Details

sample67.0ms

Algorithm

intervals

Results

27.0ms	64×	body	1280	valid
14.0ms	54×	body	640	valid
8.0ms	23×	body	2560	valid
4.0ms	25×	body	320	valid
3.0ms	71×	body	80	valid
2.0ms	19×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
done	9	9

prune7.0ms

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: 52.8b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.9b	(+ x (sqrt (+ (* x x) 1.0)))
5.1b	(log (+ x (sqrt (+ (* x x) 1.0))))
14.7b	(sqrt (+ (* x x) 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 42

Calls

3 calls:

6.0ms	(+ x (sqrt (+ (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms	(sqrt (+ (* x x) 1.0))

series19.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (sqrt (+ (* x x) 1.0)))
10.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

simplify1.5s

Counts

51 → 51

Iterations

Useful iterations: 3 (684.0ms)

Iter	Nodes	Cost
0	134	761
1	308	691
2	853	618
3	3216	600
done	5001	600

prune142.0ms

Filtered

43 candidates to 51 candidates (-18.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Merged error: 0.1b

Counts

52 → 7

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.3b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
182×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
118×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`diff-log` `frac-sub` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 286

Calls

2 calls:

18.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
54.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series29.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
17.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify1.2s

Counts

292 → 292

Iterations

Useful iterations: 2 (565.0ms)

Iter	Nodes	Cost
0	336	4436
1	860	3364
2	2949	2955
done	5000	2955

prune460.0ms

Filtered

111 candidates to 292 candidates (-163.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	290	2	292
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	290	9	299

Merged error: 0.1b

Counts

299 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.0625 (pow x 5))
0.5b	(/ 0.125 (pow x 3))
10.5b	(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
16.8b	(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

69×	`times-frac`
68×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
46×	`add-cube-cbrt`
26×	`unpow-prod-down`
19×	`associate-/r*`
15×	`add-exp-log`
12×	`cube-prod`
10×	`log-prod` `distribute-lft-out--` `sqr-pow`
9×	`add-log-exp`
8×	`frac-sub` `add-cbrt-cube` `difference-of-squares`
6×	`div-exp` `associate-/l*`
5×	`pow1` `log-div`
4×	`cube-mult` `flip3--` `unpow3` `flip--`
3×	`diff-log`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `frac-2neg` `pow-exp` `associate--l+` `clear-num` `div-inv`
1×	`associate--l-` `rem-log-exp` `log-pow`

Counts

4 → 160

Calls

4 calls:

5.0ms	(/ 0.0625 (pow x 5))
6.0ms	(/ 0.125 (pow x 3))
52.0ms	(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
51.0ms	(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 0.0625 (pow x 5))
4.0ms	(/ 0.125 (pow x 3))
11.0ms	(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
6.0ms	(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify770.0ms

Counts

172 → 172

Iterations

Useful iterations: 2 (361.0ms)

Iter	Nodes	Cost
0	318	2874
1	656	2609
2	1962	2457
done	5000	2457

prune375.0ms

Filtered

111 candidates to 172 candidates (-55.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	172	9	181

Merged error: 0.1b

Counts

181 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (log 2) (/ 0.25 (* x x)))
0.1b	(/ 0.09375 (pow x 4))
0.2b	(/ 0.25 (* x x))
8.1b	(- (+ (log 2) (/ 0.25 (* x x))) (- (/ 0.09375 (pow x 4)) (log x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
15×	`distribute-lft-out--`
14×	`add-exp-log`
13×	`add-log-exp`
12×	`unpow-prod-down`
11×	`pow1` `add-cbrt-cube`
8×	`associate-/r*` `distribute-lft-out`
7×	`log-pow`
6×	`diff-log` `associate-/l*`
5×	`div-exp`
4×	`frac-sub` `sqr-pow`
3×	`cbrt-undiv` `associate-+l+` `log-prod` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+`
2×	`sub-neg` `frac-2neg` `clear-num` `div-inv` `associate--r+`
1×	`+-commutative` `pow-to-exp` `pow-exp` `prod-exp` `associate--l+` `cbrt-unprod` `associate--r-` `difference-of-squares`

Counts

4 → 115

Calls

4 calls:

6.0ms	(+ (log 2) (/ 0.25 (* x x)))
5.0ms	(/ 0.09375 (pow x 4))
5.0ms	(/ 0.25 (* x x))
20.0ms	(- (+ (log 2) (/ 0.25 (* x x))) (- (/ 0.09375 (pow x 4)) (log x)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (log 2) (/ 0.25 (* x x)))
4.0ms	(/ 0.09375 (pow x 4))
3.0ms	(/ 0.25 (* x x))
11.0ms	(- (+ (log 2) (/ 0.25 (* x x))) (- (/ 0.09375 (pow x 4)) (log x)))

simplify789.0ms

Counts

127 → 127

Iterations

Useful iterations: 2 (306.0ms)

Iter	Nodes	Cost
0	227	2047
1	559	1900
2	1945	1780
done	5000	1780

prune398.0ms

Filtered

86 candidates to 127 candidates (-47.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	127	9	136

Merged error: 0.1b

Counts

136 → 9

regimes158.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.5b

bsearch35.0ms

Steps

Iters	Range		Point
9	0.009971872296741319	901.3230478674768	0.9623652222862653
9	-174458.2165831976	-0.46594774775336223	-0.9999789100910194

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	80
1	48	80
done	48	80

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.0s	2379×	body	1280	valid
407.0ms	1562×	body	640	valid
260.0ms	798×	body	2560	valid
128.0ms	770×	body	320	valid
88.0ms	2070×	body	80	valid
41.0ms	421×	body	160	valid

Details

sample67.0ms

simplify3.0ms

prune7.0ms

localize7.0ms

rewrite18.0ms

series19.0ms

simplify1.5s

prune142.0ms

localize14.0ms

rewrite93.0ms

series29.0ms

simplify1.2s

prune460.0ms

localize12.0ms

rewrite120.0ms

series26.0ms

simplify770.0ms

prune375.0ms

localize13.0ms

rewrite40.0ms

series45.0ms

simplify789.0ms

prune398.0ms

regimes158.0ms

bsearch35.0ms

simplify3.0ms

end0.0ms

sample2.1s

Profiling