Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1

Average Error: 2.2 → 2.3

Time: 20.3s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r21710095 = x;
        double r21710096 = y;
        double r21710097 = r21710095 / r21710096;
        double r21710098 = z;
        double r21710099 = t;
        double r21710100 = r21710098 - r21710099;
        double r21710101 = r21710097 * r21710100;
        double r21710102 = r21710101 + r21710099;
        return r21710102;
}

↓

double f(double x, double y, double z, double t) {
        double r21710103 = t;
        double r21710104 = z;
        double r21710105 = r21710104 - r21710103;
        double r21710106 = cbrt(r21710105);
        double r21710107 = 1.0;
        double r21710108 = y;
        double r21710109 = cbrt(r21710108);
        double r21710110 = r21710109 * r21710109;
        double r21710111 = r21710107 / r21710110;
        double r21710112 = r21710106 * r21710106;
        double r21710113 = x;
        double r21710114 = r21710113 / r21710109;
        double r21710115 = r21710112 * r21710114;
        double r21710116 = r21710111 * r21710115;
        double r21710117 = r21710106 * r21710116;
        double r21710118 = r21710103 + r21710117;
        return r21710118;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.2
Target	2.4
Herbie	2.3

\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

1. Initial program 2.2

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

3. Applied add-cube-cbrt 2.7

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

4. Applied associate-*r* 2.7

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

6. Applied add-cube-cbrt 2.8

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

7. Applied *-un-lft-identity 2.8

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

8. Applied times-frac 2.8

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

9. Applied associate-*l* 2.3

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

10. Final simplification 2.3

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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