Average Error: 0.1 → 0.1
Time: 17.9s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\frac{t}{\frac{16}{z}} + \left(\left(c + x \cdot y\right) - \frac{a \cdot b}{4}\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\frac{t}{\frac{16}{z}} + \left(\left(c + x \cdot y\right) - \frac{a \cdot b}{4}\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r170285 = x;
        double r170286 = y;
        double r170287 = r170285 * r170286;
        double r170288 = z;
        double r170289 = t;
        double r170290 = r170288 * r170289;
        double r170291 = 16.0;
        double r170292 = r170290 / r170291;
        double r170293 = r170287 + r170292;
        double r170294 = a;
        double r170295 = b;
        double r170296 = r170294 * r170295;
        double r170297 = 4.0;
        double r170298 = r170296 / r170297;
        double r170299 = r170293 - r170298;
        double r170300 = c;
        double r170301 = r170299 + r170300;
        return r170301;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r170302 = t;
        double r170303 = 16.0;
        double r170304 = z;
        double r170305 = r170303 / r170304;
        double r170306 = r170302 / r170305;
        double r170307 = c;
        double r170308 = x;
        double r170309 = y;
        double r170310 = r170308 * r170309;
        double r170311 = r170307 + r170310;
        double r170312 = a;
        double r170313 = b;
        double r170314 = r170312 * r170313;
        double r170315 = 4.0;
        double r170316 = r170314 / r170315;
        double r170317 = r170311 - r170316;
        double r170318 = r170306 + r170317;
        return r170318;
}

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. Using strategy rm

  6. Applied clear-num0.1

    \[\leadsto \left(\left(x \cdot y + \frac{z}{\sqrt{16}} \cdot \frac{t}{\sqrt{16}}\right) - \color{blue}{\frac{1}{\frac{4}{a \cdot b}}}\right) + c\]

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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))