Average Error: 1.9 → 0.9
Time: 12.6s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} + t
double f(double x, double y, double z, double t) {
        double r7909149 = x;
        double r7909150 = y;
        double r7909151 = r7909149 / r7909150;
        double r7909152 = z;
        double r7909153 = t;
        double r7909154 = r7909152 - r7909153;
        double r7909155 = r7909151 * r7909154;
        double r7909156 = r7909155 + r7909153;
        return r7909156;
}
↓
double f(double x, double y, double z, double t) {
        double r7909157 = x;
        double r7909158 = cbrt(r7909157);
        double r7909159 = y;
        double r7909160 = cbrt(r7909159);
        double r7909161 = r7909158 / r7909160;
        double r7909162 = z;
        double r7909163 = t;
        double r7909164 = r7909162 - r7909163;
        double r7909165 = r7909161 * r7909164;
        double r7909166 = r7909158 * r7909158;
        double r7909167 = r7909166 * r7909158;
        double r7909168 = cbrt(r7909167);
        double r7909169 = r7909158 * r7909168;
        double r7909170 = r7909160 * r7909160;
        double r7909171 = r7909169 / r7909170;
        double r7909172 = r7909165 * r7909171;
        double r7909173 = r7909172 + r7909163;
        return r7909173;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.9
Target2.1
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 1.9

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

  3. Applied add-cube-cbrt2.5

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

  4. Applied add-cube-cbrt2.6

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

  5. Applied times-frac2.6

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

  6. Applied associate-*l*0.9

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

  8. Applied add-cbrt-cube0.9

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

  9. Final simplification0.9

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(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))