Details

sample28.0ms

Algorithm

intervals

Results

14.0ms	102×	body	1280	valid
4.0ms	122×	body	80	valid
3.0ms	25×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	2×	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: 15.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.5b	(- (atan (+ N 1.0)) (atan N))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 22

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
2.0ms	(- (atan (+ N 1.0)) (atan N))

series13.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
12.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.5s

Counts

28 → 28

Iterations

Useful iterations: 4 (89.0ms)

Iter	Nodes	Cost
0	40	271
1	76	259
2	144	245
3	238	241
4	457	239
5	1155	239
6	4316	239
done	5000	239

prune52.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.2b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
3×	`associate-r`
2×	`associate-*l/` `add-log-exp`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 28

Calls

2 calls:

10.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series50.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify3.2s

Counts

34 → 34

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	55	317
1	120	312
2	347	264
3	1178	264
4	3491	264
done	5000	264

prune71.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.3b	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

2.0ms	(cbrt (+ N 1.0))
2.0ms	(cbrt (+ N 1.0))
2.0ms	(cbrt (+ N 1.0))
20.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ N 1.0))
87.0ms	(cbrt (+ N 1.0))
86.0ms	(cbrt (+ N 1.0))
106.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))

simplify1.0s

Counts

107 → 107

Iterations

Useful iterations: 3 (381.0ms)

Iter	Nodes	Cost
0	139	1485
1	307	1358
2	810	1288
3	2257	1148
done	5001	1148

prune256.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1.0))
0.3b	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.3b	(/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0)))
15.9b	(cbrt (- (* N N) (* 1.0 1.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

108×	`cbrt-prod`
80×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
56×	`times-frac`
48×	`add-cube-cbrt`
20×	`cbrt-div`
18×	`difference-of-squares`
11×	`pow1`
9×	`swap-sqr`
8×	`add-exp-log` `pow1/3` `associate-/r*` `distribute-lft-out--`
7×	`flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out` `associate-/l*`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 168

Calls

4 calls:

2.0ms	(cbrt (+ N 1.0))
19.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
12.0ms	(/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0)))
2.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (+ N 1.0))
106.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
119.0ms	(/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0)))
183.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

simplify632.0ms

Counts

180 → 180

Iterations

Useful iterations: done (627.0ms)

Iter	Nodes	Cost
0	315	3526
1	645	3258
2	1735	3152
done	5001	3126

prune515.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes21.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	31
1	25	31
done	25	31

end0.0ms

sample694.0ms

Algorithm

intervals

Results

372.0ms	2906×	body	1280	valid
118.0ms	4030×	body	80	valid
66.0ms	598×	body	640	valid
26.0ms	317×	body	320	valid
9.0ms	149×	body	160	valid