Details

analyze6.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

sample27.0ms

Algorithm

intervals

Results

8.0ms	50×	body	640	valid
5.0ms	135×	body	80	valid
4.0ms	35×	body	320	valid
4.0ms	20×	body	1280	valid
1.0ms	16×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	191	15
1	191	15

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 9.0b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
18×	`distribute-lft-out--_binary64`
17×	`distribute-lft-out_binary64`
14×	`difference-of-squares_binary64`
12×	`add-exp-log_binary64`
11×	`associate-/r*_binary64` `add-log-exp_binary64`
8×	`add-cbrt-cube_binary64` `div-inv_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`difference-of-sqr-1_binary64` `associate-/r/_binary64` `div-exp_binary64`
3×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-flip_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

6.0ms	(/.f64 1 (+.f64 x 1))
6.0ms	(/.f64 1 (-.f64 x 1))
18.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
41.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series15.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/.f64 1 (+.f64 x 1))
2.0ms	(/.f64 1 (-.f64 x 1))
3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
8.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

simplify66.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4987	1726
1	4987	1726

prune101.0ms

Filtered

88 candidates to 147 candidates (-67.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	143	4	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	4	148

Merged error: 0.1b

Counts

148 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.2b	(-.f64 x (*.f64 (+.f64 1 x) 2))
16.5b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
42×	`associate-*r/_binary64`
35×	`*-un-lft-identity_binary64`
32×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
27×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64` `frac-times_binary64`
18×	`flip3-+_binary64` `associate-/l/_binary64` `difference-of-squares_binary64` `flip-+_binary64`
10×	`associate-*l/_binary64`
9×	`associate-/r*_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-l_binary64`
6×	`pow1_binary64`
5×	`sub-neg_binary64` `distribute-lft-out--_binary64`
4×	`distribute-rgt-out--_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `unpow3_binary64`
3×	`associate-r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64`
2×	`associate-+l+_binary64` `associate-/r/_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 145

Calls

4 calls:

22.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
9.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
12.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

series12.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
3.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
2.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
1.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4940	4416
1	4940	4416

prune220.0ms

Filtered

126 candidates to 157 candidates (-24.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	157	4	161

Merged error: 0.0b

Counts

161 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.2b	(-.f64 x (*.f64 (+.f64 1 x) 2))
1.6b	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
14.8b	(/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
8×	`associate-/r*_binary64` `add-log-exp_binary64` `difference-of-squares_binary64`
6×	`associate-/l*_binary64`
5×	`pow1_binary64`
4×	`difference-of-sqr-1_binary64` `associate-/r/_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `frac-add_binary64` `associate-+l-_binary64` `inv-pow_binary64` `prod-exp_binary64` `rec-exp_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 101

Calls

4 calls:

6.0ms	(/.f64 1 (-.f64 x 1))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
23.0ms	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
9.0ms	(/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/.f64 1 (-.f64 x 1))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
11.0ms	(+.f64 (/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x))) (/.f64 1 (-.f64 x 1)))
4.0ms	(/.f64 (-.f64 x (.f64 (+.f64 1 x) 2)) (.f64 x (+.f64 1 x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5730	1305

prune69.0ms

Filtered

74 candidates to 113 candidates (-52.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	113	4	117

Merged error: 0.0b

Counts

117 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 2 (pow.f64 x 7))
0.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3)))
0.0b	(/.f64 2 (pow.f64 x 5))
0.1b	(/.f64 2 (pow.f64 x 3))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac_binary64`
71×	`*-un-lft-identity_binary64`
63×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
36×	`unpow-prod-down_binary64`
26×	`associate-/r*_binary64`
19×	`add-exp-log_binary64`
12×	`sqr-pow_binary64` `cube-prod_binary64`
10×	`add-cbrt-cube_binary64`
9×	`associate-/l*_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`distribute-lft-out_binary64` `div-inv_binary64`
4×	`pow1_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64`
1×	`flip3-+_binary64` `frac-add_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 172

Calls

4 calls:

5.0ms	(/.f64 2 (pow.f64 x 7))
43.0ms	(+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3)))
5.0ms	(/.f64 2 (pow.f64 x 5))
6.0ms	(/.f64 2 (pow.f64 x 3))

series30.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 2 (pow.f64 x 7))
15.0ms	(+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3)))
5.0ms	(/.f64 2 (pow.f64 x 5))
4.0ms	(/.f64 2 (pow.f64 x 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5005	1727

prune137.0ms

Filtered

120 candidates to 184 candidates (-53.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	181	3	184
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	181	7	188

Merged error: 0.0b

Counts

188 → 7

regimes41.0ms

Accuracy

99% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 25.4b

bsearch35.0ms

Steps

Iters	Range		Point
9	0.0006431944855483245	123093.48002160975	1149.5258451434781
10	-33961174222298.895	-252.54666457998738	-105902111.75332928

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	99	49
1	99	49

end0.0ms

sample823.0ms

Algorithm

intervals

Results

292.0ms	1875×	body	640	valid
171.0ms	4139×	body	80	valid
114.0ms	570×	body	1280	valid
114.0ms	947×	body	320	valid
36.0ms	469×	body	160	valid

Details

analyze6.0ms

sample27.0ms

simplify10.0ms

prune3.0ms

localize9.0ms

rewrite76.0ms

series15.0ms

simplify66.0ms

prune101.0ms

localize13.0ms

rewrite54.0ms

series12.0ms

simplify87.0ms

prune220.0ms

localize12.0ms

rewrite44.0ms

series20.0ms

simplify52.0ms

prune69.0ms

localize12.0ms

rewrite64.0ms

series30.0ms

simplify58.0ms

prune137.0ms

regimes41.0ms

bsearch35.0ms

simplify3.0ms

end0.0ms

sample823.0ms

Profiling