Average Error: 0.5 → 0.1
Time: 17.3s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, 60 \cdot \left(\frac{x}{z - t} - \frac{y}{z - t}\right)\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, 60 \cdot \left(\frac{x}{z - t} - \frac{y}{z - t}\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r5104 = 60.0;
        double r5105 = x;
        double r5106 = y;
        double r5107 = r5105 - r5106;
        double r5108 = r5104 * r5107;
        double r5109 = z;
        double r5110 = t;
        double r5111 = r5109 - r5110;
        double r5112 = r5108 / r5111;
        double r5113 = a;
        double r5114 = 120.0;
        double r5115 = r5113 * r5114;
        double r5116 = r5112 + r5115;
        return r5116;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r5117 = 120.0;
        double r5118 = a;
        double r5119 = 60.0;
        double r5120 = x;
        double r5121 = z;
        double r5122 = t;
        double r5123 = r5121 - r5122;
        double r5124 = r5120 / r5123;
        double r5125 = y;
        double r5126 = r5125 / r5123;
        double r5127 = r5124 - r5126;
        double r5128 = r5119 * r5127;
        double r5129 = fma(r5117, r5118, r5128);
        return r5129;
}

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. Simplified0.4

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

  8. Applied div-sub0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 +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)))