Details

sample298.0ms

Algorithm

intervals

Results

127.0ms	112×	body	1280	valid
68.0ms	25×	body	2560	valid
67.0ms	55×	body	640	valid
10.0ms	21×	body	320	valid
5.0ms	36×	body	80	valid
2.0ms	7×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize25.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (tan (+ x eps)) (tan x))
3.2b	(tan (+ x eps))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

43.0ms	(- (tan (+ x eps)) (tan x))
10.0ms	(tan (+ x eps))

series177.0ms

Counts

2 → 6

Calls

2 calls:

105.0ms	(- (tan (+ x eps)) (tan x))
71.0ms	(tan (+ x eps))

simplify1.0s

Counts

31 → 31

Iterations

Iter	Nodes
done	5000
3	1176
2	355
1	137
0	68

prune270.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.2b

localize30.0ms

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))

rewrite157.0ms

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

Counts

4 → 86

Calls

4 calls:

44.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
12.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
82.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

330.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
141.0ms	(+ (tan x) (tan eps))
151.0ms	(* (tan x) (tan eps))
554.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1663
1	411
0	170

prune652.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 17.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.7b	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `swap-sqr` `flip--`

Counts

4 → 110

Calls

4 calls:

23.0ms	(* (tan x) (tan eps))
24.0ms	(* (tan x) (tan eps))
100.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
72.0ms	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.8s

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (tan x) (tan eps))
140.0ms	(* (tan x) (tan eps))
174.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.4s	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify3.3s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	4708
1	658
0	201

prune845.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 17.1b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))) (tan x))
28.4b	(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

rewrite381.0ms

Algorithm

rewrite-expression-head

Rules

229×	`tan-quot`
147×	`frac-times`
87×	`associate-*l/`
75×	`associate-*r/`
63×	`cbrt-div`
45×	`pow1`
18×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
13×	`add-sqr-sqrt`
9×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity`
6×	`add-cube-cbrt` `add-log-exp`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up`
2×	`pow-plus` `*-commutative` `difference-of-squares`
1×	`cbrt-prod` `pow2` `sub-neg` `times-frac` `flip3--` `pow1/3` `diff-log` `swap-sqr` `pow3` `frac-sub` `rem-cbrt-cube` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

17.0ms	(* (tan x) (tan eps))
81.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
107.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))) (tan x))
156.0ms	(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

series1.1s

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (tan x) (tan eps))
183.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
609.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))) (tan x))
156.0ms	(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

simplify2.1s

Counts

171 → 171

Iterations

Iter	Nodes
done	5001
2	4475
1	883
0	356

prune1.6s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 17.1b

regimes379.0ms

Accuracy

87.9% (0.9b remaining)

Error of 15.1b against oracle of 14.2b and baseline of 21.6b

bsearch290.0ms

Steps

Iters	Range		Point
7	5.079933422117934e-58	2.9620640772918567e-56	2.3554387517440553e-56
10	-3.2052418334402957e-07	-8.353467643873847e-20	-1.538105143778487e-19

simplify7.0ms

Iterations

Iter	Nodes
done	40
1	40
0	30

end0.0ms

sample11.4s

Algorithm

intervals

Results

5.2s	3223×	body	1280	valid
2.5s	1870×	body	640	valid
2.5s	651×	body	2560	valid
465.0ms	786×	body	320	valid
224.0ms	351×	body	160	valid
183.0ms	1119×	body	80	valid