Average Error: 6.5 → 1.7
Time: 44.5s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}} \cdot \frac{\frac{\sqrt[3]{t}}{z}}{\sqrt[3]{\sqrt[3]{y - x}}}} + x\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}} \cdot \frac{\frac{\sqrt[3]{t}}{z}}{\sqrt[3]{\sqrt[3]{y - x}}}} + x
double f(double x, double y, double z, double t) {
        double r25351358 = x;
        double r25351359 = y;
        double r25351360 = r25351359 - r25351358;
        double r25351361 = z;
        double r25351362 = r25351360 * r25351361;
        double r25351363 = t;
        double r25351364 = r25351362 / r25351363;
        double r25351365 = r25351358 + r25351364;
        return r25351365;
}
↓
double f(double x, double y, double z, double t) {
        double r25351366 = y;
        double r25351367 = x;
        double r25351368 = r25351366 - r25351367;
        double r25351369 = cbrt(r25351368);
        double r25351370 = r25351369 * r25351369;
        double r25351371 = t;
        double r25351372 = cbrt(r25351371);
        double r25351373 = r25351372 * r25351372;
        double r25351374 = cbrt(r25351370);
        double r25351375 = r25351373 / r25351374;
        double r25351376 = z;
        double r25351377 = r25351372 / r25351376;
        double r25351378 = cbrt(r25351369);
        double r25351379 = r25351377 / r25351378;
        double r25351380 = r25351375 * r25351379;
        double r25351381 = r25351370 / r25351380;
        double r25351382 = r25351381 + r25351367;
        return r25351382;
}

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
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533004570453352523209034680317 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700714748507147332551979944314 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 6.5

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

  3. Applied associate-/l*1.8

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

  5. Applied add-cube-cbrt2.4

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

  6. Applied associate-/l*2.4

    \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\frac{\frac{t}{z}}{\sqrt[3]{y - x}}}}\]
  7. Using strategy rm

  8. Applied add-cube-cbrt2.4

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

  9. Applied cbrt-prod2.4

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

  10. Applied *-un-lft-identity2.4

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

  11. Applied add-cube-cbrt2.6

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

  12. Applied times-frac2.6

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

  13. Applied times-frac1.7

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

  14. Simplified1.7

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

  15. Final simplification1.7

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"

  :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)))