Details

sample231.0ms

Algorithm

intervals

Results

128.0ms	97×	body	1280	valid
56.0ms	61×	body	640	valid
15.0ms	24×	body	320	valid
11.0ms	59×	body	80	valid
6.0ms	15×	body	160	valid

simplify625.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	50
1	74	50
2	176	50
3	548	50
4	1740	50
done	5000	50

prune5.0ms

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: 0.5b

Counts

2 → 1

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.9b	(- (cos x) (cos y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

23.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
13.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))

series49.0ms

Counts

4 → 10

Calls

4 calls:

25.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
14.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
10.0ms	(- (cos x) (cos y))

simplify608.0ms

Counts

104 → 104

Iterations

Useful iterations: done (604.0ms)

Iter	Nodes	Cost
0	237	1837
1	629	1774
2	2426	1628
done	5000	1618

prune349.0ms

Filtered

70 candidates to 104 candidates (-48.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	10	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 0.2b

Counts

105 → 10

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.9b	(- (cos x) (cos y))
3.1b	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

15.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))
5.0ms	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

series56.0ms

Counts

4 → 10

Calls

4 calls:

14.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
10.0ms	(- (cos x) (cos y))
27.0ms	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

simplify1.2s

Counts

89 → 89

Iterations

Useful iterations: 3 (395.0ms)

Iter	Nodes	Cost
0	197	1357
1	426	1285
2	1315	1176
3	4407	1166
done	5000	1166

prune313.0ms

Filtered

60 candidates to 89 candidates (-48.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	89	10	99

Merged error: 0.2b

Counts

99 → 10

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.9b	(- (cos x) (cos y))
3.1b	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`pow1` `associate-r`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
9×	`add-cube-cbrt`
8×	`flip3--` `flip--`
7×	`sub-neg` `log-prod` `associate-l` `add-log-exp`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`difference-of-squares`
4×	`frac-times` `exp-sum` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
3×	`log-pow` `distribute-lft-out--`
2×	`times-frac` `associate-l/` `-commutative` `unswap-sqr`
1×	`exp-prod` `exp-to-pow` `diff-log` `rem-log-exp` `diff-cos`

Counts

4 → 97

Calls

4 calls:

24.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
12.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- (cos x) (cos y))
4.0ms	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
14.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms	(- (cos x) (cos y))
26.0ms	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

simplify579.0ms

Counts

109 → 109

Iterations

Useful iterations: done (575.0ms)

Iter	Nodes	Cost
0	220	2237
1	565	2136
2	2255	1940
done	5001	1930

prune393.0ms

Filtered

75 candidates to 109 candidates (-45.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	109	10	119

Merged error: 0.2b

Counts

119 → 10

localize41.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
1.9b	(- (cos x) (cos y))
2.0b	(log (exp (- (cos x) (cos y))))
3.1b	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
12×	`log-prod`
10×	`log-pow`
9×	`add-log-exp`
7×	`add-cube-cbrt` `exp-prod`
6×	`pow1` `exp-sum`
5×	`sub-neg`
4×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
3×	`distribute-lft-out--`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `diff-log` `rem-log-exp` `flip--` `diff-cos`
1×	`log-div` `exp-to-pow` `exp-diff` `sqrt-prod`

Counts

4 → 69

Calls

4 calls:

5.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))
6.0ms	(log (exp (- (cos x) (cos y))))
4.0ms	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

series49.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
10.0ms	(- (cos x) (cos y))
10.0ms	(log (exp (- (cos x) (cos y))))
28.0ms	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

simplify675.0ms

Counts

79 → 79

Iterations

Useful iterations: 3 (233.0ms)

Iter	Nodes	Cost
0	180	1158
1	367	1045
2	892	953
3	2551	947
done	5000	947

prune449.0ms

Filtered

57 candidates to 79 candidates (-38.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	80	9	89

Merged error: 0.2b

Counts

89 → 9

regimes193.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	58
1	47	58
done	47	58

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.6s	2784×	body	1280	valid
1.6s	1838×	body	640	valid
481.0ms	748×	body	320	valid
449.0ms	2296×	body	80	valid
144.0ms	334×	body	160	valid

Details

sample231.0ms

simplify625.0ms

prune5.0ms

localize34.0ms

rewrite48.0ms

series49.0ms

simplify608.0ms

prune349.0ms

localize38.0ms

rewrite32.0ms

series56.0ms

simplify1.2s

prune313.0ms

localize40.0ms

rewrite49.0ms

series74.0ms

simplify579.0ms

prune393.0ms

localize41.0ms

rewrite22.0ms

series49.0ms

simplify675.0ms

prune449.0ms

regimes193.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample6.6s

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