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

Average Error: 10.9 → 1.0

Time: 4.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r491091 = x;
        double r491092 = y;
        double r491093 = z;
        double r491094 = r491092 - r491093;
        double r491095 = t;
        double r491096 = r491094 * r491095;
        double r491097 = a;
        double r491098 = r491097 - r491093;
        double r491099 = r491096 / r491098;
        double r491100 = r491091 + r491099;
        return r491100;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r491101 = x;
        double r491102 = y;
        double r491103 = z;
        double r491104 = r491102 - r491103;
        double r491105 = cbrt(r491104);
        double r491106 = r491105 * r491105;
        double r491107 = a;
        double r491108 = r491107 - r491103;
        double r491109 = cbrt(r491108);
        double r491110 = r491106 / r491109;
        double r491111 = r491105 / r491109;
        double r491112 = t;
        double r491113 = r491112 / r491109;
        double r491114 = r491111 * r491113;
        double r491115 = r491110 * r491114;
        double r491116 = r491101 + r491115;
        return r491116;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.9
Target	0.6
Herbie	1.0

\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

1. Initial program 10.9

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

3. Applied add-cube-cbrt 11.3

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

4. Applied times-frac 1.7

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

6. Applied add-cube-cbrt 1.6

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

7. Applied times-frac 1.6

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

8. Applied associate-*l* 1.0

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

9. Final simplification 1.0

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

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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