Details

analyze809.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	36%	19.4%	13
45.5%	34.5%	20%	14

sample174.0ms

Algorithm

intervals

Results

81.0ms	50×	body	2048	valid
49.0ms	80×	body	1024	valid
14.0ms	50×	body	512	valid
5.0ms	8×	body	1024	invalid
4.0ms	56×	body	128	valid
3.0ms	1×	body	4096	valid
3.0ms	8×	body	512	invalid
3.0ms	19×	body	256	valid
1.0ms	4×	body	256	invalid
1.0ms	9×	body	128	invalid
0.0ms	9×	body	128	nan

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4995	22
1	4995	22

prune2.0ms

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: 47.7b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.8b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
6.6b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
8.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

584×	`times-frac_binary64`
485×	`add-sqr-sqrt_binary64`
366×	`*-un-lft-identity_binary64`
224×	`add-cube-cbrt_binary64`
174×	`associate-r_binary64`
168×	`difference-of-squares_binary64`
88×	`unpow-prod-down_binary64`
85×	`sqr-pow_binary64`
84×	`difference-of-sqr-1_binary64`
29×	`div-inv_binary64`
28×	`distribute-lft-out--_binary64`
19×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
13×	`associate-/r_binary64` `associate-/l_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `pow-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64` `-commutative_binary64`

Counts

4 → 448

Calls

4 calls:

62.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
12.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
8.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
27.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

series1.8s

Counts

4 → 12

Calls

4 calls:

611.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
354.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
307.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
577.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

simplify193.0ms

Algorithm

egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4979	14740
1	4979	14740

prune502.0ms

Filtered

266 candidates to 460 candidates (-72.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	448	12	460
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	449	12	461

Merged error: 18.9b

Counts

461 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.1b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.3b	(*.f64 1/6 i)
15.7b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac_binary64`
97×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
50×	`associate-r_binary64`
25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-/r*_binary64` `pow1_binary64`
9×	`div-inv_binary64`
7×	`cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64`
5×	`pow-prod-down_binary64` `unswap-sqr_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r/_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `flip-+_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 179

Calls

4 calls:

22.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
9.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)
9.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

series285.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
84.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
22.0ms	(*.f64 1/6 i)
84.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

simplify100.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4946	5462
1	4946	5462

prune251.0ms

Filtered

150 candidates to 191 candidates (-27.3%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	179	12	191
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	180	23	203

Merged error: 10.3b

Counts

203 → 23

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(.f64 i (+.f64 50 (.f64 50/3 i)))
0.5b	(*.f64 50/3 i)
2.9b	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
9×	`-un-lft-identity_binary64` `pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l*_binary64`
4×	`associate-*r/_binary64`
3×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip-+_binary64`

Counts

3 → 62

Calls

3 calls:

6.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
4.0ms	(*.f64 50/3 i)
6.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))

series188.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
20.0ms	(*.f64 50/3 i)
85.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))

simplify77.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5012	915

prune82.0ms

Filtered

51 candidates to 71 candidates (-39.2%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	2	20	22
Picked	0	1	1
Done	0	0	0
Total	72	22	94

Merged error: 10.3b

Counts

94 → 22

localize13.0ms

Local error

Found 4 expressions with local error:

2.9b	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))))
11.7b	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
11.7b	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
11.7b	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-*r/_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-div_binary64` `*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
3×	`associate-r_binary64` `pow1/3_binary64` `associate-l_binary64` `cbrt-prod_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 55

Calls

4 calls:

6.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))))
4.0ms	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
4.0ms	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
4.0ms	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))

series752.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))))
228.0ms	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
218.0ms	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
231.0ms	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))

simplify90.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4877	1669
1	4877	1669

prune124.0ms

Filtered

55 candidates to 67 candidates (-21.8%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	2	18	20
Picked	1	0	1
Done	0	1	1
Total	67	22	89

Merged error: 10.3b

Counts

89 → 22

regimes250.0ms

Accuracy

71.9% (5.8b remaining)

Error of 14.6b against oracle of 8.8b and baseline of 29.5b

bsearch156.0ms

Steps

Iters	Range		Point
9	0.00034675484987927325	192694.3188325816	0.11891451146914414
10	-4219889013761967.5	-189.30453191564666	-192.07922351078327

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	48
1	40	48

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.7s	1707×	body	2048	valid
1.6s	2700×	body	1024	valid
342.0ms	1188×	body	512	valid
124.0ms	1820×	body	128	valid
120.0ms	192×	body	1024	invalid
92.0ms	557×	body	256	valid
85.0ms	240×	body	512	invalid
81.0ms	28×	body	4096	valid
46.0ms	498×	body	128	invalid
32.0ms	148×	body	256	invalid
22.0ms	14×	body	2048	invalid
17.0ms	333×	body	128	nan

Details

analyze809.0ms

sample174.0ms

simplify64.0ms

prune2.0ms

localize9.0ms

rewrite187.0ms

series1.8s

simplify193.0ms

prune502.0ms

localize11.0ms

rewrite67.0ms

series285.0ms

simplify100.0ms

prune251.0ms

localize7.0ms

rewrite20.0ms

series188.0ms

simplify77.0ms

prune82.0ms

localize13.0ms

rewrite27.0ms

series752.0ms

simplify90.0ms

prune124.0ms

regimes250.0ms

bsearch156.0ms

simplify2.0ms

end0.0ms

sample5.6s

Profiling