Average Error: 6.6 → 2.0
Time: 5.9s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[x + \frac{\sqrt[3]{y - x}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y - x}}} \cdot \frac{\sqrt[3]{y - x}}{\frac{\sqrt[3]{t}}{z}}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
x + \frac{\sqrt[3]{y - x}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y - x}}} \cdot \frac{\sqrt[3]{y - x}}{\frac{\sqrt[3]{t}}{z}}
double f(double x, double y, double z, double t) {
        double r468644 = x;
        double r468645 = y;
        double r468646 = r468645 - r468644;
        double r468647 = z;
        double r468648 = r468646 * r468647;
        double r468649 = t;
        double r468650 = r468648 / r468649;
        double r468651 = r468644 + r468650;
        return r468651;
}
↓
double f(double x, double y, double z, double t) {
        double r468652 = x;
        double r468653 = y;
        double r468654 = r468653 - r468652;
        double r468655 = cbrt(r468654);
        double r468656 = t;
        double r468657 = cbrt(r468656);
        double r468658 = r468657 * r468657;
        double r468659 = r468658 / r468655;
        double r468660 = r468655 / r468659;
        double r468661 = z;
        double r468662 = r468657 / r468661;
        double r468663 = r468655 / r468662;
        double r468664 = r468660 * r468663;
        double r468665 = r468652 + r468664;
        return r468665;
}

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

Original6.6
Target2.1
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 6.6

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

  3. Applied associate-/l*1.8

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

  5. Applied *-un-lft-identity1.8

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

  6. Applied add-cube-cbrt2.3

    \[\leadsto x + \frac{y - x}{\frac{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}{1 \cdot z}}\]

  7. Applied times-frac2.3

    \[\leadsto x + \frac{y - x}{\color{blue}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{1} \cdot \frac{\sqrt[3]{t}}{z}}}\]

  8. Applied add-cube-cbrt2.5

    \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{1} \cdot \frac{\sqrt[3]{t}}{z}}\]

  9. Applied times-frac2.0

    \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{1}} \cdot \frac{\sqrt[3]{y - x}}{\frac{\sqrt[3]{t}}{z}}}\]

  10. Simplified2.0

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

  11. Final simplification2.0

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

Reproduce

herbie shell --seed 2020081 
(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)))