Details

sample165.0ms

Algorithm

intervals

Results

81.0ms	111×	body	1280	valid
40.0ms	24×	body	2560	valid
22.0ms	55×	body	640	valid
9.0ms	32×	body	320	valid
2.0ms	26×	body	80	valid
1.0ms	8×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize17.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
4.0b	(tan (+ x eps))

rewrite12.0ms

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:

8.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series141.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (tan (+ x eps)) (tan x))
49.0ms	(tan (+ x eps))

simplify2.1s

Counts

31 → 31

Iterations

Useful iterations: 4 (269.0ms)

Iter	Nodes	Cost
0	68	367
1	135	355
2	288	341
3	540	337
4	1287	335
5	3485	335
done	5000	335

prune96.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan eps) (tan x))
0.1b	(/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.6b	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite65.0ms

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:

3.0ms	(+ (tan eps) (tan x))
11.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
42.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

series758.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (tan eps) (tan x))
209.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps))))
90.0ms	(* (tan x) (tan eps))
367.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.7s

Counts

98 → 98

Iterations

Useful iterations: 3 (847.0ms)

Iter	Nodes	Cost
0	170	1724
1	385	1649
2	1051	1579
3	3027	1565
done	5000	1565

prune300.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.6b

localize18.0ms

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)))
2.6b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
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` `flip3--` `distribute-lft-in` `diff-log` `swap-sqr` `flip--`

Counts

4 → 110

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
22.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
11.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (tan x) (tan eps))
93.0ms	(* (tan x) (tan eps))
113.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
908.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify872.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (304.0ms)

Iter	Nodes	Cost
0	203	2388
1	590	2160
2	2338	1962
done	5001	1962

prune359.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan eps) (tan eps))
2.6b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan eps) (tan eps))
10.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (tan x) (tan eps))
31.0ms	(* (tan x) (tan x))
32.0ms	(* (tan eps) (tan eps))
929.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify811.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (282.0ms)

Iter	Nodes	Cost
0	210	1970
1	547	1811
2	2055	1643
done	5000	1643

prune280.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

regimes116.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	111
1	42	111
done	42	111

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.6s	3341×	body	1280	valid
1.1s	666×	body	2560	valid
773.0ms	1788×	body	640	valid
214.0ms	779×	body	320	valid
97.0ms	1078×	body	80	valid
72.0ms	348×	body	160	valid