Details

sample94.0ms

Algorithm

intervals

Results

45.0ms	122×	body	1280	valid
14.0ms	19×	body	2560	valid
12.0ms	54×	body	640	valid
5.0ms	6×	body	160	valid
4.0ms	28×	body	320	valid
1.0ms	27×	body	80	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

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))

series51.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(- (tan (+ x eps)) (tan x))
20.0ms	(tan (+ x eps))

simplify868.0ms

Counts

31 → 31

Iterations

Useful iterations: 4 (165.0ms)

Iter	Nodes	Cost
0	68	367
1	136	355
2	300	341
3	569	337
4	1193	335
5	2851	335
done	5000	335

prune66.0ms

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

localize13.0ms

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))

rewrite29.0ms

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

series192.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- 1 (* (tan x) (tan eps)))
23.0ms	(+ (tan x) (tan eps))
24.0ms	(* (tan x) (tan eps))
115.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify969.0ms

Counts

74 → 74

Iterations

Useful iterations: 3 (523.0ms)

Iter	Nodes	Cost
0	146	1093
1	364	1049
2	984	989
3	3061	974
done	5000	974

prune173.0ms

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

localize17.0ms

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))

rewrite33.0ms

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))
18.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

series206.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(log (exp (- 1 (* (tan x) (tan eps)))))
38.0ms	(exp (- 1 (* (tan x) (tan eps))))
24.0ms	(* (tan x) (tan eps))
115.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

simplify662.0ms

Counts

82 → 82

Iterations

Useful iterations: 3 (255.0ms)

Iter	Nodes	Cost
0	145	1249
1	320	1138
2	861	1045
3	2376	1030
done	5000	1030

prune171.0ms

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))

rewrite81.0ms

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)
60.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (pow (* (tan x) (tan eps)) 3)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) 1))) (tan x))

series765.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (tan x) (tan eps))
25.0ms	(* (tan x) (tan eps))
43.0ms	(pow (* (tan x) (tan eps)) 3)
672.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (pow (* (tan x) (tan eps)) 3)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) 1))) (tan x))

simplify651.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (187.0ms)

Iter	Nodes	Cost
0	196	2105
1	570	1967
2	2709	1877
done	5000	1877

prune163.0ms

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

regimes292.0ms

Accuracy

83.5% (1.2b remaining)

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

bsearch64.0ms

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	28	91
1	42	55
done	42	55

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	3322×	body	1280	valid
500.0ms	668×	body	2560	valid
393.0ms	1802×	body	640	valid
110.0ms	745×	body	320	valid
51.0ms	1108×	body	80	valid
36.0ms	355×	body	160	valid

Details

sample94.0ms

simplify3.0ms

prune3.0ms

localize8.0ms

rewrite12.0ms

series51.0ms

simplify868.0ms

prune66.0ms

localize13.0ms

rewrite29.0ms

series192.0ms

simplify969.0ms

prune173.0ms

localize17.0ms

rewrite33.0ms

series206.0ms

simplify662.0ms

prune171.0ms

localize18.0ms

rewrite81.0ms

series765.0ms

simplify651.0ms

prune163.0ms

regimes292.0ms

bsearch64.0ms

simplify3.0ms

end0.0ms

sample2.6s

Profiling