Details

sample41.0ms

Algorithm

intervals

Results

23.0ms	100×	body	1280	valid
6.0ms	121×	body	80	valid
3.0ms	17×	body	640	valid
3.0ms	18×	body	320	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: 15.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.8b	(- (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:

0.0ms	(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))
11.0ms	(- (atan (+ N 1.0)) (atan N))

simplify75.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (10.0ms)

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

prune52.0ms

Pruning

2 alts after pruning (2 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)))

series47.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify54.0ms

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

prune62.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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:

18.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
5.0ms	(cbrt (+ N 1.0))
2.0ms	(cbrt (+ N 1.0))
2.0ms	(cbrt (+ N 1.0))

series374.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
91.0ms	(cbrt (+ N 1.0))
91.0ms	(cbrt (+ N 1.0))
89.0ms	(cbrt (+ N 1.0))

simplify147.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (138.0ms)

Iter	Nodes	Cost
0	305	792
1	999	747
2	4427	693
3	5001	689

prune282.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize21.0ms

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))
17.3b	(cbrt (- (* N N) (* 1.0 1.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

17×	`cbrt-prod`
14×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `cbrt-div`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
2×	`flip3--` `flip3-+` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 57

Calls

4 calls:

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

series650.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (+ N 1.0))
274.0ms	(cbrt (+ N 1.0))
100.0ms	(cbrt (- N 1.0))
190.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

simplify137.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	421	522
1	1298	493
2	4467	476
3	5002	476

prune275.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes21.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample1.1s

Algorithm

intervals

Results

649.0ms	2858×	body	1280	valid
199.0ms	4043×	body	80	valid
113.0ms	616×	body	640	valid
45.0ms	335×	body	320	valid
14.0ms	148×	body	160	valid