Average Error: 6.5 → 0.9
Time: 19.2s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[x + \left(\left(y - x\right) \cdot \frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
x + \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}}
double f(double x, double y, double z, double t) {
        double r342645 = x;
        double r342646 = y;
        double r342647 = r342646 - r342645;
        double r342648 = z;
        double r342649 = r342647 * r342648;
        double r342650 = t;
        double r342651 = r342649 / r342650;
        double r342652 = r342645 + r342651;
        return r342652;
}
↓
double f(double x, double y, double z, double t) {
        double r342653 = x;
        double r342654 = y;
        double r342655 = r342654 - r342653;
        double r342656 = z;
        double r342657 = cbrt(r342656);
        double r342658 = r342657 * r342657;
        double r342659 = t;
        double r342660 = cbrt(r342659);
        double r342661 = r342660 * r342660;
        double r342662 = r342658 / r342661;
        double r342663 = r342655 * r342662;
        double r342664 = r342657 / r342660;
        double r342665 = r342663 * r342664;
        double r342666 = r342653 + r342665;
        return r342666;
}

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

Original6.5
Target2.0
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533004570453352523209034680317 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700714748507147332551979944314 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 6.5

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

  3. Applied *-un-lft-identity6.5

    \[\leadsto x + \frac{\left(y - x\right) \cdot z}{\color{blue}{1 \cdot t}}\]

  4. Applied times-frac2.1

    \[\leadsto x + \color{blue}{\frac{y - x}{1} \cdot \frac{z}{t}}\]

  5. Simplified2.1

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

  7. Applied add-cube-cbrt2.6

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

  8. Applied add-cube-cbrt2.7

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

  9. Applied times-frac2.7

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

  10. Applied associate-*r*0.9

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

  11. Final simplification0.9

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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