Details

analyze1.6s (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample101.0ms (0.1%)

Algorithm

1×

intervals

Results

39.0ms	84×	body	1024	valid
22.0ms	109×	body	128	valid
10.0ms	6×	body	2048	valid
6.0ms	39×	body	512	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify385.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

prune9.0ms (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: 38.7b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize44.0ms (0%)

Local error

Found 2 expressions with local error:

0.5b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.5b	(-.f64 (exp.f64 x) 1)

rewrite116.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_782`
30×	`*-un-lft-identity_binary64_760`
21×	`times-frac_binary64_766`
15×	`add-cube-cbrt_binary64_795`
10×	`difference-of-squares_binary64_729`
7×	`associate-/r*_binary64_704`
5×	`difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712`
4×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726` `associate-/l*_binary64_705`
2×	`associate-/r/_binary64_706` `pow1_binary64_821` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

2 → 63

Calls

2 calls:

69.0ms	(-.f64 (exp.f64 x) 1)
23.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

series183.0ms (0.1%)

Counts

2 → 6

Calls

2 calls:

154.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
28.0ms	(-.f64 (exp.f64 x) 1)

simplify290.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (225.0ms)

Iter	Nodes	Cost
0	4915	1129
1	4915	1129

prune1.0s (0.7%)

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	36	33	69
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	34	70

Merged error: 0.0b

Counts

70 → 34

Compiler

Compiled 1452 to 799 computations (45% saved)

localize33.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
0.1b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.1b	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
0.3b	(*.f64 x 1/6)

rewrite126.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
17×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
15×	`add-cbrt-cube_binary64_796`
14×	`add-exp-log_binary64_798`
13×	`pow1_binary64_821`
9×	`associate-l_binary64_701` `times-frac_binary64_766`
7×	`associate-r_binary64_700`
6×	`associate-*r/_binary64_702`
5×	`prod-exp_binary64_809` `distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
4×	`add-log-exp_binary64_799`
3×	`flip3-+_binary64_763` `associate-/r_binary64_704` `flip-+_binary64_734` `associate-/l_binary64_705` `*-commutative_binary64_691`
2×	`unswap-sqr_binary64_728` `associate-/r/_binary64_706`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

4 → 93

Calls

4 calls:

30.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
27.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
23.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
16.0ms	(*.f64 x 1/6)

series486.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

172.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
159.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
109.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
46.0ms	(*.f64 x 1/6)

simplify408.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (317.0ms)

Iter	Nodes	Cost
0	4908	1844
1	4908	1844

prune3.8s (2.5%)

Pruning

64 alts after pruning (62 fresh and 2 done)

	Pruned	Kept	Total
New	74	31	105
Fresh	1	31	32
Picked	0	1	1
Done	0	1	1
Total	75	64	139

Merged error: 0.0b

Counts

139 → 64

Compiler

Compiled 3533 to 2296 computations (35% saved)

localize45.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (neg.f64 (exp.f64 x)) (.f64 x (-.f64 -1 (.f64 x (+.f64 (*.f64 x 1/6) 1/2)))))
0.0b	(.f64 x (-.f64 -1 (.f64 x (+.f64 (*.f64 x 1/6) 1/2))))
0.1b	(.f64 x (+.f64 (.f64 x 1/6) 1/2))
0.3b	(*.f64 x 1/6)

rewrite173.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_782`
16×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
15×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
10×	`associate-/l*_binary64_705` `pow1_binary64_821` `times-frac_binary64_766`
9×	`associate-r_binary64_700` `associate-l_binary64_701`
6×	`distribute-lft-neg-in_binary64_717` `associate-*r/_binary64_702` `distribute-rgt-neg-in_binary64_718`
4×	`prod-exp_binary64_809` `add-log-exp_binary64_799` `cbrt-unprod_binary64_793`
3×	`unswap-sqr_binary64_728` `distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `pow-prod-down_binary64_831` `*-commutative_binary64_691`
2×	`neg-mul-1_binary64_756` `cbrt-undiv_binary64_794` `associate-/r/_binary64_706` `cancel-sign-sub-inv_binary64_726` `div-exp_binary64_811` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`
1×	`frac-2neg_binary64_771` `flip3-+_binary64_763` `distribute-frac-neg_binary64_723` `associate-/r*_binary64_704` `div-inv_binary64_757` `neg-sub0_binary64_755` `flip-+_binary64_734` `div-sub_binary64_765` `clear-num_binary64_759`

Counts

4 → 103

Calls

4 calls:

63.0ms	(.f64 x (-.f64 -1 (.f64 x (+.f64 (*.f64 x 1/6) 1/2))))
30.0ms	(.f64 x (+.f64 (.f64 x 1/6) 1/2))
29.0ms	(/.f64 (neg.f64 (exp.f64 x)) (.f64 x (-.f64 -1 (.f64 x (+.f64 (*.f64 x 1/6) 1/2)))))
17.0ms	(*.f64 x 1/6)

series466.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

230.0ms	(.f64 x (+.f64 (.f64 x 1/6) 1/2))
121.0ms	(/.f64 (neg.f64 (exp.f64 x)) (.f64 x (-.f64 -1 (.f64 x (+.f64 (*.f64 x 1/6) 1/2)))))
67.0ms	(.f64 x (-.f64 -1 (.f64 x (+.f64 (*.f64 x 1/6) 1/2))))
47.0ms	(*.f64 x 1/6)

simplify240.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4997	2037
1	4997	2037

prune6.9s (4.7%)

Pruning

84 alts after pruning (82 fresh and 2 done)

	Pruned	Kept	Total
New	85	30	115
Fresh	9	52	61
Picked	1	0	1
Done	0	2	2
Total	95	84	179

Merged error: 0.0b

Counts

179 → 84

Compiler

Compiled 4334 to 2938 computations (32.2% saved)

localize50.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 x 1/6) 1/2)
0.0b	(/.f64 (/.f64 (neg.f64 (exp.f64 x)) x) (-.f64 -1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
0.1b	(.f64 x (+.f64 (.f64 x 1/6) 1/2))
0.3b	(*.f64 x 1/6)

rewrite211.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

222×	`times-frac_binary64_766`
127×	`add-sqr-sqrt_binary64_782`
123×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
36×	`distribute-lft-neg-in_binary64_717` `distribute-rgt-neg-in_binary64_718`
34×	`associate-/l*_binary64_705`
13×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
12×	`neg-mul-1_binary64_756`
8×	`pow1_binary64_821`
6×	`add-log-exp_binary64_799` `associate-r_binary64_700` `associate-l_binary64_701`
5×	`div-inv_binary64_757`
3×	`cbrt-undiv_binary64_794` `associate-/r*_binary64_704` `div-exp_binary64_811`
2×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `associate-/r/_binary64_706` `flip3-+_binary64_763` `distribute-frac-neg_binary64_723` `flip-+_binary64_734` `div-sub_binary64_765` `associate-r/_binary64_702` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `-commutative_binary64_691`
1×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `distribute-lft-in_binary64_709` `neg-sub0_binary64_755` `distribute-rgt-in_binary64_710` `+-commutative_binary64_690` `sum-log_binary64_851` `clear-num_binary64_759` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 209

Calls

4 calls:

50.0ms	(/.f64 (/.f64 (neg.f64 (exp.f64 x)) x) (-.f64 -1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
27.0ms	(.f64 x (+.f64 (.f64 x 1/6) 1/2))
14.0ms	(*.f64 x 1/6)
13.0ms	(+.f64 (*.f64 x 1/6) 1/2)

series373.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

150.0ms	(.f64 x (+.f64 (.f64 x 1/6) 1/2))
103.0ms	(/.f64 (/.f64 (neg.f64 (exp.f64 x)) x) (-.f64 -1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
81.0ms	(+.f64 (*.f64 x 1/6) 1/2)
38.0ms	(*.f64 x 1/6)

simplify803.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (307.0ms)

Iter	Nodes	Cost
0	4923	7585
1	4923	7585

prune12.3s (8.3%)

Pruning

115 alts after pruning (113 fresh and 2 done)

	Pruned	Kept	Total
New	168	53	221
Fresh	21	60	81
Picked	0	1	1
Done	1	1	2
Total	190	115	305

Merged error: 0.0b

Counts

305 → 115

Compiler

Compiled 6113 to 3402 computations (44.3% saved)

regimes9.8s (6.6%)

Compiler: Compiled 27131 to 19637 computations (27.6% saved)

bsearch1.2min (46.6%)

Compiler: Compiled 2 to 2 computations (0% saved)

simplify25.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	102	42
1	102	42

end0.0ms (0%)

sample39.7s (26.6%)

Algorithm

1×

intervals

Results

1.6s	2612×	body	1024	valid
461.0ms	1329×	body	512	valid
301.0ms	3144×	body	128	valid
192.0ms	638×	body	256	valid
183.0ms	277×	body	2048	valid

Compiler

Compiled 8868 to 6436 computations (27.4% saved)

Pareto

Details

analyze1.6s (1.1%)

sample101.0ms (0.1%)

simplify385.0ms (0.3%)

prune9.0ms (0%)

localize44.0ms (0%)

rewrite116.0ms (0.1%)

series183.0ms (0.1%)

simplify290.0ms (0.2%)

prune1.0s (0.7%)

localize33.0ms (0%)

rewrite126.0ms (0.1%)

series486.0ms (0.3%)

simplify408.0ms (0.3%)

prune3.8s (2.5%)

localize45.0ms (0%)

rewrite173.0ms (0.1%)

series466.0ms (0.3%)

simplify240.0ms (0.2%)

prune6.9s (4.7%)

localize50.0ms (0%)

rewrite211.0ms (0.1%)

series373.0ms (0.2%)

simplify803.0ms (0.5%)

prune12.3s (8.3%)

regimes9.8s (6.6%)

bsearch1.2min (46.6%)

simplify25.0ms (0%)

end0.0ms (0%)

sample39.7s (26.6%)

Profiling