Details

sample86.0ms

Algorithm

intervals

Results

44.0ms	122×	body	1280	valid
14.0ms	19×	body	2560	valid
11.0ms	54×	body	640	valid
4.0ms	28×	body	320	valid
1.0ms	27×	body	80	valid
1.0ms	6×	body	160	valid

simplify3.0ms

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

localize12.0ms

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))

series42.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify1.9s

Counts

31 → 31

Iterations

Useful iterations: 4 (261.0ms)

Iter	Nodes	Cost
0	68	367
1	136	355
2	289	341
3	542	337
4	1299	335
5	3504	335
done	5001	335

prune67.0ms

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

localize11.0ms

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))

rewrite27.0ms

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

series184.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(- 1 (* (tan x) (tan eps)))
23.0ms	(+ (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
112.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.9s

Counts

74 → 74

Iterations

Useful iterations: 3 (743.0ms)

Iter	Nodes	Cost
0	146	1093
1	338	1049
2	893	989
3	2551	974
done	5000	974

prune178.0ms

Filtered

57 candidates to 74 candidates (-29.8%)

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

localize14.0ms

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))

series198.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(log (exp (- 1 (* (tan x) (tan eps)))))
35.0ms	(exp (- 1 (* (tan x) (tan eps))))
23.0ms	(* (tan x) (tan eps))
112.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

simplify1.2s

Counts

82 → 82

Iterations

Useful iterations: 3 (490.0ms)

Iter	Nodes	Cost
0	145	1249
1	310	1138
2	822	1045
3	2282	1030
done	5001	1030

prune170.0ms

Filtered

59 candidates to 82 candidates (-39.0%)

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))

rewrite75.0ms

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)
55.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (pow (* (tan x) (tan eps)) 3)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) 1))) (tan x))

series714.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
37.0ms	(pow (* (tan x) (tan eps)) 3)
632.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (pow (* (tan x) (tan eps)) 3)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) 1))) (tan x))

simplify759.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (199.0ms)

Iter	Nodes	Cost
0	196	2105
1	548	1967
2	2584	1877
done	5001	1877

prune171.0ms

Filtered

70 candidates to 96 candidates (-37.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	95	19	114

Merged error: 14.4b

Counts

114 → 19

regimes289.0ms

Accuracy

83.5% (1.2b remaining)

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

bsearch60.0ms

Steps

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

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	91
1	42	55
done	42	55

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	3322×	body	1280	valid
487.0ms	668×	body	2560	valid
393.0ms	1802×	body	640	valid
108.0ms	745×	body	320	valid
53.0ms	1108×	body	80	valid
34.0ms	355×	body	160	valid

Details

sample86.0ms

simplify3.0ms

prune3.0ms

localize12.0ms

rewrite12.0ms

series42.0ms

simplify1.9s

prune67.0ms

localize11.0ms

rewrite27.0ms

series184.0ms

simplify1.9s

prune178.0ms

localize14.0ms

rewrite32.0ms

series198.0ms

simplify1.2s

prune170.0ms

localize18.0ms

rewrite75.0ms

series714.0ms

simplify759.0ms

prune171.0ms

regimes289.0ms

bsearch60.0ms

simplify4.0ms

end0.0ms

sample2.6s

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