Average Error: 6.4 → 1.8
Time: 18.0s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\frac{\sqrt[3]{y - x}}{\frac{t}{\sqrt[3]{z}}} \cdot \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)\right) + x\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\frac{\sqrt[3]{y - x}}{\frac{t}{\sqrt[3]{z}}} \cdot \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)\right) + x
double f(double x, double y, double z, double t) {
        double r23139587 = x;
        double r23139588 = y;
        double r23139589 = r23139588 - r23139587;
        double r23139590 = z;
        double r23139591 = r23139589 * r23139590;
        double r23139592 = t;
        double r23139593 = r23139591 / r23139592;
        double r23139594 = r23139587 + r23139593;
        return r23139594;
}
↓
double f(double x, double y, double z, double t) {
        double r23139595 = y;
        double r23139596 = x;
        double r23139597 = r23139595 - r23139596;
        double r23139598 = cbrt(r23139597);
        double r23139599 = t;
        double r23139600 = z;
        double r23139601 = cbrt(r23139600);
        double r23139602 = r23139599 / r23139601;
        double r23139603 = r23139598 / r23139602;
        double r23139604 = r23139601 * r23139601;
        double r23139605 = r23139598 * r23139598;
        double r23139606 = r23139604 * r23139605;
        double r23139607 = r23139603 * r23139606;
        double r23139608 = r23139607 + r23139596;
        return r23139608;
}

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

Original6.4
Target1.8
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 6.4

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

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

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

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

  7. Applied times-frac2.4

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

  8. Applied add-cube-cbrt2.5

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

  9. Applied times-frac1.8

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

  10. Simplified1.8

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

  11. Final simplification1.8

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

Reproduce

herbie shell --seed 2019162 
(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)))