Details

sample27.0ms

Algorithm

intervals

Results

13.0ms	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

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite4.0ms

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))
3.0ms	(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
11.0ms	(- (atan (+ N 1.0)) (atan N))

simplify79.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2491	142
5	5001	142

prune51.0ms

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)))

series49.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify59.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	121	151
1	432	127
2	2321	127
3	5002	127

prune65.0ms

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:

3.0ms	(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)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ N 1.0))
90.0ms	(cbrt (+ N 1.0))
90.0ms	(cbrt (+ N 1.0))
110.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))

simplify152.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (142.0ms)

Iter	Nodes	Cost
0	305	792
1	1006	747
2	4433	693
3	5002	689

prune291.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

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)))

rewrite48.0ms

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))
20.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
15.0ms	(/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0)))
2.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (+ N 1.0))
103.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
127.0ms	(/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0)))
196.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	646	1927
1	2415	1866
2	5001	1789

prune581.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes27.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	17
1	25	17

end0.0ms

sample693.0ms

Algorithm

intervals

Results

374.0ms	2906×	body	1280	valid
116.0ms	4030×	body	80	valid
65.0ms	598×	body	640	valid
26.0ms	317×	body	320	valid
12.0ms	149×	body	160	valid