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

Average Error: 0.0 → 0.0

Time: 2.9s

Precision: binary64

Math

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

↓

\[\mathsf{fma}\left(-0.5, y \cdot z, 0.125 \cdot x\right) + t \]

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 (+ (fma -0.5 (* y z) (* 0.125 x)) 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 fma(-0.5, (y * z), (0.125 * x)) + t;
}

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

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

Derivation

1. Initial program 0.0

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

2. Taylor expanded in x around 0 0.0

   \[\leadsto \color{blue}{\left(0.125 \cdot x - 0.5 \cdot \left(y \cdot z\right)\right)} + t \]

3. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5, y \cdot z, 0.125 \cdot x\right)} + t \]

4. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(-0.5, y \cdot z, 0.125 \cdot x\right) + t \]

Reproduce

herbie shell --seed 2021280 
(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))