Details

sample86.0ms

Algorithm

intervals

Results

20.0ms	100×	body	2560	nan
17.0ms	500×	body	80	nan
13.0ms	83×	body	1280	nan
10.0ms	256×	body	80	valid
4.0ms	30×	body	640	nan
2.0ms	20×	body	320	nan
0.0ms	5×	body	160	nan

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	11	9
done	11	9

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: 32.9b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(log (+ x (sqrt (- (* x x) 1.0))))
30.5b	(sqrt (- (* x x) 1.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 31

Calls

2 calls:

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

series14.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms	(sqrt (- (* x x) 1.0))

simplify1.4s

Counts

37 → 37

Iterations

Useful iterations: 3 (613.0ms)

Iter	Nodes	Cost
0	125	556
1	268	503
2	765	456
3	3116	448
done	5000	448

prune77.0ms

Filtered

31 candidates to 37 candidates (-19.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	3	38

Merged error: 0.0b

Counts

38 → 3

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
11×	`*-un-lft-identity`
9×	`associate-r`
7×	`pow1` `add-cube-cbrt` `associate-l`
5×	`add-exp-log`
4×	`frac-times` `flip3-+` `add-cbrt-cube` `flip-+` `unswap-sqr`
3×	`log-prod` `flip3--` `pow-prod-down` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `add-log-exp` `difference-of-squares`
1×	`sqrt-unprod` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 56

Calls

2 calls:

3.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series30.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
15.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify2.0s

Counts

62 → 62

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	178	1279
1	389	1092
2	1181	1042
3	4602	1026
done	5000	1026

prune152.0ms

Filtered

48 candidates to 62 candidates (-29.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	62	3	65

Merged error: 0.0b

Counts

65 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))
0.1b	(/ 0.09375 (pow x 4))
0.2b	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
0.5b	(/ 0.25 (* x x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

15.0ms	(+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))
5.0ms	(/ 0.09375 (pow x 4))
24.0ms	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
5.0ms	(/ 0.25 (* x x))

series26.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))
4.0ms	(/ 0.09375 (pow x 4))
10.0ms	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
3.0ms	(/ 0.25 (* x x))

simplify760.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (270.0ms)

Iter	Nodes	Cost
0	205	1755
1	457	1653
2	1449	1529
done	5000	1529

prune199.0ms

Filtered

82 candidates to 123 candidates (-50.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	123	3	126

Merged error: 0b

Counts

126 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
0.5b	(/ 0.25 (* x x))
0.5b	(/ 0.25 (* x x))
0.5b	(* (sqrt (- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))) (sqrt (- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

612×	`*-un-lft-identity`
450×	`distribute-lft-out--`
282×	`sqrt-prod`
244×	`pow1`
225×	`log-pow`
129×	`swap-sqr`
100×	`distribute-lft-out`
39×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `associate-r` `associate-l`
16×	`add-exp-log` `add-cbrt-cube`
12×	`sqrt-div`
8×	`sqrt-pow1` `pow1/2` `add-log-exp`
7×	`flip3--` `flip--`
6×	`times-frac` `associate-/l*`
5×	`diff-log` `pow-prod-up` `difference-of-squares`
4×	`cbrt-undiv` `frac-times` `div-exp` `associate--l+` `unswap-sqr`
3×	`log-prod` `pow-prod-down` `prod-exp` `pow-sqr` `cbrt-unprod` `associate--r+`
2×	`sub-neg` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r*` `div-inv`
1×	`pow2` `pow-plus` `sqrt-unprod` `sum-log` `rem-square-sqrt` `*-commutative` `associate--r-`

Counts

4 → 274

Calls

4 calls:

22.0ms	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
10.0ms	(/ 0.25 (* x x))
5.0ms	(/ 0.25 (* x x))
53.0ms	(* (sqrt (- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))) (sqrt (- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))))

series33.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
8.0ms	(/ 0.25 (* x x))
3.0ms	(/ 0.25 (* x x))
11.0ms	(* (sqrt (- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))) (sqrt (- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))))

simplify2.1s

Counts

286 → 286

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	176	9828
1	356	5611
2	1067	5320
3	4976	5219
done	5000	5219

prune329.0ms

Filtered

87 candidates to 286 candidates (-228.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	286	3	289

Merged error: 0b

Counts

289 → 3

regimes102.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
done	13	14

end0.0ms

sample2.7s

Algorithm

intervals

Results

604.0ms	3003×	body	2560	nan
560.0ms	15817×	body	80	nan
411.0ms	2477×	body	1280	nan
324.0ms	8000×	body	80	valid
165.0ms	1227×	body	640	nan
62.0ms	596×	body	320	nan
24.0ms	304×	body	160	nan

Details

sample86.0ms

simplify4.0ms

prune3.0ms

localize11.0ms

rewrite12.0ms

series14.0ms

simplify1.4s

prune77.0ms

localize11.0ms

rewrite18.0ms

series30.0ms

simplify2.0s

prune152.0ms

localize13.0ms

rewrite52.0ms

series26.0ms

simplify760.0ms

prune199.0ms

localize19.0ms

rewrite116.0ms

series33.0ms

simplify2.1s

prune329.0ms

regimes102.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

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