Average Error: 1.4 → 1.2
Time: 6.6s
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 r548216 = x;
        double r548217 = y;
        double r548218 = z;
        double r548219 = t;
        double r548220 = r548218 - r548219;
        double r548221 = a;
        double r548222 = r548218 - r548221;
        double r548223 = r548220 / r548222;
        double r548224 = r548217 * r548223;
        double r548225 = r548216 + r548224;
        return r548225;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r548226 = y;
        double r548227 = z;
        double r548228 = a;
        double r548229 = r548227 - r548228;
        double r548230 = t;
        double r548231 = r548227 - r548230;
        double r548232 = r548229 / r548231;
        double r548233 = r548226 / r548232;
        double r548234 = x;
        double r548235 = r548233 + r548234;
        return r548235;
}

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

Derivation

  1. Initial program 1.4

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

  2. Simplified1.4

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

  4. Applied clear-num1.5

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

  6. Applied fma-udef1.5

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

  7. Simplified1.2

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

  8. Final simplification1.2

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

Reproduce

herbie shell --seed 2020033 +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)))))