Average Error: 0.1 → 0.1
Time: 10.3s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\left(x \cdot y + \frac{z}{\sqrt{16}} \cdot \frac{t}{\sqrt{16}}\right) - \frac{a \cdot b}{4}\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(\left(x \cdot y + \frac{z}{\sqrt{16}} \cdot \frac{t}{\sqrt{16}}\right) - \frac{a \cdot b}{4}\right) + c
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r250789 = x;
        double r250790 = y;
        double r250791 = r250789 * r250790;
        double r250792 = z;
        double r250793 = t;
        double r250794 = r250792 * r250793;
        double r250795 = 16.0;
        double r250796 = r250794 / r250795;
        double r250797 = r250791 + r250796;
        double r250798 = a;
        double r250799 = b;
        double r250800 = r250798 * r250799;
        double r250801 = 4.0;
        double r250802 = r250800 / r250801;
        double r250803 = r250797 - r250802;
        double r250804 = c;
        double r250805 = r250803 + r250804;
        return r250805;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r250806 = x;
        double r250807 = y;
        double r250808 = r250806 * r250807;
        double r250809 = z;
        double r250810 = 16.0;
        double r250811 = sqrt(r250810);
        double r250812 = r250809 / r250811;
        double r250813 = t;
        double r250814 = r250813 / r250811;
        double r250815 = r250812 * r250814;
        double r250816 = r250808 + r250815;
        double r250817 = a;
        double r250818 = b;
        double r250819 = r250817 * r250818;
        double r250820 = 4.0;
        double r250821 = r250819 / r250820;
        double r250822 = r250816 - r250821;
        double r250823 = c;
        double r250824 = r250822 + r250823;
        return r250824;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{\color{blue}{\sqrt{16} \cdot \sqrt{16}}}\right) - \frac{a \cdot b}{4}\right) + c\]

  4. Applied times-frac0.1

    \[\leadsto \left(\left(x \cdot y + \color{blue}{\frac{z}{\sqrt{16}} \cdot \frac{t}{\sqrt{16}}}\right) - \frac{a \cdot b}{4}\right) + c\]

  5. Final simplification0.1

    \[\leadsto \left(\left(x \cdot y + \frac{z}{\sqrt{16}} \cdot \frac{t}{\sqrt{16}}\right) - \frac{a \cdot b}{4}\right) + c\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16)) (/ (* a b) 4)) c))