Average Error: 0.1 → 0.0
Time: 8.9s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{a}{4}, -b, c\right)\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{a}{4}, -b, c\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r187043 = x;
        double r187044 = y;
        double r187045 = r187043 * r187044;
        double r187046 = z;
        double r187047 = t;
        double r187048 = r187046 * r187047;
        double r187049 = 16.0;
        double r187050 = r187048 / r187049;
        double r187051 = r187045 + r187050;
        double r187052 = a;
        double r187053 = b;
        double r187054 = r187052 * r187053;
        double r187055 = 4.0;
        double r187056 = r187054 / r187055;
        double r187057 = r187051 - r187056;
        double r187058 = c;
        double r187059 = r187057 + r187058;
        return r187059;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r187060 = z;
        double r187061 = 16.0;
        double r187062 = r187060 / r187061;
        double r187063 = t;
        double r187064 = x;
        double r187065 = y;
        double r187066 = a;
        double r187067 = 4.0;
        double r187068 = r187066 / r187067;
        double r187069 = b;
        double r187070 = -r187069;
        double r187071 = c;
        double r187072 = fma(r187068, r187070, r187071);
        double r187073 = fma(r187064, r187065, r187072);
        double r187074 = fma(r187062, r187063, r187073);
        return r187074;
}

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

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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))