Average Error: 0.2 → 0.1
Time: 12.7s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\frac{z \cdot t}{16} + x \cdot y\right) - \left(a \cdot \frac{b}{4} - c\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(\frac{z \cdot t}{16} + x \cdot y\right) - \left(a \cdot \frac{b}{4} - c\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r11009986 = x;
        double r11009987 = y;
        double r11009988 = r11009986 * r11009987;
        double r11009989 = z;
        double r11009990 = t;
        double r11009991 = r11009989 * r11009990;
        double r11009992 = 16.0;
        double r11009993 = r11009991 / r11009992;
        double r11009994 = r11009988 + r11009993;
        double r11009995 = a;
        double r11009996 = b;
        double r11009997 = r11009995 * r11009996;
        double r11009998 = 4.0;
        double r11009999 = r11009997 / r11009998;
        double r11010000 = r11009994 - r11009999;
        double r11010001 = c;
        double r11010002 = r11010000 + r11010001;
        return r11010002;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r11010003 = z;
        double r11010004 = t;
        double r11010005 = r11010003 * r11010004;
        double r11010006 = 16.0;
        double r11010007 = r11010005 / r11010006;
        double r11010008 = x;
        double r11010009 = y;
        double r11010010 = r11010008 * r11010009;
        double r11010011 = r11010007 + r11010010;
        double r11010012 = a;
        double r11010013 = b;
        double r11010014 = 4.0;
        double r11010015 = r11010013 / r11010014;
        double r11010016 = r11010012 * r11010015;
        double r11010017 = c;
        double r11010018 = r11010016 - r11010017;
        double r11010019 = r11010011 - r11010018;
        return r11010019;
}

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 *-un-lft-identity0.2

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

  4. Applied times-frac0.1

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

  5. Simplified0.1

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

  7. Applied associate-+l-0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(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))