Details

sample192.0ms

Algorithm

intervals

Results

69.0ms	74×	body	2560	valid
61.0ms	120×	body	1280	valid
15.0ms	33×	body	640	valid
7.0ms	18×	body	1280	overflowed
7.0ms	316×	pre	80	true
3.0ms	10×	body	640	overflowed
2.0ms	4×	body	2560	overflowed
2.0ms	8×	body	320	valid
2.0ms	8×	body	320	overflowed
1.0ms	16×	body	80	overflowed
1.0ms	16×	body	80	valid
1.0ms	5×	body	160	valid
1.0ms	4×	body	160	overflowed

simplify887.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	240	24
4	659	24
5	3001	24
done	5001	24

prune4.0ms

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: 60.0b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
1.8b	(- (exp (* a eps)) 1.0)
2.5b	(- (exp (* b eps)) 1.0)
2.7b	(- (exp (* (+ a b) eps)) 1.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

11.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series46.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
8.0ms	(- (exp (* a eps)) 1.0)
9.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify416.0ms

Counts

88 → 88

Iterations

Useful iterations: done (413.0ms)

Iter	Nodes	Cost
0	143	1364
1	350	1326
2	1305	1196
done	5000	1190

prune144.0ms

Filtered

63 candidates to 88 candidates (-39.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 47.0b

Counts

89 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (exp (* (+ a b) eps)) 1.0)
2.7b	(* (- (exp (* a eps)) 1.0) (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
4.2b	(* (* 1/6 (pow eps 3)) b)
11.6b	(* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`add-exp-log`
14×	`-un-lft-identity` `associate-l*`
13×	`add-cbrt-cube`
11×	`prod-exp`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`pow1`
6×	`add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`frac-times` `unpow-prod-down` `flip3--` `flip3-+` `associate-*r/` `flip--` `flip-+`
3×	`*-commutative`
2×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-prod-down` `associate-*l/` `pow-exp` `distribute-lft-out--` `unpow2` `difference-of-squares` `sqr-pow`
1×	`sub-neg` `diff-log`

Counts

4 → 94

Calls

4 calls:

5.0ms	(- (exp (* (+ a b) eps)) 1.0)
17.0ms	(* (- (exp (* a eps)) 1.0) (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
7.0ms	(* (* 1/6 (pow eps 3)) b)
14.0ms	(* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (exp (* (+ a b) eps)) 1.0)
63.0ms	(* (- (exp (* a eps)) 1.0) (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
5.0ms	(* (* 1/6 (pow eps 3)) b)
24.0ms	(* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))

simplify943.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (245.0ms)

Iter	Nodes	Cost
0	228	2722
1	710	2556
2	3547	2341
done	5001	2341

prune309.0ms

Filtered

72 candidates to 106 candidates (-47.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	102	8	110

Merged error: 46.8b

Counts

110 → 8

localize32.0ms

Local error

Found 4 expressions with local error:

11.6b	(* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))
20.1b	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
20.1b	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
20.1b	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `cbrt-prod`
8×	`associate-l`
6×	`cbrt-div` `add-cbrt-cube`
4×	`pow1` `unpow-prod-down` `flip3-+` `flip-+` `add-log-exp` `unswap-sqr`
3×	`pow1/3` `associate-r` `prod-exp`
2×	`associate-*r/` `unpow2` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 70

Calls

4 calls:

12.0ms	(* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))
11.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
11.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
11.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))
64.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
67.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
68.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))

simplify531.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (137.0ms)

Iter	Nodes	Cost
0	146	2943
1	430	2776
2	1816	2558
done	5000	2558

prune599.0ms

Filtered

67 candidates to 82 candidates (-22.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	81	9	90

Merged error: 46.8b

Counts

90 → 9

localize42.0ms

Local error

Found 4 expressions with local error:

20.1b	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
20.1b	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
20.1b	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
20.1b	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

12.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
11.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
11.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
10.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
64.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
66.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))
68.0ms	(cbrt (+ (* (pow b 2) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* eps b)))

simplify1.2s

Counts

64 → 64

Iterations

Useful iterations: 3 (263.0ms)

Iter	Nodes	Cost
0	89	2880
1	238	2776
2	819	2532
3	3204	2272
done	5001	2272

prune844.0ms

Filtered

64 candidates to 64 candidates (0.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	64	9	73

Merged error: 46.8b

Counts

73 → 9

regimes340.0ms

Accuracy

53.7% (3.8b remaining)

Error of 52.4b against oracle of 48.6b and baseline of 56.8b

bsearch143.0ms

Steps

Iters	Range		Point
9	0.009971872296741319	14848.343200454	0.11914520210130385
5	-1.5116149063123207e+67	-5.390869519443976e+66	-8.689142308994358e+66

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	175
1	76	175
done	76	175

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.3s	2563×	body	2560	valid
1.8s	3421×	body	1280	valid
347.0ms	1070×	body	640	valid
301.0ms	729×	body	1280	overflowed
201.0ms	10079×	pre	80	true
105.0ms	368×	body	640	overflowed
93.0ms	159×	body	2560	overflowed
76.0ms	332×	body	320	valid
41.0ms	549×	body	80	overflowed
37.0ms	185×	body	320	overflowed
34.0ms	480×	body	80	valid
20.0ms	137×	body	160	valid
12.0ms	86×	body	160	overflowed

Details

sample192.0ms

simplify887.0ms

prune4.0ms

localize23.0ms

rewrite27.0ms

series46.0ms

simplify416.0ms

prune144.0ms

localize26.0ms

rewrite46.0ms

series108.0ms

simplify943.0ms

prune309.0ms

localize32.0ms

rewrite46.0ms

series225.0ms

simplify531.0ms

prune599.0ms

localize42.0ms

rewrite46.0ms

series265.0ms

simplify1.2s

prune844.0ms

regimes340.0ms

bsearch143.0ms

simplify6.0ms

end0.0ms

sample5.9s

Profiling