Average Error: 1.5 → 0.6
Time: 5.0s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + \left(y \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\]
x + y \cdot \frac{z - t}{a - t}
↓
x + \left(y \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}
double f(double x, double y, double z, double t, double a) {
        double r579176 = x;
        double r579177 = y;
        double r579178 = z;
        double r579179 = t;
        double r579180 = r579178 - r579179;
        double r579181 = a;
        double r579182 = r579181 - r579179;
        double r579183 = r579180 / r579182;
        double r579184 = r579177 * r579183;
        double r579185 = r579176 + r579184;
        return r579185;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r579186 = x;
        double r579187 = y;
        double r579188 = z;
        double r579189 = t;
        double r579190 = r579188 - r579189;
        double r579191 = cbrt(r579190);
        double r579192 = r579191 * r579191;
        double r579193 = a;
        double r579194 = r579193 - r579189;
        double r579195 = cbrt(r579194);
        double r579196 = r579195 * r579195;
        double r579197 = r579192 / r579196;
        double r579198 = r579187 * r579197;
        double r579199 = r579191 / r579195;
        double r579200 = r579198 * r579199;
        double r579201 = r579186 + r579200;
        return r579201;
}

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

Original1.5
Target0.4
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.5

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

  3. Applied add-cube-cbrt2.0

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

  4. Applied add-cube-cbrt1.8

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

  5. Applied times-frac1.8

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

  6. Applied associate-*r*0.6

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

  7. Final simplification0.6

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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