Details

sample235.0ms

Algorithm

intervals

Results

131.0ms	97×	body	1280	valid
57.0ms	61×	body	640	valid
15.0ms	24×	body	320	valid
11.0ms	59×	body	80	valid
6.0ms	15×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	50
1	74	50
2	176	50
3	542	50
4	1695	50
done	5001	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

localize35.0ms

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))

rewrite47.0ms

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:

20.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
15.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))

series50.0ms

Counts

4 → 10

Calls

4 calls:

24.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
15.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
10.0ms	(- (cos x) (cos y))

simplify916.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (232.0ms)

Iter	Nodes	Cost
0	237	1837
1	624	1770
2	2211	1618
done	5000	1618

prune343.0ms

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

localize42.0ms

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)))))

rewrite29.0ms

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:

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

series53.0ms

Counts

4 → 10

Calls

4 calls:

18.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
10.0ms	(- (cos x) (cos y))
25.0ms	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

simplify1.9s

Counts

89 → 89

Iterations

Useful iterations: 3 (1000.0ms)

Iter	Nodes	Cost
0	197	1357
1	424	1284
2	1206	1173
3	4184	1166
done	5001	1166

prune317.0ms

Filtered

62 candidates to 89 candidates (-43.5%)

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

localize46.0ms

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)))))

rewrite47.0ms

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:

21.0ms	(* (* (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	(- (cos x) (cos y))
5.0ms	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
23.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms	(- (cos x) (cos y))
25.0ms	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

simplify886.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (213.0ms)

Iter	Nodes	Cost
0	220	2237
1	560	2128
2	2050	1930
done	5000	1930

prune388.0ms

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

localize42.0ms

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)))))

series47.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
9.0ms	(- (cos x) (cos y))
10.0ms	(log (exp (- (cos x) (cos y))))
27.0ms	(log (exp (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))))

simplify1.0s

Counts

79 → 79

Iterations

Useful iterations: 3 (355.0ms)

Iter	Nodes	Cost
0	180	1158
1	360	1045
2	838	953
3	2449	947
done	5001	947

prune219.0ms

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

regimes188.0ms

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

sample6.7s

Algorithm

intervals

Results

3.6s	2784×	body	1280	valid
1.6s	1838×	body	640	valid
478.0ms	748×	body	320	valid
461.0ms	2296×	body	80	valid
142.0ms	334×	body	160	valid

Details

sample235.0ms

simplify1.2s

prune5.0ms

localize35.0ms

rewrite47.0ms

series50.0ms

simplify916.0ms

prune343.0ms

localize42.0ms

rewrite29.0ms

series53.0ms

simplify1.9s

prune317.0ms

localize46.0ms

rewrite47.0ms

series82.0ms

simplify886.0ms

prune388.0ms

localize42.0ms

rewrite22.0ms

series47.0ms

simplify1.0s

prune219.0ms

regimes188.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample6.7s

Profiling