Details

sample315.0ms

Algorithm

intervals

Results

147.0ms	97×	body	1280	valid
73.0ms	26×	body	2560	valid
52.0ms	63×	body	640	valid
14.0ms	25×	body	320	valid
6.0ms	38×	body	80	valid
3.0ms	7×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize12.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
3.1b	(tan (+ x eps))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

20.0ms	(- (tan (+ x eps)) (tan x))
37.0ms	(tan (+ x eps))

series161.0ms

Counts

2 → 6

Calls

2 calls:

105.0ms	(- (tan (+ x eps)) (tan x))
56.0ms	(tan (+ x eps))

simplify862.0ms

Counts

31 → 31

Iterations

Useful iterations: done (861.0ms)

Iter	Nodes	Cost
0	68	367
1	135	355
2	349	341
3	1136	337
done	5000	335

prune553.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.3b	(* (tan x) (tan eps))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

18.0ms	(+ (tan x) (tan eps))
32.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
23.0ms	(* (tan x) (tan eps))
114.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ (tan x) (tan eps))
352.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
124.0ms	(* (tan x) (tan eps))
593.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.1s

Counts

98 → 98

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	172	1724
1	421	1649
2	1674	1579
done	5001	1578

prune672.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin eps) (tan x)) (cos eps))))
0.2b	(/ (* (sin eps) (tan x)) (cos eps))
0.2b	(* (sin eps) (tan x))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin eps) (tan x)) (cos eps)))) (tan x))

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
28×	`times-frac`
20×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`difference-of-squares`
9×	`associate-/r*`
7×	`distribute-lft-out`
6×	`pow1` `distribute-lft-out--` `add-log-exp`
5×	`tan-quot` `associate-/l*`
4×	`associate-/l/`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`flip3--` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod` `div-inv`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 108

Calls

4 calls:

68.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin eps) (tan x)) (cos eps))))
18.0ms	(/ (* (sin eps) (tan x)) (cos eps))
32.0ms	(* (sin eps) (tan x))
250.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin eps) (tan x)) (cos eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

363.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin eps) (tan x)) (cos eps))))
146.0ms	(/ (* (sin eps) (tan x)) (cos eps))
129.0ms	(* (sin eps) (tan x))
519.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin eps) (tan x)) (cos eps)))) (tan x))

simplify1.3s

Counts

120 → 120

Iterations

Useful iterations: 2 (448.0ms)

Iter	Nodes	Cost
0	220	2503
1	517	2396
2	2298	2278
done	5000	2278

prune674.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin eps) (tan x))
0.2b	(/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (+ (tan x) (tan eps)))
0.3b	(/ 1 (/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (+ (tan x) (tan eps))))
5.5b	(- (/ 1 (/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite596.0ms

Algorithm

rewrite-expression-head

Rules

224×	`*-un-lft-identity`
219×	`times-frac`
173×	`add-sqr-sqrt`
94×	`add-cube-cbrt`
47×	`difference-of-squares`
35×	`associate-/r*`
31×	`distribute-lft-out`
23×	`distribute-lft-out--`
19×	`add-exp-log`
16×	`associate-/r/`
13×	`add-cbrt-cube`
12×	`tan-quot`
9×	`associate-/l*`
8×	`div-exp`
7×	`pow1` `div-inv`
6×	`add-log-exp`
5×	`flip3-+` `frac-add` `flip-+`
4×	`cbrt-undiv`
3×	`associate-r` `associate-l`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `frac-sub` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 239

Calls

4 calls:

27.0ms	(* (sin eps) (tan x))
88.0ms	(/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (+ (tan x) (tan eps)))
82.0ms	(/ 1 (/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (+ (tan x) (tan eps))))
368.0ms	(- (/ 1 (/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (+ (tan x) (tan eps)))) (tan x))

series1.6s

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (sin eps) (tan x))
458.0ms	(/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (+ (tan x) (tan eps)))
330.0ms	(/ 1 (/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (+ (tan x) (tan eps))))
633.0ms	(- (/ 1 (/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (+ (tan x) (tan eps)))) (tan x))

simplify2.4s

Counts

251 → 251

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	353	7264
1	924	6666
2	4804	6384
done	5000	6380

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.1b

regimes377.0ms

Accuracy

94.1% (0.5b remaining)

Error of 13.3b against oracle of 12.7b and baseline of 21.8b

bsearch296.0ms

Steps

Iters	Range		Point
9	2.7678748271846947e-45	1.079856064773702e-36	8.698952610821154e-38
9	-8.373513646867551e-26	-2.820206666116141e-32	-3.0310550645177685e-26

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	95
1	58	95
done	58	95

end0.0ms

sample10.8s

Algorithm

intervals

Results

4.4s	3245×	body	1280	valid
2.9s	1842×	body	640	valid
1.7s	635×	body	2560	valid
951.0ms	792×	body	320	valid
258.0ms	1131×	body	80	valid
114.0ms	355×	body	160	valid