Average Error: 0.1 → 0.0
Time: 3.6s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\mathsf{fma}\left(z, \frac{t}{16}, y \cdot x + \mathsf{fma}\left(-\frac{a}{4}, b, c\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\mathsf{fma}\left(z, \frac{t}{16}, y \cdot x + \mathsf{fma}\left(-\frac{a}{4}, b, c\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r245017 = x;
        double r245018 = y;
        double r245019 = r245017 * r245018;
        double r245020 = z;
        double r245021 = t;
        double r245022 = r245020 * r245021;
        double r245023 = 16.0;
        double r245024 = r245022 / r245023;
        double r245025 = r245019 + r245024;
        double r245026 = a;
        double r245027 = b;
        double r245028 = r245026 * r245027;
        double r245029 = 4.0;
        double r245030 = r245028 / r245029;
        double r245031 = r245025 - r245030;
        double r245032 = c;
        double r245033 = r245031 + r245032;
        return r245033;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r245034 = z;
        double r245035 = t;
        double r245036 = 16.0;
        double r245037 = r245035 / r245036;
        double r245038 = y;
        double r245039 = x;
        double r245040 = r245038 * r245039;
        double r245041 = a;
        double r245042 = 4.0;
        double r245043 = r245041 / r245042;
        double r245044 = -r245043;
        double r245045 = b;
        double r245046 = c;
        double r245047 = fma(r245044, r245045, r245046);
        double r245048 = r245040 + r245047;
        double r245049 = fma(r245034, r245037, r245048);
        return r245049;
}

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

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

  4. Applied fma-udef0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019362 +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))