Average Error: 0.1 → 0.1
Time: 15.5s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\left(x \cdot y + \frac{z}{\sqrt{16}} \cdot \frac{t}{\sqrt{16}}\right) - \frac{1}{\frac{4}{a \cdot b}}\right) + c\]
\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{1}{\frac{4}{a \cdot b}}\right) + c
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r830010 = x;
        double r830011 = y;
        double r830012 = r830010 * r830011;
        double r830013 = z;
        double r830014 = t;
        double r830015 = r830013 * r830014;
        double r830016 = 16.0;
        double r830017 = r830015 / r830016;
        double r830018 = r830012 + r830017;
        double r830019 = a;
        double r830020 = b;
        double r830021 = r830019 * r830020;
        double r830022 = 4.0;
        double r830023 = r830021 / r830022;
        double r830024 = r830018 - r830023;
        double r830025 = c;
        double r830026 = r830024 + r830025;
        return r830026;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r830027 = x;
        double r830028 = y;
        double r830029 = r830027 * r830028;
        double r830030 = z;
        double r830031 = 16.0;
        double r830032 = sqrt(r830031);
        double r830033 = r830030 / r830032;
        double r830034 = t;
        double r830035 = r830034 / r830032;
        double r830036 = r830033 * r830035;
        double r830037 = r830029 + r830036;
        double r830038 = 1.0;
        double r830039 = 4.0;
        double r830040 = a;
        double r830041 = b;
        double r830042 = r830040 * r830041;
        double r830043 = r830039 / r830042;
        double r830044 = r830038 / r830043;
        double r830045 = r830037 - r830044;
        double r830046 = c;
        double r830047 = r830045 + r830046;
        return r830047;
}

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

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

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))