Average Error: 0.1 → 0.1
Time: 22.6s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(\frac{t}{16}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4}\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(\frac{t}{16}, z, \mathsf{fma}\left(y, x, c\right) - \frac{b \cdot a}{4}\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r7639781 = x;
        double r7639782 = y;
        double r7639783 = r7639781 * r7639782;
        double r7639784 = z;
        double r7639785 = t;
        double r7639786 = r7639784 * r7639785;
        double r7639787 = 16.0;
        double r7639788 = r7639786 / r7639787;
        double r7639789 = r7639783 + r7639788;
        double r7639790 = a;
        double r7639791 = b;
        double r7639792 = r7639790 * r7639791;
        double r7639793 = 4.0;
        double r7639794 = r7639792 / r7639793;
        double r7639795 = r7639789 - r7639794;
        double r7639796 = c;
        double r7639797 = r7639795 + r7639796;
        return r7639797;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r7639798 = t;
        double r7639799 = 16.0;
        double r7639800 = r7639798 / r7639799;
        double r7639801 = z;
        double r7639802 = y;
        double r7639803 = x;
        double r7639804 = c;
        double r7639805 = fma(r7639802, r7639803, r7639804);
        double r7639806 = b;
        double r7639807 = a;
        double r7639808 = r7639806 * r7639807;
        double r7639809 = 4.0;
        double r7639810 = r7639808 / r7639809;
        double r7639811 = r7639805 - r7639810;
        double r7639812 = fma(r7639800, r7639801, r7639811);
        return r7639812;
}

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. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 +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))