Average Error: 0.1 → 0.1
Time: 5.1s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a}{\sqrt{4}} \cdot \frac{b}{\sqrt{4}}\right) + c\]
\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 \cdot t}{16}\right) - \frac{a}{\sqrt{4}} \cdot \frac{b}{\sqrt{4}}\right) + c
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r190557 = x;
        double r190558 = y;
        double r190559 = r190557 * r190558;
        double r190560 = z;
        double r190561 = t;
        double r190562 = r190560 * r190561;
        double r190563 = 16.0;
        double r190564 = r190562 / r190563;
        double r190565 = r190559 + r190564;
        double r190566 = a;
        double r190567 = b;
        double r190568 = r190566 * r190567;
        double r190569 = 4.0;
        double r190570 = r190568 / r190569;
        double r190571 = r190565 - r190570;
        double r190572 = c;
        double r190573 = r190571 + r190572;
        return r190573;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r190574 = x;
        double r190575 = y;
        double r190576 = r190574 * r190575;
        double r190577 = z;
        double r190578 = t;
        double r190579 = r190577 * r190578;
        double r190580 = 16.0;
        double r190581 = r190579 / r190580;
        double r190582 = r190576 + r190581;
        double r190583 = a;
        double r190584 = 4.0;
        double r190585 = sqrt(r190584);
        double r190586 = r190583 / r190585;
        double r190587 = b;
        double r190588 = r190587 / r190585;
        double r190589 = r190586 * r190588;
        double r190590 = r190582 - r190589;
        double r190591 = c;
        double r190592 = r190590 + r190591;
        return r190592;
}

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

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

  4. Applied times-frac0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020027 
(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))