Average Error: 2.1 → 1.0
Time: 21.7s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[x + \left(\sqrt{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \left(\left|\frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right| \cdot \left(y - x\right)\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
x + \left(\sqrt{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \left(\left|\frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right| \cdot \left(y - x\right)\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}
double f(double x, double y, double z, double t) {
        double r436323 = x;
        double r436324 = y;
        double r436325 = r436324 - r436323;
        double r436326 = z;
        double r436327 = t;
        double r436328 = r436326 / r436327;
        double r436329 = r436325 * r436328;
        double r436330 = r436323 + r436329;
        return r436330;
}
↓
double f(double x, double y, double z, double t) {
        double r436331 = x;
        double r436332 = z;
        double r436333 = cbrt(r436332);
        double r436334 = r436333 * r436333;
        double r436335 = t;
        double r436336 = cbrt(r436335);
        double r436337 = r436336 * r436336;
        double r436338 = r436334 / r436337;
        double r436339 = sqrt(r436338);
        double r436340 = r436333 / r436336;
        double r436341 = fabs(r436340);
        double r436342 = y;
        double r436343 = r436342 - r436331;
        double r436344 = r436341 * r436343;
        double r436345 = r436339 * r436344;
        double r436346 = r436345 * r436340;
        double r436347 = r436331 + r436346;
        return r436347;
}

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

Original2.1
Target2.2
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 2.1

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

  3. Applied add-cube-cbrt2.6

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

  4. Applied add-cube-cbrt2.7

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

  5. Applied times-frac2.7

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

  6. Applied associate-*r*1.0

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

  7. Simplified1.0

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

  9. Applied add-sqr-sqrt1.0

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

  10. Applied associate-*l*1.0

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

  11. Simplified1.0

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

  12. Final simplification1.0

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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