Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A

Average Error: 1.3 → 1.2

Time: 15.0s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r478493 = x;
        double r478494 = y;
        double r478495 = z;
        double r478496 = t;
        double r478497 = r478495 - r478496;
        double r478498 = a;
        double r478499 = r478495 - r478498;
        double r478500 = r478497 / r478499;
        double r478501 = r478494 * r478500;
        double r478502 = r478493 + r478501;
        return r478502;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r478503 = y;
        double r478504 = z;
        double r478505 = a;
        double r478506 = r478504 - r478505;
        double r478507 = t;
        double r478508 = r478504 - r478507;
        double r478509 = r478506 / r478508;
        double r478510 = r478503 / r478509;
        double r478511 = x;
        double r478512 = r478510 + r478511;
        return r478512;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.3
Target	1.2
Herbie	1.2

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

Derivation

1. Split input into 2 regimes

2. if t < 1.287048790828237e+120

   1. Initial program 1.0

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

   3. Applied clear-num 1.1

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

   5. Applied *-un-lft-identity 1.1

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

   6. Applied associate-*l* 1.1

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

   7. Simplified 1.0

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

   if 1.287048790828237e+120 < t

   1. Initial program 3.3

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

   3. Applied clear-num 3.3

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

   5. Applied *-un-lft-identity 3.3

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

   6. Applied associate-*l* 3.3

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

   7. Simplified 3.1

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

   9. Applied add-cube-cbrt 3.6

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

   10. Applied *-un-lft-identity 3.6

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

   11. Applied times-frac 3.6

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

   12. Applied add-cube-cbrt 3.8

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

   13. Applied times-frac 5.1

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

   14. Simplified 5.1

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

4. Final simplification 1.2

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

Reproduce

herbie shell --seed 2019297 
(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)))))