Average Error: 1.4 → 1.3
Time: 4.7s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\frac{y}{\frac{a - t}{z - t}} + x\]
x + y \cdot \frac{z - t}{a - t}
↓
\frac{y}{\frac{a - t}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r1128474 = x;
        double r1128475 = y;
        double r1128476 = z;
        double r1128477 = t;
        double r1128478 = r1128476 - r1128477;
        double r1128479 = a;
        double r1128480 = r1128479 - r1128477;
        double r1128481 = r1128478 / r1128480;
        double r1128482 = r1128475 * r1128481;
        double r1128483 = r1128474 + r1128482;
        return r1128483;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1128484 = y;
        double r1128485 = a;
        double r1128486 = t;
        double r1128487 = r1128485 - r1128486;
        double r1128488 = z;
        double r1128489 = r1128488 - r1128486;
        double r1128490 = r1128487 / r1128489;
        double r1128491 = r1128484 / r1128490;
        double r1128492 = x;
        double r1128493 = r1128491 + r1128492;
        return r1128493;
}

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
Target0.4
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.4

    \[x + y \cdot \frac{z - t}{a - t}\]
  2. Using strategy rm

  3. Applied clear-num1.4

    \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}}\]
  4. Using strategy rm

  5. Applied pow11.4

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

  6. Applied pow11.4

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

  7. Applied pow-prod-down1.4

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

  8. Simplified1.3

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

  9. Final simplification1.3

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

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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