Average Error: 0.2 → 0.1
Time: 15.6s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(x \cdot y - \left(\frac{a \cdot b}{4} - c\right)\right) + \frac{t}{\frac{16}{z}}\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(x \cdot y - \left(\frac{a \cdot b}{4} - c\right)\right) + \frac{t}{\frac{16}{z}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r185282 = x;
        double r185283 = y;
        double r185284 = r185282 * r185283;
        double r185285 = z;
        double r185286 = t;
        double r185287 = r185285 * r185286;
        double r185288 = 16.0;
        double r185289 = r185287 / r185288;
        double r185290 = r185284 + r185289;
        double r185291 = a;
        double r185292 = b;
        double r185293 = r185291 * r185292;
        double r185294 = 4.0;
        double r185295 = r185293 / r185294;
        double r185296 = r185290 - r185295;
        double r185297 = c;
        double r185298 = r185296 + r185297;
        return r185298;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r185299 = x;
        double r185300 = y;
        double r185301 = r185299 * r185300;
        double r185302 = a;
        double r185303 = b;
        double r185304 = r185302 * r185303;
        double r185305 = 4.0;
        double r185306 = r185304 / r185305;
        double r185307 = c;
        double r185308 = r185306 - r185307;
        double r185309 = r185301 - r185308;
        double r185310 = t;
        double r185311 = 16.0;
        double r185312 = z;
        double r185313 = r185311 / r185312;
        double r185314 = r185310 / r185313;
        double r185315 = r185309 + r185314;
        return r185315;
}

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 0.2

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

  3. Applied add-sqr-sqrt0.2

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

  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

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

Reproduce

herbie shell --seed 2019291 
(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))