Average Error: 1.3 → 1.2
Time: 12.4s
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 r438380 = x;
        double r438381 = y;
        double r438382 = z;
        double r438383 = t;
        double r438384 = r438382 - r438383;
        double r438385 = a;
        double r438386 = r438385 - r438383;
        double r438387 = r438384 / r438386;
        double r438388 = r438381 * r438387;
        double r438389 = r438380 + r438388;
        return r438389;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r438390 = y;
        double r438391 = a;
        double r438392 = t;
        double r438393 = r438391 - r438392;
        double r438394 = z;
        double r438395 = r438394 - r438392;
        double r438396 = r438393 / r438395;
        double r438397 = r438390 / r438396;
        double r438398 = x;
        double r438399 = r438397 + r438398;
        return r438399;
}

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

Original1.3
Target0.3
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.4275099853550002e-37 or 9.032302851762362e-182 < y

    1. Initial program 0.6

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

    3. Applied clear-num0.7

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

    5. Applied pow10.7

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

    6. Applied pow10.7

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

    7. Applied pow-prod-down0.7

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

    8. Simplified0.6

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

    if -1.4275099853550002e-37 < y < 9.032302851762362e-182

    1. Initial program 2.6

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

    3. Applied clear-num2.6

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

    5. Applied pow12.6

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

    6. Applied pow12.6

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

    7. Applied pow-prod-down2.6

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

    8. Simplified2.4

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

    10. Applied div-inv2.4

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

    11. Applied *-un-lft-identity2.4

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

    12. Applied times-frac0.2

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

    13. Simplified0.2

      \[\leadsto x + {\left(\frac{1}{a - t} \cdot \color{blue}{\left(y \cdot \left(z - t\right)\right)}\right)}^{1}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019294 
(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 -8.50808486055124107e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.8944268627920891e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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