Average Error: 10.9 → 1.2
Time: 3.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x
double f(double x, double y, double z, double t, double a) {
        double r560719 = x;
        double r560720 = y;
        double r560721 = z;
        double r560722 = t;
        double r560723 = r560721 - r560722;
        double r560724 = r560720 * r560723;
        double r560725 = a;
        double r560726 = r560725 - r560722;
        double r560727 = r560724 / r560726;
        double r560728 = r560719 + r560727;
        return r560728;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r560729 = z;
        double r560730 = a;
        double r560731 = t;
        double r560732 = r560730 - r560731;
        double r560733 = r560729 / r560732;
        double r560734 = r560731 / r560732;
        double r560735 = r560733 - r560734;
        double r560736 = y;
        double r560737 = r560735 * r560736;
        double r560738 = x;
        double r560739 = r560737 + r560738;
        return r560739;
}

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

Original10.9
Target1.1
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.9

    \[x + \frac{y \cdot \left(z - t\right)}{a - t}\]

  2. Simplified2.7

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

  4. Applied clear-num2.9

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

  6. Applied fma-udef2.9

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

  7. Simplified2.8

    \[\leadsto \color{blue}{\frac{z - t}{\frac{a - t}{y}}} + x\]
  8. Using strategy rm

  9. Applied associate-/r/1.2

    \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot y} + x\]
  10. Using strategy rm

  11. Applied div-sub1.2

    \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \cdot y + x\]

  12. Final simplification1.2

    \[\leadsto \left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y + x\]

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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