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 r577605 = x;
        double r577606 = y;
        double r577607 = z;
        double r577608 = t;
        double r577609 = r577607 - r577608;
        double r577610 = r577606 * r577609;
        double r577611 = a;
        double r577612 = r577611 - r577608;
        double r577613 = r577610 / r577612;
        double r577614 = r577605 + r577613;
        return r577614;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r577615 = z;
        double r577616 = a;
        double r577617 = t;
        double r577618 = r577616 - r577617;
        double r577619 = r577615 / r577618;
        double r577620 = r577617 / r577618;
        double r577621 = r577619 - r577620;
        double r577622 = y;
        double r577623 = r577621 * r577622;
        double r577624 = x;
        double r577625 = r577623 + r577624;
        return r577625;
}

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))))