Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	143×	body	80	valid
5.0ms	269×	body	80	nan
5.0ms	54×	body	1280	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

localize5.0ms

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))

series103.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(sqrt (+ x 1.0))
72.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify886.0ms

Counts

41 → 41

Iterations

Useful iterations: 3 (195.0ms)

Iter	Nodes	Cost
0	84	488
1	186	440
2	543	410
3	2015	402
done	5001	402

prune83.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
19.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
33.0ms	(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series268.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(sqrt (+ x 1.0))
68.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
170.0ms	(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify705.0ms

Counts

89 → 89

Iterations

Useful iterations: done (703.0ms)

Iter	Nodes	Cost
0	163	1403
1	389	1159
2	1386	1054
done	5000	1048

prune188.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 0 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))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

19.0ms	(/ (+ 0 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))
2.0ms	(cbrt (+ x 1.0))

series495.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (+ 0 1.0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
110.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
100.0ms	(cbrt (+ x 1.0))
91.0ms	(cbrt (+ x 1.0))

simplify1.4s

Counts

104 → 104

Iterations

Useful iterations: 2 (312.0ms)

Iter	Nodes	Cost
0	339	2760
1	899	2508
2	4126	2361
done	5000	2361

prune414.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

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))))))

rewrite50.0ms

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))
39.0ms	(* (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))) (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ x 1.0))
106.0ms	(cbrt (+ x 1.0))
92.0ms	(cbrt (+ x 1.0))
104.0ms	(* (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))) (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

simplify585.0ms

Counts

111 → 111

Iterations

Useful iterations: 2 (140.0ms)

Iter	Nodes	Cost
0	186	2214
1	403	1723
2	1568	1534
done	5000	1534

prune402.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes38.0ms

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: 2 (1.0ms)

Iter	Nodes	Cost
0	9	11
1	12	11
2	16	9
done	16	9

end0.0ms

sample690.0ms

Algorithm

intervals

Results

145.0ms	8101×	body	80	nan
145.0ms	1713×	body	1280	valid
86.0ms	1251×	body	640	valid
82.0ms	4067×	body	80	valid
33.0ms	615×	body	320	valid
12.0ms	354×	body	160	valid