887689 = a;
        double r887690 = 120.0;
        double r887691 = r887689 * r887690;
        double r887692 = r887688 + r887691;
        return r887692;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r887693 = 120.0;
        double r887694 = a;
        double r887695 = 60.0;
        double r887696 = x;
        double r887697 = y;
        double r887698 = r887696 - r887697;
        double r887699 = z;
        double r887700 = t;
        double r887701 = r887699 - r887700;
        double r887702 = r887698 / r887701;
        double r887703 = r887695 * r887702;
        double r887704 = fma(r887693, r887694, r887703);
        return r887704;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.5
Target0.1
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 2020046 +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)))