Average Error: 0.1 → 0.0
Time: 5.8s
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 r239324 = x;
        double r239325 = y;
        double r239326 = r239324 * r239325;
        double r239327 = z;
        double r239328 = t;
        double r239329 = r239327 * r239328;
        double r239330 = 16.0;
        double r239331 = r239329 / r239330;
        double r239332 = r239326 + r239331;
        double r239333 = a;
        double r239334 = b;
        double r239335 = r239333 * r239334;
        double r239336 = 4.0;
        double r239337 = r239335 / r239336;
        double r239338 = r239332 - r239337;
        double r239339 = c;
        double r239340 = r239338 + r239339;
        return r239340;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r239341 = x;
        double r239342 = y;
        double r239343 = r239341 * r239342;
        double r239344 = z;
        double r239345 = 16.0;
        double r239346 = sqrt(r239345);
        double r239347 = r239344 / r239346;
        double r239348 = t;
        double r239349 = r239348 / r239346;
        double r239350 = r239347 * r239349;
        double r239351 = r239343 + r239350;
        double r239352 = a;
        double r239353 = b;
        double r239354 = r239352 * r239353;
        double r239355 = 4.0;
        double r239356 = r239354 / r239355;
        double r239357 = r239351 - r239356;
        double r239358 = c;
        double r239359 = r239357 + r239358;
        return r239359;
}

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-frac0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020002 
(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))