Details

analyze4.0ms

Algorithm

Search

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

sample26.0ms

Algorithm

intervals

Results

13.0ms	67×	body	1024	valid
4.0ms	132×	body	128	valid
3.0ms	32×	body	512	valid
1.0ms	7×	body	2048	valid
1.0ms	18×	body	256	valid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

prune1.0ms

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: 30.4b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.2b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
20×	`distribute-lft-out_binary64`
18×	`distribute-lft-out--_binary64`
14×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64` `difference-of-sqr-1_binary64`
4×	`associate-/r/_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `frac-sub_binary64`

Counts

3 → 113

Calls

3 calls:

8.0ms	(/.f64 x (+.f64 x 1))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
41.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series124.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/.f64 x (+.f64 x 1))
25.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
74.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify78.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4942	2299
1	4942	2299

prune134.0ms

Filtered

77 candidates to 122 candidates (-58.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	4	123

Merged error: 0.0b

Counts

123 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (+.f64 x 1))
0.3b	(cbrt.f64 (+.f64 x 1))
0.3b	(cbrt.f64 (+.f64 x 1))
2.2b	(-.f64 (/.f64 x (+.f64 x 1)) (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (-.f64 x 1)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `flip-+_binary64` `frac-sub_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r/_binary64` `flip--_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 56

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 x 1))
12.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (-.f64 x 1)))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(cbrt.f64 (+.f64 x 1))
52.0ms	(cbrt.f64 (+.f64 x 1))
41.0ms	(cbrt.f64 (+.f64 x 1))
118.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (-.f64 x 1)))))

simplify77.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4893	1184
1	4893	1184

prune114.0ms

Filtered

60 candidates to 68 candidates (-13.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
0.3b	(/.f64 3 (pow.f64 x 3))
0.5b	(/.f64 -1 (*.f64 x x))
6.6b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64` `times-frac_binary64`
39×	`add-sqr-sqrt_binary64`
35×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-/r*_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
9×	`unpow3_binary64`
6×	`distribute-lft-out_binary64` `associate-/l*_binary64`
5×	`div-exp_binary64`
4×	`pow1_binary64` `distribute-rgt-out_binary64` `sqr-pow_binary64` `div-inv_binary64` `cube-mult_binary64`
3×	`cbrt-undiv_binary64` `frac-sub_binary64`
2×	`flip3-+_binary64` `diff-log_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `distribute-rgt1-in_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 128

Calls

4 calls:

30.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
6.0ms	(/.f64 3 (pow.f64 x 3))
5.0ms	(/.f64 -1 (*.f64 x x))
44.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
45.0ms	(/.f64 3 (pow.f64 x 3))
31.0ms	(/.f64 -1 (*.f64 x x))
34.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify58.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5319	2247

prune107.0ms

Filtered

87 candidates to 140 candidates (-60.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	140	4	144

Merged error: 0b

Counts

144 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 1 (/.f64 1 (.f64 x x))) (/.f64 3 x))
0.5b	(/.f64 -1 (*.f64 x x))
0.5b	(/.f64 1 (*.f64 x x))
6.6b	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 (+.f64 1 (/.f64 1 (*.f64 x x))) (/.f64 3 x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64` `add-cbrt-cube_binary64`
16×	`add-cube-cbrt_binary64` `times-frac_binary64`
14×	`pow1_binary64`
13×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64` `pow-flip_binary64`
5×	`cbrt-undiv_binary64` `associate-l_binary64` `prod-exp_binary64` `div-exp_binary64` `frac-sub_binary64`
4×	`flip3-+_binary64` `cbrt-unprod_binary64` `div-inv_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
2×	`pow-prod-down_binary64` `associate-/r_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `inv-pow_binary64` `pow-sqr_binary64` `flip--_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 105

Calls

4 calls:

12.0ms	(.f64 (+.f64 1 (/.f64 1 (.f64 x x))) (/.f64 3 x))
5.0ms	(/.f64 -1 (*.f64 x x))
6.0ms	(/.f64 1 (*.f64 x x))
9.0ms	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 (+.f64 1 (/.f64 1 (*.f64 x x))) (/.f64 3 x)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(.f64 (+.f64 1 (/.f64 1 (.f64 x x))) (/.f64 3 x))
37.0ms	(/.f64 -1 (*.f64 x x))
21.0ms	(/.f64 1 (*.f64 x x))
30.0ms	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 (+.f64 1 (/.f64 1 (*.f64 x x))) (/.f64 3 x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5061	1805

prune87.0ms

Filtered

77 candidates to 117 candidates (-51.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	117	4	121

Merged error: 0b

Counts

121 → 4

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch43.0ms

Steps

Iters	Range		Point
10	0.001726028966807259	56161084.205591924	10786.998680762768
9	-26846056192.86527	-7.948560220524073	-11799.423822239964

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	115	73
1	115	73

end0.0ms

sample599.0ms

Algorithm

intervals

Results

231.0ms	1991×	body	1024	valid
129.0ms	4306×	body	128	valid
89.0ms	994×	body	512	valid
30.0ms	514×	body	256	valid
28.0ms	195×	body	2048	valid

Details

analyze4.0ms

sample26.0ms

simplify75.0ms

prune1.0ms

localize6.0ms

rewrite70.0ms

series124.0ms

simplify78.0ms

prune134.0ms

localize17.0ms

rewrite29.0ms

series250.0ms

simplify77.0ms

prune114.0ms

localize9.0ms

rewrite96.0ms

series212.0ms

simplify58.0ms

prune107.0ms

localize12.0ms

rewrite42.0ms

series190.0ms

simplify65.0ms

prune87.0ms

regimes25.0ms

bsearch43.0ms

simplify4.0ms

end0.0ms

sample599.0ms

Profiling