Details

sample333.0ms

Algorithm

intervals

Results

157.0ms	113×	body	1280	valid
87.0ms	20×	body	2560	valid
47.0ms	55×	body	640	valid
13.0ms	25×	body	320	valid
5.0ms	15×	body	160	valid
5.0ms	28×	body	80	valid

simplify8.0ms

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: 37.0b

localize19.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (tan (+ x eps)) (tan x))
4.1b	(tan (+ x eps))

rewrite70.0ms

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:

22.0ms	(- (tan (+ x eps)) (tan x))
47.0ms	(tan (+ x eps))

series212.0ms

Counts

2 → 6

Calls

2 calls:

147.0ms	(- (tan (+ x eps)) (tan x))
64.0ms	(tan (+ x eps))

simplify750.0ms

Counts

31 → 31

Iterations

Useful iterations: done (748.0ms)

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

prune146.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
3.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3-+` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

15.0ms	(- 1 (* (tan x) (tan eps)))
17.0ms	(+ (tan x) (tan eps))
25.0ms	(* (tan x) (tan eps))
146.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series999.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(- 1 (* (tan x) (tan eps)))
136.0ms	(+ (tan x) (tan eps))
134.0ms	(* (tan x) (tan eps))
538.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.2s

Counts

74 → 74

Iterations

Useful iterations: 2 (435.0ms)

Iter	Nodes	Cost
0	146	1093
1	375	1049
2	1614	989
done	5000	989

prune399.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.5b	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

rewrite452.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
41×	`tan-quot`
21×	`add-sqr-sqrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
10×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
4×	`pow-sqr` `pow-prod-up`
3×	`times-frac` `*-commutative` `difference-of-squares`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `sub-neg` `flip3--` `diff-log` `swap-sqr` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 108

Calls

4 calls:

16.0ms	(* (tan x) (tan eps))
22.0ms	(* (tan x) (tan eps))
113.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
292.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

series1.9s

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (tan x) (tan eps))
118.0ms	(* (tan x) (tan eps))
160.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.5s	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

simplify1.5s

Counts

120 → 120

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	181	2248
1	523	2140
2	2916	1898
done	5002	1889

prune551.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))
3.5b	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

30.0ms	(* (tan x) (tan eps))
31.0ms	(* (tan x) (tan eps))
86.0ms	(* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))
159.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

series2.1s

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (tan x) (tan eps))
136.0ms	(* (tan x) (tan eps))
249.0ms	(* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))
1.6s	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

simplify2.6s

Counts

108 → 108

Iterations

Useful iterations: 2 (534.0ms)

Iter	Nodes	Cost
0	202	2443
1	591	2369
2	3893	2066
done	5002	2066

prune564.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 16.7b

regimes233.0ms

Accuracy

87.5% (0.9b remaining)

Error of 15.1b against oracle of 14.1b and baseline of 21.6b

bsearch237.0ms

Steps

Iters	Range		Point
6	5.657564454157724e-27	3.4928798111313496e-26	7.609705691109876e-27
8	-6.739795712749816e-68	-3.8540338292272195e-72	-1.0634119210767955e-69

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	104
1	50	104
2	51	104
done	51	104

end0.0ms

sample9.8s

Algorithm

intervals

Results

5.1s	3304×	body	1280	valid
1.9s	1885×	body	640	valid
1.8s	609×	body	2560	valid
382.0ms	763×	body	320	valid
146.0ms	1085×	body	80	valid
101.0ms	354×	body	160	valid