Average Error: 1.2 → 1.1
Time: 5.6s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{y}{\frac{z - a}{z - t}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{y}{\frac{z - a}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r678242 = x;
        double r678243 = y;
        double r678244 = z;
        double r678245 = t;
        double r678246 = r678244 - r678245;
        double r678247 = a;
        double r678248 = r678244 - r678247;
        double r678249 = r678246 / r678248;
        double r678250 = r678243 * r678249;
        double r678251 = r678242 + r678250;
        return r678251;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r678252 = y;
        double r678253 = z;
        double r678254 = a;
        double r678255 = r678253 - r678254;
        double r678256 = t;
        double r678257 = r678253 - r678256;
        double r678258 = r678255 / r678257;
        double r678259 = r678252 / r678258;
        double r678260 = x;
        double r678261 = r678259 + r678260;
        return r678261;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.2
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.2

    \[x + y \cdot \frac{z - t}{z - a}\]

  2. Simplified1.2

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

  4. Applied clear-num1.3

    \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{1}{\frac{z - a}{z - t}}}, x\right)\]
  5. Using strategy rm

  6. Applied fma-udef1.3

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

  7. Simplified1.1

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

  8. Final simplification1.1

    \[\leadsto \frac{y}{\frac{z - a}{z - t}} + x\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (* y (/ (- z t) (- z a)))))