Details

sample69.0ms

Algorithm

intervals

Results

27.0ms	51×	body	2560	valid
15.0ms	40×	body	1280	valid
8.0ms	41×	body	640	valid
4.0ms	33×	body	320	valid
4.0ms	79×	body	80	valid
1.0ms	12×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize14.0ms

Local error

Found 2 expressions with local error:

1.7b	(- 1.0 (cos x))
14.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

6.0ms	(- 1.0 (cos x))
44.0ms	(/ (- 1.0 (cos x)) (* x x))

series101.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- 1.0 (cos x))
59.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.2s

Counts

48 → 48

Iterations

Useful iterations: 2 (138.0ms)

Iter	Nodes	Cost
0	88	507
1	212	489
2	548	441
3	1500	441
done	5000	441

prune174.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
13.6b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

22.0ms	(* 1/720 (pow x 4))
24.0ms	(* 1/24 (pow x 2))
112.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series197.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(* 1/720 (pow x 4))
47.0ms	(* 1/24 (pow x 2))
69.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify2.6s

Counts

75 → 75

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	121	780
1	272	701
2	685	643
3	2993	629
done	5002	626

prune306.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
13.6b	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `associate-+r+` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `unpow2`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

3 → 67

Calls

3 calls:

24.0ms	(* 1/720 (pow x 4))
22.0ms	(* 1/24 (pow x 2))
31.0ms	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

series196.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(* 1/720 (pow x 4))
33.0ms	(* 1/24 (pow x 2))
83.0ms	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

simplify2.7s

Counts

76 → 76

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	121	782
1	275	699
2	684	639
3	3137	639
done	5000	632

prune252.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(/ (/ (- 1.0 (cos x)) x) x)
1.7b	(- 1.0 (cos x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

24.0ms	(/ (- 1.0 (cos x)) x)
30.0ms	(/ (/ (- 1.0 (cos x)) x) x)
14.0ms	(- 1.0 (cos x))

series135.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- 1.0 (cos x)) x)
62.0ms	(/ (/ (- 1.0 (cos x)) x) x)
24.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

156 → 156

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	229	2262
1	522	2156
2	1254	2046
3	3200	2024
done	5000	2009

prune346.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.4b

bsearch83.0ms

Steps

Iters	Range		Point
9	3.244205803610274e-06	1902.9075791774285	0.028553554432783436
8	-45.38980787391071	-0.005411406272604966	-0.03306643978524941

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	39
1	34	31
done	34	31

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	1640×	body	2560	valid
1.0s	1251×	body	1280	valid
479.0ms	1452×	body	640	valid
167.0ms	947×	body	320	valid
129.0ms	2232×	body	80	valid
97.0ms	478×	body	160	valid