Average Error: 6.5 → 0.9
Time: 13.7s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[x + \left(\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(y - x\right)\right) \cdot \frac{1}{\frac{\sqrt[3]{t}}{\sqrt[3]{z}}}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
x + \left(\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(y - x\right)\right) \cdot \frac{1}{\frac{\sqrt[3]{t}}{\sqrt[3]{z}}}
double f(double x, double y, double z, double t) {
        double r353111 = x;
        double r353112 = y;
        double r353113 = r353112 - r353111;
        double r353114 = z;
        double r353115 = r353113 * r353114;
        double r353116 = t;
        double r353117 = r353115 / r353116;
        double r353118 = r353111 + r353117;
        return r353118;
}
↓
double f(double x, double y, double z, double t) {
        double r353119 = x;
        double r353120 = z;
        double r353121 = cbrt(r353120);
        double r353122 = r353121 * r353121;
        double r353123 = t;
        double r353124 = cbrt(r353123);
        double r353125 = r353124 * r353124;
        double r353126 = r353122 / r353125;
        double r353127 = y;
        double r353128 = r353127 - r353119;
        double r353129 = r353126 * r353128;
        double r353130 = 1.0;
        double r353131 = r353124 / r353121;
        double r353132 = r353130 / r353131;
        double r353133 = r353129 * r353132;
        double r353134 = r353119 + r353133;
        return r353134;
}

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 associate-/l*2.0

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

  5. Applied add-cube-cbrt2.5

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

  6. Applied add-cube-cbrt2.7

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

  7. Applied times-frac2.7

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

  8. Applied *-un-lft-identity2.7

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

  9. Applied times-frac1.0

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

  10. Simplified0.9

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

  12. Applied div-inv0.9

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

  13. Applied associate-*r*0.9

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

  14. Final simplification0.9

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

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.0255111955330046e-135) (- x (* (/ z t) (- x y))) (if (< x 4.2750321637007147e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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