Details

analyze106.0ms (2.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	168	9
1	168	9
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

Symmetry

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample29.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms	82×	body	1024	valid
3.0ms	35×	body	512	valid
2.0ms	100×	body	128	valid
2.0ms	14×	body	2048	valid
1.0ms	25×	body	256	valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	168	9
1	168	9

prune2.0ms (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

Error

39.5b

Counts

2 → 1

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
4.5b	(-.f64 (exp.f64 x) 1)

rewrite78.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

39.1b

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-/l*_binary64_705`
5×	`difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712`
4×	`add-log-exp_binary64_799` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
3×	`cancel-sign-sub-inv_binary64_726` `associate-/r*_binary64_704`
2×	`pow1_binary64_821` `flip3--_binary64_764` `flip--_binary64_735` `associate-/l/_binary64_707`
1×	`diff-log_binary64_852` `sub-neg_binary64_753` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `div-sub_binary64_765` `clear-num_binary64_759` `div-inv_binary64_757`

Counts

2 → 64

Calls

2 calls:

7.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
4.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 893 to 496 computations (44.5% saved)

series64.0ms (1.6%)

Error

0.1b

Counts

2 → 12

Calls

2 calls:

34.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
17.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 242 to 192 computations (20.7% saved)

simplify65.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4961	1076
1	4961	1076

prune62.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	4	77

Error

0.0b

Counts

77 → 4

Compiler

Compiled 944 to 524 computations (44.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/6 (*.f64 x 1/24))
0.1b	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
0.2b	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
0.3b	(*.f64 x 1/24)

rewrite97.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

16×	`add-sqr-sqrt_binary64_782`
10×	`pow1_binary64_821` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
9×	`associate-l_binary64_701` `associate-r_binary64_700`
6×	`add-log-exp_binary64_799`
4×	`associate-*r/_binary64_702`
3×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691` `flip3-+_binary64_763` `flip-+_binary64_734`
2×	`distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709`
1×	`sum-log_binary64_851` `+-commutative_binary64_690`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
5.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
4.0ms	(*.f64 x 1/24)
3.0ms	(+.f64 1/6 (*.f64 x 1/24))

Compiler

Compiled 1504 to 1164 computations (22.6% saved)

series153.0ms (3.8%)

Error

0.0b

Counts

4 → 20

Calls

4 calls:

52.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
37.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
33.0ms	(+.f64 1/6 (*.f64 x 1/24))
18.0ms	(*.f64 x 1/24)

Compiler

Compiled 630 to 531 computations (15.7% saved)

simplify84.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4884	1083
1	4884	1083

prune91.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	93	4	97

Error

0.0b

Counts

97 → 4

Compiler

Compiled 1632 to 1264 computations (22.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (-.f64 (exp.f64 x) 1))
0.0b	(/.f64 1 (/.f64 x (-.f64 (exp.f64 x) 1)))
4.5b	(-.f64 (exp.f64 x) 1)

rewrite222.0ms (5.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

186×	`times-frac_binary64_766`
156×	`add-sqr-sqrt_binary64_782`
139×	`*-un-lft-identity_binary64_760`
88×	`add-cube-cbrt_binary64_795`
34×	`difference-of-squares_binary64_729` `associate-/r*_binary64_704`
17×	`difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712`
16×	`add-exp-log_binary64_798`
11×	`associate-/r/_binary64_706`
10×	`add-cbrt-cube_binary64_796`
8×	`div-exp_binary64_811`
6×	`flip3--_binary64_764` `flip--_binary64_735` `div-inv_binary64_757` `associate-/l*_binary64_705`
5×	`add-log-exp_binary64_799`
4×	`pow1_binary64_821` `cbrt-undiv_binary64_794`
3×	`cancel-sign-sub-inv_binary64_726`
2×	`1-exp_binary64_804` `rec-exp_binary64_810` `frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`diff-log_binary64_852` `sub-neg_binary64_753` `inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

3 → 195

Calls

3 calls:

11.0ms	(/.f64 1 (/.f64 x (-.f64 (exp.f64 x) 1)))
6.0ms	(/.f64 x (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 3714 to 2341 computations (37% saved)

series114.0ms (2.8%)

Error

0.0b

Counts

3 → 18

Calls

3 calls:

50.0ms	(/.f64 x (-.f64 (exp.f64 x) 1))
35.0ms	(/.f64 1 (/.f64 x (-.f64 (exp.f64 x) 1)))
18.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 402 to 334 computations (16.9% saved)

simplify114.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4926	4012
1	4926	4012

prune171.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	212	5	217

Error

0.0b

Counts

217 → 5

Compiler

Compiled 3314 to 1949 computations (41.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 1 (+.f64 (.f64 x (+.f64 (.f64 x 1/12) -1/2)) (*.f64 (pow.f64 x 4) -1/720))))
0.3b	(*.f64 (pow.f64 x 4) -1/720)
0.3b	(*.f64 x 1/12)
11.1b	(+.f64 (.f64 x (+.f64 (.f64 x 1/12) -1/2)) (*.f64 (pow.f64 x 4) -1/720))

rewrite177.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

26×	`*-un-lft-identity_binary64_760`
25×	`add-sqr-sqrt_binary64_782`
18×	`add-cube-cbrt_binary64_795`
15×	`add-exp-log_binary64_798`
12×	`times-frac_binary64_766`
10×	`add-cbrt-cube_binary64_796` `associate-l_binary64_701`
7×	`pow1_binary64_821`
6×	`add-log-exp_binary64_799` `associate-r_binary64_700`
4×	`prod-exp_binary64_809` `unswap-sqr_binary64_728` `unpow-prod-down_binary64_839` `distribute-lft-out_binary64_711` `associate-/r*_binary64_704`
3×	`associate-/l*_binary64_705`
2×	`flip3-+_binary64_763` `flip-+_binary64_734` `associate-+l+_binary64_693` `cbrt-unprod_binary64_793` `*-commutative_binary64_691` `sqr-pow_binary64_732` `div-exp_binary64_811` `associate-/r/_binary64_706`
1×	`sum-log_binary64_851` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `+-commutative_binary64_690` `pow-prod-down_binary64_831` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `inv-pow_binary64_845` `pow-flip_binary64_834` `1-exp_binary64_804` `rec-exp_binary64_810` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757`

Counts

4 → 93

Calls

4 calls:

10.0ms	(/.f64 1 (+.f64 1 (+.f64 (.f64 x (+.f64 (.f64 x 1/12) -1/2)) (*.f64 (pow.f64 x 4) -1/720))))
8.0ms	(+.f64 (.f64 x (+.f64 (.f64 x 1/12) -1/2)) (*.f64 (pow.f64 x 4) -1/720))
5.0ms	(*.f64 (pow.f64 x 4) -1/720)
4.0ms	(*.f64 x 1/12)

Compiler

Compiled 2516 to 2091 computations (16.9% saved)

series226.0ms (5.6%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

122.0ms	(+.f64 (.f64 x (+.f64 (.f64 x 1/12) -1/2)) (*.f64 (pow.f64 x 4) -1/720))
38.0ms	(*.f64 (pow.f64 x 4) -1/720)
27.0ms	(/.f64 1 (+.f64 1 (+.f64 (.f64 x (+.f64 (.f64 x 1/12) -1/2)) (*.f64 (pow.f64 x 4) -1/720))))
23.0ms	(*.f64 x 1/12)

Compiler

Compiled 733 to 647 computations (11.7% saved)

simplify110.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4939	2126
1	4939	2126

prune151.0ms (3.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	114	5	119

Error

0.0b

Counts

119 → 5

Compiler

Compiled 2569 to 2118 computations (17.6% saved)

regimes148.0ms (3.7%)

Accuracy

Total 0.5b remaining (99.3%)

Threshold costs 0.5b (99.3%)

Compiler

Compiled 1137 to 882 computations (22.4% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	42
1	47	42

Removed

()

end0.0ms (0%)

sample1.7s (42.6%)

Algorithm

1×

intervals

Results

410.0ms	2634×	body	1024	valid
119.0ms	1346×	body	512	valid
70.0ms	3034×	body	128	valid
52.0ms	294×	body	2048	valid
40.0ms	692×	body	256	valid

Compiler

Compiled 582 to 449 computations (22.9% saved)

Details

analyze106.0ms (2.6%)

sample29.0ms (0.7%)

simplify14.0ms (0.4%)

prune2.0ms (0%)

localize4.0ms (0.1%)

rewrite78.0ms (1.9%)

series64.0ms (1.6%)

simplify65.0ms (1.6%)

prune62.0ms (1.5%)

localize8.0ms (0.2%)

rewrite97.0ms (2.4%)

series153.0ms (3.8%)

simplify84.0ms (2.1%)

prune91.0ms (2.3%)

localize6.0ms (0.1%)

rewrite222.0ms (5.5%)

series114.0ms (2.8%)

simplify114.0ms (2.8%)

prune171.0ms (4.2%)

localize11.0ms (0.3%)

rewrite177.0ms (4.4%)

series226.0ms (5.6%)

simplify110.0ms (2.7%)

prune151.0ms (3.7%)

regimes148.0ms (3.7%)

bsearch3.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.7s (42.6%)

Profiling