Average Error: 1.4 → 1.3
Time: 10.7s
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 r570999 = x;
        double r571000 = y;
        double r571001 = z;
        double r571002 = t;
        double r571003 = r571001 - r571002;
        double r571004 = a;
        double r571005 = r571001 - r571004;
        double r571006 = r571003 / r571005;
        double r571007 = r571000 * r571006;
        double r571008 = r570999 + r571007;
        return r571008;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r571009 = y;
        double r571010 = z;
        double r571011 = a;
        double r571012 = r571010 - r571011;
        double r571013 = t;
        double r571014 = r571010 - r571013;
        double r571015 = r571012 / r571014;
        double r571016 = r571009 / r571015;
        double r571017 = x;
        double r571018 = r571016 + r571017;
        return r571018;
}

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

Original1.4
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  2. Simplified1.4

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

  4. Applied clear-num1.5

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

  6. Applied fma-udef1.5

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

  7. Simplified1.3

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

  8. Final simplification1.3

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

Reproduce

herbie shell --seed 2020045 +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)))))