Average Error: 1.4 → 1.4
Time: 4.6s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{z - t}{z - a} \cdot y + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{z - t}{z - a} \cdot y + x
double f(double x, double y, double z, double t, double a) {
        double r641510 = x;
        double r641511 = y;
        double r641512 = z;
        double r641513 = t;
        double r641514 = r641512 - r641513;
        double r641515 = a;
        double r641516 = r641512 - r641515;
        double r641517 = r641514 / r641516;
        double r641518 = r641511 * r641517;
        double r641519 = r641510 + r641518;
        return r641519;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r641520 = z;
        double r641521 = t;
        double r641522 = r641520 - r641521;
        double r641523 = a;
        double r641524 = r641520 - r641523;
        double r641525 = r641522 / r641524;
        double r641526 = y;
        double r641527 = r641525 * r641526;
        double r641528 = x;
        double r641529 = r641527 + r641528;
        return r641529;
}

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
Target1.2
Herbie1.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  3. Applied add-cbrt-cube20.7

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

  4. Applied add-cbrt-cube40.3

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

  5. Applied cbrt-undiv41.2

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

  6. Simplified11.0

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

  8. Applied *-un-lft-identity11.0

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

  9. Applied associate-*l*11.0

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

  10. Simplified1.4

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

  11. Final simplification1.4

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

Reproduce

herbie shell --seed 2019362 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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