Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	54×	body	1280	valid
5.0ms	269×	body	80	nan
3.0ms	143×	body	80	valid
3.0ms	39×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 26.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite27.0ms

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:

4.0ms	(sqrt (+ x 1.0))
22.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series105.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(sqrt (+ x 1.0))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.8s

Counts

41 → 41

Iterations

Useful iterations: 4 (906.0ms)

Iter	Nodes	Cost
0	84	488
1	183	440
2	452	410
3	1178	402
4	3298	389
done	5000	389

prune85.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

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)))

rewrite50.0ms

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:

4.0ms	(sqrt (+ x 1.0))
20.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
24.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series237.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(sqrt (+ x 1.0))
66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
140.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.3s

Counts

80 → 80

Iterations

Useful iterations: 3 (587.0ms)

Iter	Nodes	Cost
0	152	1125
1	343	1018
2	924	935
3	3288	919
done	5000	919

prune162.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

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))

rewrite37.0ms

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:

16.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
13.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
2.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))

series447.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
94.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
85.0ms	(cbrt (+ x 1.0))
87.0ms	(cbrt (+ x 1.0))

simplify1.0s

Counts

98 → 98

Iterations

Useful iterations: 2 (440.0ms)

Iter	Nodes	Cost
0	328	2505
1	852	2346
2	3277	2209
done	5001	2209

prune338.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

53×	`pow1`
28×	`sqrt-pow1`
24×	`sqrt-div`
20×	`pow-prod-down`
18×	`cbrt-div`
17×	`*-un-lft-identity`
14×	`associate-*r/`
13×	`add-sqr-sqrt`
12×	`cbrt-prod`
11×	`add-cube-cbrt`
10×	`pow1/2` `pow-prod-up`
9×	`flip3-+` `flip-+`
6×	`add-exp-log` `pow-sqr` `add-cbrt-cube`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `sqrt-prod` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`associate-*l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
41.0ms	(* (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))) (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

series369.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ x 1.0))
90.0ms	(cbrt (+ x 1.0))
90.0ms	(cbrt (+ x 1.0))
97.0ms	(* (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))) (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

simplify1.9s

Counts

111 → 111

Iterations

Useful iterations: 3 (706.0ms)

Iter	Nodes	Cost
0	186	2214
1	401	1723
2	1243	1534
3	4853	1375
done	5000	1375

prune349.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample678.0ms

Algorithm

intervals

Results

151.0ms	1713×	body	1280	valid
139.0ms	8101×	body	80	nan
86.0ms	1251×	body	640	valid
78.0ms	4067×	body	80	valid
31.0ms	615×	body	320	valid
12.0ms	354×	body	160	valid