Average Error: 11.1 → 1.3
Time: 6.2s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\frac{\frac{z - t}{a - t}}{\frac{1}{y}} + x\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\frac{\frac{z - t}{a - t}}{\frac{1}{y}} + x
double f(double x, double y, double z, double t, double a) {
        double r774485 = x;
        double r774486 = y;
        double r774487 = z;
        double r774488 = t;
        double r774489 = r774487 - r774488;
        double r774490 = r774486 * r774489;
        double r774491 = a;
        double r774492 = r774491 - r774488;
        double r774493 = r774490 / r774492;
        double r774494 = r774485 + r774493;
        return r774494;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r774495 = z;
        double r774496 = t;
        double r774497 = r774495 - r774496;
        double r774498 = a;
        double r774499 = r774498 - r774496;
        double r774500 = r774497 / r774499;
        double r774501 = 1.0;
        double r774502 = y;
        double r774503 = r774501 / r774502;
        double r774504 = r774500 / r774503;
        double r774505 = x;
        double r774506 = r774504 + r774505;
        return r774506;
}

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

Original11.1
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 11.1

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

  2. Simplified2.8

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

  4. Applied clear-num3.0

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

  6. Applied fma-udef3.0

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

  7. Simplified2.8

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

  9. Applied div-inv2.9

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

  10. Applied associate-/r*1.3

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

  11. Final simplification1.3

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

Reproduce

herbie shell --seed 2020060 +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))))