Average Error: 0.4 → 0.1
Time: 44.6s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(60, \frac{x - y}{z - t}, a \cdot 120\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(60, \frac{x - y}{z - t}, a \cdot 120\right)
double f(double x, double y, double z, double t, double a) {
        double r36197672 = 60.0;
        double r36197673 = x;
        double r36197674 = y;
        double r36197675 = r36197673 - r36197674;
        double r36197676 = r36197672 * r36197675;
        double r36197677 = z;
        double r36197678 = t;
        double r36197679 = r36197677 - r36197678;
        double r36197680 = r36197676 / r36197679;
        double r36197681 = a;
        double r36197682 = 120.0;
        double r36197683 = r36197681 * r36197682;
        double r36197684 = r36197680 + r36197683;
        return r36197684;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r36197685 = 60.0;
        double r36197686 = x;
        double r36197687 = y;
        double r36197688 = r36197686 - r36197687;
        double r36197689 = z;
        double r36197690 = t;
        double r36197691 = r36197689 - r36197690;
        double r36197692 = r36197688 / r36197691;
        double r36197693 = a;
        double r36197694 = 120.0;
        double r36197695 = r36197693 * r36197694;
        double r36197696 = fma(r36197685, r36197692, r36197695);
        return r36197696;
}

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. Using strategy rm

  3. Applied *-un-lft-identity0.4

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

  4. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{60}{1} \cdot \frac{x - y}{z - t}} + a \cdot 120\]

  5. Applied fma-def0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 +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)))