Details

sample276.0ms

Algorithm

intervals

Results

153.0ms	100×	body	1280	valid
44.0ms	62×	body	640	valid
37.0ms	14×	body	2560	valid
12.0ms	22×	body	320	valid
7.0ms	42×	body	80	valid
5.0ms	16×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize18.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (tan (+ x eps)) (tan x))
3.0b	(tan (+ x eps))

rewrite107.0ms

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:

42.0ms	(- (tan (+ x eps)) (tan x))
63.0ms	(tan (+ x eps))

series229.0ms

Counts

2 → 6

Calls

2 calls:

134.0ms	(- (tan (+ x eps)) (tan x))
95.0ms	(tan (+ x eps))

simplify2.6s

Counts

31 → 31

Iterations

Useful iterations: 4 (464.0ms)

Iter	Nodes	Cost
0	68	367
1	135	355
2	278	341
3	528	337
4	1109	335
5	2471	335
done	5000	335

prune156.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite202.0ms

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:

39.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
24.0ms	(+ (tan x) (tan eps))
28.0ms	(* (tan x) (tan eps))
108.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

354.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
128.0ms	(+ (tan x) (tan eps))
145.0ms	(* (tan x) (tan eps))
568.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.6s

Counts

98 → 98

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	172	1724
1	397	1649
2	1095	1579
3	2939	1563
done	5000	1563

prune427.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (sin x) (sin eps))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite514.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

17.0ms	(+ (tan x) (tan eps))
26.0ms	(* (sin x) (sin eps))
19.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
448.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

158.0ms	(+ (tan x) (tan eps))
89.0ms	(* (sin x) (sin eps))
159.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
629.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify1.1s

Counts

83 → 83

Iterations

Useful iterations: 2 (331.0ms)

Iter	Nodes	Cost
0	166	1443
1	420	1424
2	1560	1238
done	5000	1238

prune475.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.7b	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

26.0ms	(* (sin x) (sin eps))
37.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
38.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
1.1s	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

series976.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin x) (sin eps))
163.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
165.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
583.0ms	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

simplify979.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (277.0ms)

Iter	Nodes	Cost
0	165	2902
1	457	2834
2	1952	2500
done	5000	2500

prune405.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.1b

regimes251.0ms

Accuracy

87.2% (1.0b remaining)

Error of 15.3b against oracle of 14.3b and baseline of 22.1b

bsearch229.0ms

Steps

Iters	Range		Point
6	1.3493999398179835e-87	1.8173234671108943e-86	1.4987700485030514e-86
7	-6.595773337079076e-15	-8.563893768759747e-17	-8.700802725045611e-17

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	127
1	48	127
done	48	127

end0.0ms

sample9.4s

Algorithm

intervals

Results

5.0s	3324×	body	1280	valid
1.9s	603×	body	2560	valid
1.5s	1842×	body	640	valid
325.0ms	796×	body	320	valid
181.0ms	355×	body	160	valid
137.0ms	1080×	body	80	valid