Average Error: 0.1 → 0.1
Time: 21.2s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
↓
\[\left(\left(z \cdot \frac{t}{16.0} + x \cdot y\right) - \frac{a \cdot b}{4.0}\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c
↓
\left(\left(z \cdot \frac{t}{16.0} + x \cdot y\right) - \frac{a \cdot b}{4.0}\right) + c
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r13020069 = x;
        double r13020070 = y;
        double r13020071 = r13020069 * r13020070;
        double r13020072 = z;
        double r13020073 = t;
        double r13020074 = r13020072 * r13020073;
        double r13020075 = 16.0;
        double r13020076 = r13020074 / r13020075;
        double r13020077 = r13020071 + r13020076;
        double r13020078 = a;
        double r13020079 = b;
        double r13020080 = r13020078 * r13020079;
        double r13020081 = 4.0;
        double r13020082 = r13020080 / r13020081;
        double r13020083 = r13020077 - r13020082;
        double r13020084 = c;
        double r13020085 = r13020083 + r13020084;
        return r13020085;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r13020086 = z;
        double r13020087 = t;
        double r13020088 = 16.0;
        double r13020089 = r13020087 / r13020088;
        double r13020090 = r13020086 * r13020089;
        double r13020091 = x;
        double r13020092 = y;
        double r13020093 = r13020091 * r13020092;
        double r13020094 = r13020090 + r13020093;
        double r13020095 = a;
        double r13020096 = b;
        double r13020097 = r13020095 * r13020096;
        double r13020098 = 4.0;
        double r13020099 = r13020097 / r13020098;
        double r13020100 = r13020094 - r13020099;
        double r13020101 = c;
        double r13020102 = r13020100 + r13020101;
        return r13020102;
}

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

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.1

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{\color{blue}{1 \cdot 16.0}}\right) - \frac{a \cdot b}{4.0}\right) + c\]

  4. Applied times-frac0.1

    \[\leadsto \left(\left(x \cdot y + \color{blue}{\frac{z}{1} \cdot \frac{t}{16.0}}\right) - \frac{a \cdot b}{4.0}\right) + c\]

  5. Simplified0.1

    \[\leadsto \left(\left(x \cdot y + \color{blue}{z} \cdot \frac{t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]

  6. Final simplification0.1

    \[\leadsto \left(\left(z \cdot \frac{t}{16.0} + x \cdot y\right) - \frac{a \cdot b}{4.0}\right) + c\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))