Details

sample4.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 30.844116%

Guaranteed chance to sample good point: 45.302502%

Results

73.0ms	129×	body	1280	valid
45.0ms	39×	body	1280	nan
27.0ms	55×	body	640	valid
19.0ms	128×	body	80	overflowed
14.0ms	19×	body	640	nan
6.0ms	20×	body	320	valid
6.0ms	15×	body	320	nan
6.0ms	8×	body	640	invalid
4.0ms	45×	body	80	valid
3.0ms	2×	body	1280	invalid
3.0ms	6×	body	320	invalid
1.0ms	7×	body	160	valid
1.0ms	7×	body	80	invalid
1.0ms	5×	body	160	nan
1.0ms	12×	body	80	nan
0.0ms	1×	body	160	invalid

simplify32.0ms

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

prune3.0ms

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: 35.2b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite19.0ms

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:

3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
8.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series73.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(pow x (/ 1.0 n))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
44.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	552	688
1	1885	669
2	5002	641

prune184.0ms

Filtered

71 candidates to 88 candidates (-23.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 23.3b

Counts

89 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
1.4b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
64×	`unpow-prod-down`
55×	`*-un-lft-identity`
36×	`sqrt-prod`
32×	`difference-of-squares`
26×	`pow-unpow`
24×	`add-cube-cbrt`
23×	`associate-r`
18×	`times-frac` `sqr-pow`
10×	`pow1`
9×	`distribute-lft-out`
8×	`add-exp-log` `distribute-lft-out--`
7×	`associate-l`
6×	`pow-pow` `add-cbrt-cube` `add-log-exp`
4×	`frac-times` `flip3--` `flip--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `pow-exp` `sqrt-pow2` `div-inv`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 154

Calls

4 calls:

28.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
30.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
30.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
103.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify90.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	697	2349
1	3117	2202
2	5002	2186

prune476.0ms

Filtered

114 candidates to 166 candidates (-45.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	166	4	170

Merged error: 23.3b

Counts

170 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.1b	(exp (log (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))))
0.2b	(log (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
1.4b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
73×	`unpow-prod-down`
48×	`difference-of-squares`
46×	`log-prod`
45×	`*-un-lft-identity`
40×	`sqrt-prod`
25×	`sqr-pow`
23×	`exp-sum`
16×	`add-cube-cbrt`
13×	`pow-unpow`
12×	`distribute-lft-out--`
9×	`times-frac`
8×	`pow1`
6×	`add-exp-log` `add-log-exp`
4×	`log-div` `exp-prod` `add-cbrt-cube` `distribute-lft-out`
3×	`flip3--` `pow-pow` `flip--`
2×	`exp-diff` `log-pow`
1×	`pow-to-exp` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `rem-log-exp` `pow-exp` `sqrt-pow2` `div-inv` `rem-exp-log`

Counts

4 → 137

Calls

4 calls:

6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
13.0ms	(exp (log (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))))
14.0ms	(log (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series596.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
105.0ms	(exp (log (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))))
359.0ms	(log (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
103.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify72.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	677	2249
1	2420	2154
2	5002	2131

prune455.0ms

Filtered

97 candidates to 149 candidates (-53.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	149	4	153

Merged error: 23.3b

Counts

153 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.1b	(exp (cbrt (pow (log (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))) 3)))
0.2b	(log (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
1.4b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
55×	`unpow-prod-down`
38×	`*-un-lft-identity`
32×	`difference-of-squares`
28×	`sqrt-prod`
23×	`log-prod`
18×	`add-cube-cbrt` `sqr-pow`
17×	`exp-prod`
14×	`cbrt-prod`
13×	`pow-unpow`
9×	`pow1` `times-frac`
8×	`distribute-lft-out--`
7×	`add-log-exp`
6×	`add-exp-log`
4×	`cube-prod` `add-cbrt-cube`
3×	`pow-pow` `log-pow` `distribute-lft-out`
2×	`log-div` `flip3--` `flip--`
1×	`cube-mult` `pow-to-exp` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `unpow3` `rem-log-exp` `pow-exp` `sqrt-pow2` `div-inv` `rem-exp-log`

Counts

4 → 125

Calls

4 calls:

6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
4.0ms	(exp (cbrt (pow (log (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))) 3)))
12.0ms	(log (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
103.0ms	(exp (cbrt (pow (log (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))) 3)))
356.0ms	(log (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
106.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify77.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	699	1927
1	2644	1847
2	5003	1845

prune474.0ms

Filtered

91 candidates to 137 candidates (-50.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	137	4	141

Merged error: 23.3b

Counts

141 → 4

regimes229.0ms

Accuracy

83.3% (1.9b remaining)

Error of 24.3b against oracle of 22.4b and baseline of 33.7b

bsearch110.0ms

Steps

Iters	Range		Point
7	560757003.8783413	13735597815.735905	914165034.2743983
6	-246.9799932410125	-33.975248266551965	-41.86171116093254

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	58
1	64	58
2	64	58

end0.0ms

sample11.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 30.844116%

Guaranteed chance to sample good point: 45.302502%

Results

2.1s	3803×	body	1280	valid
1.3s	1127×	body	1280	nan
670.0ms	951×	body	640	nan
666.0ms	1512×	body	640	valid
626.0ms	4126×	body	80	overflowed
234.0ms	753×	body	320	valid
188.0ms	271×	body	640	invalid
188.0ms	437×	body	320	nan
149.0ms	1564×	body	80	valid
123.0ms	89×	body	1280	invalid
72.0ms	368×	body	160	valid
69.0ms	170×	body	320	invalid
48.0ms	215×	body	160	nan
32.0ms	460×	body	80	nan
23.0ms	95×	body	160	invalid
18.0ms	151×	body	80	invalid

Details

sample4.6s

simplify32.0ms

prune3.0ms

localize8.0ms

rewrite19.0ms

series73.0ms

simplify50.0ms

prune184.0ms

localize12.0ms

rewrite60.0ms

series360.0ms

simplify90.0ms

prune476.0ms

localize15.0ms

rewrite52.0ms

series596.0ms

simplify72.0ms

prune455.0ms

localize18.0ms

rewrite40.0ms

series595.0ms

simplify77.0ms

prune474.0ms

regimes229.0ms

bsearch110.0ms

simplify2.0ms

end0.0ms

sample11.6s

Profiling