Average Error: 1.4 → 1.3
Time: 10.2s
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 r601753 = x;
        double r601754 = y;
        double r601755 = z;
        double r601756 = t;
        double r601757 = r601755 - r601756;
        double r601758 = a;
        double r601759 = r601755 - r601758;
        double r601760 = r601757 / r601759;
        double r601761 = r601754 * r601760;
        double r601762 = r601753 + r601761;
        return r601762;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r601763 = y;
        double r601764 = z;
        double r601765 = a;
        double r601766 = r601764 - r601765;
        double r601767 = t;
        double r601768 = r601764 - r601767;
        double r601769 = r601766 / r601768;
        double r601770 = r601763 / r601769;
        double r601771 = x;
        double r601772 = r601770 + r601771;
        return r601772;
}

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)))))