Average Error: 0.1 → 0.0
Time: 5.8s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
↓
\[\mathsf{fma}\left(\frac{t}{16.0}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4.0}\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c
↓
\mathsf{fma}\left(\frac{t}{16.0}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4.0}\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3154022 = x;
        double r3154023 = y;
        double r3154024 = r3154022 * r3154023;
        double r3154025 = z;
        double r3154026 = t;
        double r3154027 = r3154025 * r3154026;
        double r3154028 = 16.0;
        double r3154029 = r3154027 / r3154028;
        double r3154030 = r3154024 + r3154029;
        double r3154031 = a;
        double r3154032 = b;
        double r3154033 = r3154031 * r3154032;
        double r3154034 = 4.0;
        double r3154035 = r3154033 / r3154034;
        double r3154036 = r3154030 - r3154035;
        double r3154037 = c;
        double r3154038 = r3154036 + r3154037;
        return r3154038;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3154039 = t;
        double r3154040 = 16.0;
        double r3154041 = r3154039 / r3154040;
        double r3154042 = z;
        double r3154043 = y;
        double r3154044 = x;
        double r3154045 = c;
        double r3154046 = fma(r3154043, r3154044, r3154045);
        double r3154047 = b;
        double r3154048 = a;
        double r3154049 = r3154047 * r3154048;
        double r3154050 = 4.0;
        double r3154051 = r3154049 / r3154050;
        double r3154052 = r3154046 - r3154051;
        double r3154053 = fma(r3154041, r3154042, r3154052);
        return r3154053;
}

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

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(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))