Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, B

Average Error: 0.0 → 0.0

Time: 31.8s

Precision: 64

Math

\[\left(\frac{1.0}{8.0} \cdot x - \frac{y \cdot z}{2.0}\right) + t\]

↓

\[\mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z \cdot y}{2.0}\right)\]

C

double f(double x, double y, double z, double t) {
        double r32755643 = 1.0;
        double r32755644 = 8.0;
        double r32755645 = r32755643 / r32755644;
        double r32755646 = x;
        double r32755647 = r32755645 * r32755646;
        double r32755648 = y;
        double r32755649 = z;
        double r32755650 = r32755648 * r32755649;
        double r32755651 = 2.0;
        double r32755652 = r32755650 / r32755651;
        double r32755653 = r32755647 - r32755652;
        double r32755654 = t;
        double r32755655 = r32755653 + r32755654;
        return r32755655;
}

↓

double f(double x, double y, double z, double t) {
        double r32755656 = x;
        double r32755657 = 8.0;
        double r32755658 = r32755656 / r32755657;
        double r32755659 = 1.0;
        double r32755660 = t;
        double r32755661 = z;
        double r32755662 = y;
        double r32755663 = r32755661 * r32755662;
        double r32755664 = 2.0;
        double r32755665 = r32755663 / r32755664;
        double r32755666 = r32755660 - r32755665;
        double r32755667 = fma(r32755658, r32755659, r32755666);
        return r32755667;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\left(\frac{x}{8.0} + t\right) - \frac{z}{2.0} \cdot y\]

Derivation

1. Initial program 0.0

   \[\left(\frac{1.0}{8.0} \cdot x - \frac{y \cdot z}{2.0}\right) + t\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z \cdot y}{2.0}\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(\frac{x}{8.0}, 1.0, t - \frac{z \cdot y}{2.0}\right)\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"

  :herbie-target
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))