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

Average Error: 0.1 → 0.1

Time: 1.4s

Precision: binary64

Math

\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

↓

\[\left(0.125 \cdot x - \frac{y \cdot z}{2}\right) + t\]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

↓

(FPCore (x y z t) :precision binary64 (+ (- (* 0.125 x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

↓

double code(double x, double y, double z, double t) {
	return ((0.125 * x) - ((y * z) / 2.0)) + t;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	0.1
Target	0.0
Herbie	0.1

\[\left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y\]

Derivation

1. Initial program 0.1

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

2. Simplified 0.1

   \[\leadsto \color{blue}{\left(0.125 \cdot x - \frac{y \cdot z}{2}\right) + t}\]

3. Final simplification 0.1

   \[\leadsto \left(0.125 \cdot x - \frac{y \cdot z}{2}\right) + t\]

Reproduce

herbie shell --seed 2020224 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

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

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