Average Error: 10.7 → 0.5
Time: 9.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{\frac{y}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{\frac{y}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}
double f(double x, double y, double z, double t, double a) {
        double r693259 = x;
        double r693260 = y;
        double r693261 = z;
        double r693262 = t;
        double r693263 = r693261 - r693262;
        double r693264 = r693260 * r693263;
        double r693265 = a;
        double r693266 = r693265 - r693262;
        double r693267 = r693264 / r693266;
        double r693268 = r693259 + r693267;
        return r693268;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r693269 = x;
        double r693270 = y;
        double r693271 = a;
        double r693272 = t;
        double r693273 = r693271 - r693272;
        double r693274 = cbrt(r693273);
        double r693275 = r693274 * r693274;
        double r693276 = z;
        double r693277 = r693276 - r693272;
        double r693278 = cbrt(r693277);
        double r693279 = r693278 * r693278;
        double r693280 = r693275 / r693279;
        double r693281 = r693270 / r693280;
        double r693282 = r693274 / r693278;
        double r693283 = r693281 / r693282;
        double r693284 = r693269 + r693283;
        return r693284;
}

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

Original10.7
Target1.3
Herbie0.5
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*1.3

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

  5. Applied add-cube-cbrt1.8

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

  6. Applied add-cube-cbrt1.6

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

  7. Applied times-frac1.6

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

  8. Applied associate-/r*0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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