Average Error: 0.5 → 0.6
Time: 4.2m
Precision: 64
\[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
↓
\[\left(x1 + \left(\frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} \cdot \left(2 \cdot \left(x1 \cdot \left(\frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - 3\right)\right)\right) + \left(\sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - 6} \cdot \sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - 6}\right) \cdot \left(\sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - 6} \cdot \left(x1 \cdot x1\right)\right)\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x1\right) - x2 \cdot 2}{x1 \cdot x1 + 1} + x1\right)\right)\]
x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)
↓
\left(x1 + \left(\frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} \cdot \left(2 \cdot \left(x1 \cdot \left(\frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - 3\right)\right)\right) + \left(\sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - 6} \cdot \sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - 6}\right) \cdot \left(\sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - 6} \cdot \left(x1 \cdot x1\right)\right)\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x1\right) - x2 \cdot 2}{x1 \cdot x1 + 1} + x1\right)\right)
double f(double x1, double x2) {
        double r35111745 = x1;
        double r35111746 = 2.0;
        double r35111747 = r35111746 * r35111745;
        double r35111748 = 3.0;
        double r35111749 = r35111748 * r35111745;
        double r35111750 = r35111749 * r35111745;
        double r35111751 = x2;
        double r35111752 = r35111746 * r35111751;
        double r35111753 = r35111750 + r35111752;
        double r35111754 = r35111753 - r35111745;
        double r35111755 = r35111745 * r35111745;
        double r35111756 = 1.0;
        double r35111757 = r35111755 + r35111756;
        double r35111758 = r35111754 / r35111757;
        double r35111759 = r35111747 * r35111758;
        double r35111760 = r35111758 - r35111748;
        double r35111761 = r35111759 * r35111760;
        double r35111762 = 4.0;
        double r35111763 = r35111762 * r35111758;
        double r35111764 = 6.0;
        double r35111765 = r35111763 - r35111764;
        double r35111766 = r35111755 * r35111765;
        double r35111767 = r35111761 + r35111766;
        double r35111768 = r35111767 * r35111757;
        double r35111769 = r35111750 * r35111758;
        double r35111770 = r35111768 + r35111769;
        double r35111771 = r35111755 * r35111745;
        double r35111772 = r35111770 + r35111771;
        double r35111773 = r35111772 + r35111745;
        double r35111774 = r35111750 - r35111752;
        double r35111775 = r35111774 - r35111745;
        double r35111776 = r35111775 / r35111757;
        double r35111777 = r35111748 * r35111776;
        double r35111778 = r35111773 + r35111777;
        double r35111779 = r35111745 + r35111778;
        return r35111779;
}
↓
double f(double x1, double x2) {
        double r35111780 = x1;
        double r35111781 = x2;
        double r35111782 = 2.0;
        double r35111783 = r35111781 * r35111782;
        double r35111784 = 3.0;
        double r35111785 = r35111780 * r35111784;
        double r35111786 = r35111780 * r35111785;
        double r35111787 = r35111780 - r35111786;
        double r35111788 = r35111783 - r35111787;
        double r35111789 = r35111780 * r35111780;
        double r35111790 = 1.0;
        double r35111791 = r35111789 + r35111790;
        double r35111792 = r35111788 / r35111791;
        double r35111793 = r35111792 - r35111784;
        double r35111794 = r35111780 * r35111793;
        double r35111795 = r35111782 * r35111794;
        double r35111796 = r35111792 * r35111795;
        double r35111797 = 4.0;
        double r35111798 = r35111797 * r35111792;
        double r35111799 = 6.0;
        double r35111800 = r35111798 - r35111799;
        double r35111801 = cbrt(r35111800);
        double r35111802 = r35111801 * r35111801;
        double r35111803 = r35111801 * r35111789;
        double r35111804 = r35111802 * r35111803;
        double r35111805 = r35111796 + r35111804;
        double r35111806 = r35111780 + r35111805;
        double r35111807 = r35111806 * r35111791;
        double r35111808 = r35111786 * r35111792;
        double r35111809 = r35111786 - r35111780;
        double r35111810 = r35111809 - r35111783;
        double r35111811 = r35111810 / r35111791;
        double r35111812 = r35111784 * r35111811;
        double r35111813 = r35111812 + r35111780;
        double r35111814 = r35111808 + r35111813;
        double r35111815 = r35111807 + r35111814;
        return r35111815;
}

Error

Bits error versus x1

Bits error versus x2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

  2. Simplified0.5

    \[\leadsto \color{blue}{\left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x1\right) - x2 \cdot 2}{1 + x1 \cdot x1}\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1}\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(4 \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1} - 6\right) \cdot \left(x1 \cdot x1\right) + \left(\left(\left(\frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1} - 3\right) \cdot x1\right) \cdot 2\right) \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1}\right) + x1\right)}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt0.6

    \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x1\right) - x2 \cdot 2}{1 + x1 \cdot x1}\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1}\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(\color{blue}{\left(\left(\sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1} - 6} \cdot \sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1} - 6}\right) \cdot \sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1} - 6}\right)} \cdot \left(x1 \cdot x1\right) + \left(\left(\left(\frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1} - 3\right) \cdot x1\right) \cdot 2\right) \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1}\right) + x1\right)\]

  5. Applied associate-*l*0.6

    \[\leadsto \left(\left(x1 + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - x1\right) - x2 \cdot 2}{1 + x1 \cdot x1}\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1}\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(\color{blue}{\left(\sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1} - 6} \cdot \sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1} - 6}\right) \cdot \left(\sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1} - 6} \cdot \left(x1 \cdot x1\right)\right)} + \left(\left(\left(\frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1} - 3\right) \cdot x1\right) \cdot 2\right) \cdot \frac{x2 \cdot 2 - \left(x1 - \left(3 \cdot x1\right) \cdot x1\right)}{1 + x1 \cdot x1}\right) + x1\right)\]

  6. Final simplification0.6

    \[\leadsto \left(x1 + \left(\frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} \cdot \left(2 \cdot \left(x1 \cdot \left(\frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - 3\right)\right)\right) + \left(\sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - 6} \cdot \sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - 6}\right) \cdot \left(\sqrt[3]{4 \cdot \frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} - 6} \cdot \left(x1 \cdot x1\right)\right)\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{x2 \cdot 2 - \left(x1 - x1 \cdot \left(x1 \cdot 3\right)\right)}{x1 \cdot x1 + 1} + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x1\right) - x2 \cdot 2}{x1 \cdot x1 + 1} + x1\right)\right)\]

Reproduce

herbie shell --seed 2019120 
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6))) (+ (* x1 x1) 1)) (* (* (* 3 x1) x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (* (* x1 x1) x1)) x1) (* 3 (/ (- (- (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))))))