Details

sample214.0ms

Algorithm

intervals

Results

70.0ms	133×	body	1280	valid
24.0ms	25×	body	1280	nan
24.0ms	53×	body	640	valid
19.0ms	128×	body	80	overflowed
17.0ms	25×	body	640	nan
14.0ms	100×	body	80	valid
9.0ms	191×	body	80	nan
7.0ms	23×	body	320	valid
6.0ms	15×	body	320	nan
3.0ms	17×	body	160	valid
1.0ms	4×	body	160	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.6b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.1b	(pow x (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series479.0ms

Counts

3 → 9

Calls

3 calls:

146.0ms	(pow (+ x 1.0) (/ 1.0 n))
54.0ms	(pow x (/ 1.0 n))
278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	476	639
1	1600	623
2	5001	609

prune224.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 21.3b

Counts

89 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
0.1b	(pow (sqrt x) (/ 1.0 n))
0.1b	(pow (sqrt x) (/ 1.0 n))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
57×	`unpow-prod-down`
34×	`add-cube-cbrt` `*-un-lft-identity`
28×	`sqrt-prod`
26×	`pow-unpow`
18×	`add-exp-log` `times-frac`
16×	`unswap-sqr`
15×	`sqr-pow`
12×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`prod-exp`
8×	`pow1` `pow-to-exp` `pow-exp`
6×	`pow-pow` `add-cbrt-cube` `add-log-exp`
3×	`difference-of-squares`
2×	`sqrt-pow1` `pow1/2` `sqrt-pow2` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod`

Counts

4 → 151

Calls

4 calls:

9.0ms	(* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
4.0ms	(pow (sqrt x) (/ 1.0 n))
4.0ms	(pow (sqrt x) (/ 1.0 n))
6.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))

series1.2s

Counts

4 → 12

Calls

4 calls:

270.0ms	(* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
207.0ms	(pow (sqrt x) (/ 1.0 n))
212.0ms	(pow (sqrt x) (/ 1.0 n))
505.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))

simplify66.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	498	1347
1	2054	1268
2	5001	1254

prune336.0ms

Filtered

163 candidates to 100 candidates (61.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	162	9	171

Merged error: 21.3b

Counts

171 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (log (sqrt x)) (/ 1.0 n)))
0.1b	(pow (sqrt x) (/ 1.0 n))
0.4b	(* (log (sqrt x)) (/ 1.0 n))
3.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`pow-unpow` `associate-r`
10×	`pow1` `add-exp-log`
9×	`add-cbrt-cube`
7×	`add-log-exp`
6×	`unpow-prod-down` `associate-l`
3×	`pow-pow` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `pow-exp` `-commutative` `sqrt-pow2` `flip--` `rem-exp-log` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

2.0ms	(exp (* (log (sqrt x)) (/ 1.0 n)))
4.0ms	(pow (sqrt x) (/ 1.0 n))
8.0ms	(* (log (sqrt x)) (/ 1.0 n))
6.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

210.0ms	(exp (* (log (sqrt x)) (/ 1.0 n)))
215.0ms	(pow (sqrt x) (/ 1.0 n))
159.0ms	(* (log (sqrt x)) (/ 1.0 n))
733.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	592	835
1	2383	729
2	5002	725

prune294.0ms

Filtered

102 candidates to 74 candidates (72.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	102	9	111

Merged error: 21.3b

Counts

111 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt x)) (/ 1.0 n))
3.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))
3.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))
3.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`times-frac` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l`
3×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 71

Calls

4 calls:

8.0ms	(* (log (sqrt x)) (/ 1.0 n))
6.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))
6.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))
7.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (log (sqrt x)) (/ 1.0 n))
735.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))
760.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))
747.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (exp (* (log (sqrt x)) (/ 1.0 n)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	469	1236
1	1773	1098
2	5001	1055

prune528.0ms

Filtered

83 candidates to 67 candidates (80.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	83	9	92

Merged error: 21.3b

Counts

92 → 9

regimes235.0ms

Accuracy

81.9% (2.0b remaining)

Error of 24.2b against oracle of 22.2b and baseline of 33.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	69
1	43	69

end0.0ms

sample7.1s

Algorithm

intervals

Results

2.1s	3883×	body	1280	valid
1.2s	1050×	body	1280	nan
843.0ms	1831×	body	640	valid
666.0ms	930×	body	640	nan
623.0ms	3981×	body	80	overflowed
313.0ms	6166×	body	80	nan
300.0ms	3038×	body	80	valid
285.0ms	886×	body	320	valid
204.0ms	456×	body	320	nan
91.0ms	475×	body	160	valid
47.0ms	214×	body	160	nan

Details

sample214.0ms

simplify34.0ms

prune2.0ms

localize9.0ms

rewrite21.0ms

series479.0ms

simplify47.0ms

prune224.0ms

localize11.0ms

rewrite29.0ms

series1.2s

simplify66.0ms

prune336.0ms

localize20.0ms

rewrite24.0ms

series1.3s

simplify60.0ms

prune294.0ms

localize21.0ms

rewrite29.0ms

series2.4s

simplify50.0ms

prune528.0ms

regimes235.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample7.1s

Profiling