Average Error: 0.1 → 0.1
Time: 16.7s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)\right) + c
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r224218 = x;
        double r224219 = y;
        double r224220 = r224218 * r224219;
        double r224221 = z;
        double r224222 = t;
        double r224223 = r224221 * r224222;
        double r224224 = 16.0;
        double r224225 = r224223 / r224224;
        double r224226 = r224220 + r224225;
        double r224227 = a;
        double r224228 = b;
        double r224229 = r224227 * r224228;
        double r224230 = 4.0;
        double r224231 = r224229 / r224230;
        double r224232 = r224226 - r224231;
        double r224233 = c;
        double r224234 = r224232 + r224233;
        return r224234;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r224235 = 0.0625;
        double r224236 = t;
        double r224237 = z;
        double r224238 = r224236 * r224237;
        double r224239 = r224235 * r224238;
        double r224240 = x;
        double r224241 = y;
        double r224242 = r224240 * r224241;
        double r224243 = r224239 + r224242;
        double r224244 = 0.25;
        double r224245 = a;
        double r224246 = b;
        double r224247 = r224245 * r224246;
        double r224248 = r224244 * r224247;
        double r224249 = r224243 - r224248;
        double r224250 = c;
        double r224251 = r224249 + r224250;
        return r224251;
}

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 associate-/l*0.2

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

  4. Taylor expanded around inf 0.1

    \[\leadsto \color{blue}{\left(\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)\right)} + c\]

  5. Final simplification0.1

    \[\leadsto \left(\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)\right) + c\]

Reproduce

herbie shell --seed 2019306 
(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))