Details

sample43.0ms

Algorithm

intervals

Results

10.0ms	62×	body	1280	valid
6.0ms	198×	body	80	nan
5.0ms	42×	body	640	valid
4.0ms	121×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.8b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

14.0ms	(sqrt (+ x 1.0))
92.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series124.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(sqrt (+ x 1.0))
90.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.5s

Counts

41 → 41

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	84	488
1	183	440
2	432	410
3	1028	402
4	2702	390
done	5000	382

prune153.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

15.0ms	(sqrt (+ x 1.0))
64.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
63.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series345.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(sqrt (+ x 1.0))
85.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
206.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.1s

Counts

80 → 80

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	152	1125
1	343	1018
2	891	935
3	2607	919
done	5000	915

prune307.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
0.2b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 86

Calls

4 calls:

35.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
41.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
8.0ms	(cbrt (+ x 1.0))
8.0ms	(cbrt (+ x 1.0))

series697.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
161.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
106.0ms	(cbrt (+ x 1.0))
162.0ms	(cbrt (+ x 1.0))

simplify1.7s

Counts

98 → 98

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	328	2505
1	851	2346
2	3058	2209
done	5000	2197

prune563.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (sqrt (+ x 1.0)))
0.3b	(cbrt (sqrt (+ x 1.0)))
0.3b	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

66×	`cbrt-prod`
43×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
36×	`sqrt-prod`
21×	`add-cube-cbrt`
18×	`cbrt-div`
16×	`sqrt-div`
14×	`swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

13.0ms	(cbrt (+ x 1.0))
7.0ms	(cbrt (sqrt (+ x 1.0)))
5.0ms	(cbrt (sqrt (+ x 1.0)))
70.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))

series594.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt (+ x 1.0))
169.0ms	(cbrt (sqrt (+ x 1.0)))
114.0ms	(cbrt (sqrt (+ x 1.0)))
146.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))

simplify2.3s

Counts

129 → 129

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	182	2091
1	367	1910
2	920	1826
3	2315	1640
done	5000	1507

prune590.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes77.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.2s

Algorithm

intervals

Results

827.0ms	1772×	body	1280	valid
380.0ms	8006×	body	80	nan
286.0ms	1252×	body	640	valid
200.0ms	4002×	body	80	valid
69.0ms	657×	body	320	valid
22.0ms	317×	body	160	valid