Average Error: 0.1 → 0.0
Time: 18.2s
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 r9965068 = x;
        double r9965069 = y;
        double r9965070 = r9965068 * r9965069;
        double r9965071 = z;
        double r9965072 = t;
        double r9965073 = r9965071 * r9965072;
        double r9965074 = 16.0;
        double r9965075 = r9965073 / r9965074;
        double r9965076 = r9965070 + r9965075;
        double r9965077 = a;
        double r9965078 = b;
        double r9965079 = r9965077 * r9965078;
        double r9965080 = 4.0;
        double r9965081 = r9965079 / r9965080;
        double r9965082 = r9965076 - r9965081;
        double r9965083 = c;
        double r9965084 = r9965082 + r9965083;
        return r9965084;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r9965085 = t;
        double r9965086 = 16.0;
        double r9965087 = r9965085 / r9965086;
        double r9965088 = z;
        double r9965089 = y;
        double r9965090 = x;
        double r9965091 = c;
        double r9965092 = fma(r9965089, r9965090, r9965091);
        double r9965093 = b;
        double r9965094 = a;
        double r9965095 = r9965093 * r9965094;
        double r9965096 = 4.0;
        double r9965097 = r9965095 / r9965096;
        double r9965098 = r9965092 - r9965097;
        double r9965099 = fma(r9965087, r9965088, r9965098);
        return r9965099;
}

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 2019164 +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))