Details

sample94.0ms

Algorithm

intervals

Results

45.0ms	122×	body	1280	valid
14.0ms	19×	body	2560	valid
12.0ms	54×	body	640	valid
4.0ms	28×	body	320	valid
1.0ms	27×	body	80	valid
1.0ms	6×	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

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 36.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (tan (+ x eps)) (tan x))
3.6b	(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:

7.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series45.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(- (tan (+ x eps)) (tan x))
18.0ms	(tan (+ x eps))

simplify1.0s

Counts

31 → 31

Iterations

Useful iterations: 4 (163.0ms)

Iter	Nodes	Cost
0	68	367
1	136	355
2	302	341
3	555	337
4	1262	335
5	3074	335
done	5000	335

prune72.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	23	8	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	8	32

Merged error: 14.6b

Counts

32 → 8

localize12.0ms

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))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite32.0ms

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:

3.0ms	(- 1 (* (tan x) (tan eps)))
5.0ms	(+ (tan x) (tan eps))
6.0ms	(* (tan x) (tan eps))
16.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series193.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- 1 (* (tan x) (tan eps)))
24.0ms	(+ (tan x) (tan eps))
24.0ms	(* (tan x) (tan eps))
115.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify801.0ms

Counts

74 → 74

Iterations

Useful iterations: 3 (301.0ms)

Iter	Nodes	Cost
0	146	1093
1	364	1066
2	1038	990
3	2786	974
done	5000	974

prune172.0ms

Filtered

58 candidates to 74 candidates (-27.6%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	56	18	74
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	62	20	82

Merged error: 14.4b

Counts

82 → 20

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(log (exp (- 1 (* (tan x) (tan eps)))))
0.2b	(exp (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.8b	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

4.0ms	(log (exp (- 1 (* (tan x) (tan eps)))))
4.0ms	(exp (- 1 (* (tan x) (tan eps))))
6.0ms	(* (tan x) (tan eps))
17.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

series206.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(log (exp (- 1 (* (tan x) (tan eps)))))
39.0ms	(exp (- 1 (* (tan x) (tan eps))))
24.0ms	(* (tan x) (tan eps))
114.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

simplify674.0ms

Counts

82 → 82

Iterations

Useful iterations: 3 (253.0ms)

Iter	Nodes	Cost
0	145	1249
1	320	1143
2	906	1048
3	2520	1030
done	5000	1030

prune175.0ms

Filtered

58 candidates to 82 candidates (-41.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	3	16	19
Picked	1	0	1
Done	0	0	0
Total	84	18	102

Merged error: 14.4b

Counts

102 → 18

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.4b	(pow (* (tan x) (tan eps)) 3)
2.8b	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (pow (* (tan x) (tan eps)) 3)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) 1))) (tan x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
13×	`tan-quot`
11×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
9×	`add-cube-cbrt`
6×	`associate-r` `associate-l` `add-log-exp`
3×	`cube-div` `frac-times` `pow-unpow` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod` `difference-of-squares`
2×	`pow-pow` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `flip3--` `diff-log` `unpow3` `cube-prod` `frac-sub` `flip--` `distribute-lft-out--` `sqr-pow`

Counts

4 → 84

Calls

4 calls:

6.0ms	(* (tan x) (tan eps))
6.0ms	(* (tan x) (tan eps))
6.0ms	(pow (* (tan x) (tan eps)) 3)
58.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (pow (* (tan x) (tan eps)) 3)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) 1))) (tan x))

series752.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (tan x) (tan eps))
24.0ms	(* (tan x) (tan eps))
43.0ms	(pow (* (tan x) (tan eps)) 3)
661.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (pow (* (tan x) (tan eps)) 3)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) 1))) (tan x))

simplify867.0ms

Counts

96 → 96

Iterations

Useful iterations: done (864.0ms)

Iter	Nodes	Cost
0	196	2105
1	570	2038
2	2587	1880
done	5000	1877

prune164.0ms

Filtered

72 candidates to 96 candidates (-33.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	95	19	114

Merged error: 14.4b

Counts

114 → 19

regimes270.0ms

Accuracy

83.6% (1.2b remaining)

Error of 16.0b against oracle of 14.8b and baseline of 21.8b

bsearch62.0ms

Steps

Iters	Range		Point
7	1.4651069296553002e-100	9.132868286318998e-99	8.962372584124604e-99
6	-3.999592858071278e-34	-2.5507132976570226e-35	-3.879859333564107e-34

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	95
1	45	59
done	45	59

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3322×	body	1280	valid
498.0ms	668×	body	2560	valid
400.0ms	1802×	body	640	valid
117.0ms	745×	body	320	valid
52.0ms	1108×	body	80	valid
40.0ms	355×	body	160	valid

Details

sample94.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite12.0ms

series45.0ms

simplify1.0s

prune72.0ms

localize12.0ms

rewrite32.0ms

series193.0ms

simplify801.0ms

prune172.0ms

localize19.0ms

rewrite32.0ms

series206.0ms

simplify674.0ms

prune175.0ms

localize18.0ms

rewrite79.0ms

series752.0ms

simplify867.0ms

prune164.0ms

regimes270.0ms

bsearch62.0ms

simplify3.0ms

end0.0ms

sample2.6s

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