Average Error: 1.2 → 1.1
Time: 20.5s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + y \cdot \frac{z - t}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r25125211 = x;
        double r25125212 = y;
        double r25125213 = z;
        double r25125214 = t;
        double r25125215 = r25125213 - r25125214;
        double r25125216 = a;
        double r25125217 = r25125216 - r25125214;
        double r25125218 = r25125215 / r25125217;
        double r25125219 = r25125212 * r25125218;
        double r25125220 = r25125211 + r25125219;
        return r25125220;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25125221 = x;
        double r25125222 = y;
        double r25125223 = a;
        double r25125224 = t;
        double r25125225 = r25125223 - r25125224;
        double r25125226 = z;
        double r25125227 = r25125226 - r25125224;
        double r25125228 = r25125225 / r25125227;
        double r25125229 = r25125222 / r25125228;
        double r25125230 = r25125221 + r25125229;
        return r25125230;
}

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

Original1.2
Target0.5
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.2

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

  3. Applied add-cube-cbrt1.7

    \[\leadsto x + \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} \cdot \frac{z - t}{a - t}\]

  4. Applied associate-*l*1.7

    \[\leadsto x + \color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \frac{z - t}{a - t}\right)}\]
  5. Using strategy rm

  6. Applied pow11.7

    \[\leadsto x + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \color{blue}{{\left(\frac{z - t}{a - t}\right)}^{1}}\right)\]

  7. Applied pow11.7

    \[\leadsto x + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\color{blue}{{\left(\sqrt[3]{y}\right)}^{1}} \cdot {\left(\frac{z - t}{a - t}\right)}^{1}\right)\]

  8. Applied pow-prod-down1.7

    \[\leadsto x + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \color{blue}{{\left(\sqrt[3]{y} \cdot \frac{z - t}{a - t}\right)}^{1}}\]

  9. Applied pow11.7

    \[\leadsto x + \left(\sqrt[3]{y} \cdot \color{blue}{{\left(\sqrt[3]{y}\right)}^{1}}\right) \cdot {\left(\sqrt[3]{y} \cdot \frac{z - t}{a - t}\right)}^{1}\]

  10. Applied pow11.7

    \[\leadsto x + \left(\color{blue}{{\left(\sqrt[3]{y}\right)}^{1}} \cdot {\left(\sqrt[3]{y}\right)}^{1}\right) \cdot {\left(\sqrt[3]{y} \cdot \frac{z - t}{a - t}\right)}^{1}\]

  11. Applied pow-prod-down1.7

    \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)}^{1}} \cdot {\left(\sqrt[3]{y} \cdot \frac{z - t}{a - t}\right)}^{1}\]

  12. Applied pow-prod-down1.7

    \[\leadsto x + \color{blue}{{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \frac{z - t}{a - t}\right)\right)}^{1}}\]

  13. Simplified1.1

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

  14. Final simplification1.1

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"

  :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)))))