Average Error: 2.1 → 1.0
Time: 14.7s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[x + \left(\sqrt{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \left(\left(y - x\right) \cdot \left|\frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right|\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\]
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(y - x\right) \cdot \left|\frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right|\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}
double f(double x, double y, double z, double t) {
        double r493506 = x;
        double r493507 = y;
        double r493508 = r493507 - r493506;
        double r493509 = z;
        double r493510 = t;
        double r493511 = r493509 / r493510;
        double r493512 = r493508 * r493511;
        double r493513 = r493506 + r493512;
        return r493513;
}
↓
double f(double x, double y, double z, double t) {
        double r493514 = x;
        double r493515 = z;
        double r493516 = cbrt(r493515);
        double r493517 = r493516 * r493516;
        double r493518 = t;
        double r493519 = cbrt(r493518);
        double r493520 = r493519 * r493519;
        double r493521 = r493517 / r493520;
        double r493522 = sqrt(r493521);
        double r493523 = y;
        double r493524 = r493523 - r493514;
        double r493525 = r493516 / r493519;
        double r493526 = fabs(r493525);
        double r493527 = r493524 * r493526;
        double r493528 = r493522 * r493527;
        double r493529 = r493528 * r493525;
        double r493530 = r493514 + r493529;
        return r493530;
}

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

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

  12. Final simplification1.0

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

Reproduce

herbie shell --seed 2019212 
(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))))