Average Error: 6.1 → 1.6
Time: 17.7s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\frac{\sqrt[3]{t}}{\frac{\sqrt[3]{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}}{\sqrt[3]{t}}} \cdot \frac{\frac{\sqrt[3]{t}}{z}}{\sqrt[3]{\sqrt[3]{y - x}}}} + x\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\frac{\sqrt[3]{t}}{\frac{\sqrt[3]{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}}{\sqrt[3]{t}}} \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 r20667049 = x;
        double r20667050 = y;
        double r20667051 = r20667050 - r20667049;
        double r20667052 = z;
        double r20667053 = r20667051 * r20667052;
        double r20667054 = t;
        double r20667055 = r20667053 / r20667054;
        double r20667056 = r20667049 + r20667055;
        return r20667056;
}
↓
double f(double x, double y, double z, double t) {
        double r20667057 = y;
        double r20667058 = x;
        double r20667059 = r20667057 - r20667058;
        double r20667060 = cbrt(r20667059);
        double r20667061 = r20667060 * r20667060;
        double r20667062 = t;
        double r20667063 = cbrt(r20667062);
        double r20667064 = cbrt(r20667061);
        double r20667065 = r20667064 / r20667063;
        double r20667066 = r20667063 / r20667065;
        double r20667067 = z;
        double r20667068 = r20667063 / r20667067;
        double r20667069 = cbrt(r20667060);
        double r20667070 = r20667068 / r20667069;
        double r20667071 = r20667066 * r20667070;
        double r20667072 = r20667061 / r20667071;
        double r20667073 = r20667072 + r20667058;
        return r20667073;
}

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

Original6.1
Target1.9
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 6.1

    \[x + \frac{\left(y - x\right) \cdot z}{t}\]
  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-cbrt2.3

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

  6. Applied associate-/l*2.3

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

  8. Applied add-cube-cbrt2.3

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

  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-cbrt2.5

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

  12. Applied times-frac2.5

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

  13. Applied times-frac1.6

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

  14. Simplified1.6

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

  15. Final simplification1.6

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

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)))