Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D

Average Error: 0.2 → 0.1

Time: 1.4s

Precision: binary64

Math

\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]

↓

\[3 + \left(x \cdot \left(x \cdot 9\right) + x \cdot -12\right)\]

FPCore

(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))

↓

(FPCore (x) :precision binary64 (+ 3.0 (+ (* x (* x 9.0)) (* x -12.0))))

C

double code(double x) {
	return 3.0 * ((((x * 3.0) * x) - (x * 4.0)) + 1.0);
}

↓

double code(double x) {
	return 3.0 + ((x * (x * 9.0)) + (x * -12.0));
}

Error

Bits error versus x

Target

Original	0.2
Target	0.1
Herbie	0.1

\[3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right)\]

Derivation

1. Initial program 0.2

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]

2. Simplified 0.1

   \[\leadsto \color{blue}{3 + x \cdot \left(x \cdot 9 + -12\right)}\]
3. Using strategy rm

4. Applied distribute-lft-in_binary64 0.1

   \[\leadsto 3 + \color{blue}{\left(x \cdot \left(x \cdot 9\right) + x \cdot -12\right)}\]

5. Final simplification 0.1

   \[\leadsto 3 + \left(x \cdot \left(x \cdot 9\right) + x \cdot -12\right)\]

Reproduce

herbie shell --seed 2020219 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x)))

  (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))