Details

sample338.0ms

Algorithm

intervals

Results

152.0ms	107×	body	1280	valid
54.0ms	40×	body	80	valid
50.0ms	17×	body	2560	valid
45.0ms	49×	body	640	valid
14.0ms	24×	body	320	valid
7.0ms	19×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize10.0ms

Local error

Found 2 expressions with local error:

3.2b	(- (tan (+ x eps)) (tan x))
3.9b	(tan (+ x eps))

rewrite44.0ms

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:

32.0ms	(- (tan (+ x eps)) (tan x))
11.0ms	(tan (+ x eps))

series231.0ms

Counts

2 → 6

Calls

2 calls:

139.0ms	(- (tan (+ x eps)) (tan x))
92.0ms	(tan (+ x eps))

simplify830.0ms

Counts

31 → 31

Iterations

Useful iterations: done (828.0ms)

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

prune144.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
4.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite155.0ms

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:

11.0ms	(- 1 (* (tan x) (tan eps)))
14.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
112.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

183.0ms	(- 1 (* (tan x) (tan eps)))
144.0ms	(+ (tan x) (tan eps))
158.0ms	(* (tan x) (tan eps))
550.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts

74 → 74

Iterations

Useful iterations: 2 (380.0ms)

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

prune393.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.9b

localize21.0ms

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)))
4.5b	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

rewrite406.0ms

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:

20.0ms	(* (tan x) (tan eps))
17.0ms	(* (tan x) (tan eps))
103.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
258.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

series2.4s

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (tan x) (tan eps))
147.0ms	(* (tan x) (tan eps))
205.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.9s	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

simplify1.6s

Counts

120 → 120

Iterations

Useful iterations: done (1.6s)

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

prune529.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (* (* (tan x) (tan eps)) (tan x)) (tan eps))
0.2b	(* (* (tan x) (tan eps)) (tan x))
4.5b	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (* (tan x) (tan eps)) (tan x)) (tan eps))) (+ 1 (* (tan x) (tan eps))))) (tan x))

rewrite496.0ms

Algorithm

rewrite-expression-head

Rules

49×	`tan-quot`
23×	`frac-times` `associate-*l/`
20×	`pow1` `add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
11×	`associate-*r/`
10×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-r`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`associate-l`
3×	`times-frac` `*-commutative` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

24.0ms	(* (tan x) (tan eps))
139.0ms	(* (* (* (tan x) (tan eps)) (tan x)) (tan eps))
81.0ms	(* (* (tan x) (tan eps)) (tan x))
245.0ms	(- (/ (+ (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:

150.0ms	(* (tan x) (tan eps))
133.0ms	(* (* (* (tan x) (tan eps)) (tan x)) (tan eps))
123.0ms	(* (* (tan x) (tan eps)) (tan x))
1.5s	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (* (tan x) (tan eps)) (tan x)) (tan eps))) (+ 1 (* (tan x) (tan eps))))) (tan x))

simplify2.4s

Counts

111 → 111

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	211	2301
1	604	2244
2	3921	1999
done	5001	1969

prune533.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.9b

regimes335.0ms

Accuracy

85.6% (1.0b remaining)

Error of 15.7b against oracle of 14.7b and baseline of 21.7b

bsearch137.0ms

Steps

Iters	Range		Point
7	1.8363952280958253e-30	3.491579857798755e-29	3.2835570632738646e-29
3	-6.090218421389466e-10	-4.2121688277347143e-10	-4.284746753953384e-10

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	99
1	61	99
done	61	99

end0.0ms

sample11.3s

Algorithm

intervals

Results

5.4s	3387×	body	1280	valid
2.3s	1790×	body	640	valid
1.8s	614×	body	2560	valid
722.0ms	321×	body	160	valid
487.0ms	744×	body	320	valid
205.0ms	1144×	body	80	valid