Details

sample26.0ms

Algorithm

intervals

Results

11.0ms	84×	body	1280	valid
4.0ms	128×	body	80	valid
3.0ms	25×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	4×	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: 16.3b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

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))
5.0ms	(- (atan (+ N 1.0)) (atan N))

series14.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
12.0ms	(- (atan (+ N 1.0)) (atan N))

simplify76.0ms

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

prune49.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.1b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite23.0ms

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:

22.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series47.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify58.0ms

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

prune67.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
14.3b	(cbrt (* (+ N 1.0) N))
14.3b	(cbrt (* (+ N 1.0) N))
14.3b	(cbrt (* (+ N 1.0) N))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

20.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
6.0ms	(cbrt (* (+ N 1.0) N))
6.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))

series418.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
98.0ms	(cbrt (* (+ N 1.0) N))
104.0ms	(cbrt (* (+ N 1.0) N))
97.0ms	(cbrt (* (+ N 1.0) N))

simplify44.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	353	803
1	1280	743
2	5001	669

prune255.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt N) (cbrt (* (+ N 1.0) N)))
0.6b	(cbrt N)
14.3b	(cbrt (* (+ N 1.0) N))
14.3b	(cbrt (* (+ N 1.0) N))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

14.0ms	(* (cbrt N) (cbrt (* (+ N 1.0) N)))
1.0ms	(cbrt N)
6.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))

series493.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (cbrt N) (cbrt (* (+ N 1.0) N)))
190.0ms	(cbrt N)
99.0ms	(cbrt (* (+ N 1.0) N))
97.0ms	(cbrt (* (+ N 1.0) N))

simplify41.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	360	572
1	1240	535
2	5002	503

prune252.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes26.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

end0.0ms

sample729.0ms

Algorithm

intervals

Results

373.0ms	2876×	body	1280	valid
123.0ms	4033×	body	80	valid
67.0ms	637×	body	640	valid
25.0ms	300×	body	320	valid
10.0ms	154×	body	160	valid