Details

analyze46.0ms (1.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 7 to 7 computations (0% saved)

sample33.0ms (0.9%)

Algorithm

1×

intervals

Results

15.0ms	89×	body	1280	valid
6.0ms	45×	body	640	valid
2.0ms	82×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	14×	body	160	valid
0.0ms	6×	body	80	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify114.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4816	9
1	4816	9

prune2.0ms (0.1%)

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: 29.3b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
4.0b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `insert-posit16`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

2 → 27

Calls

2 calls:

5.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
2.0ms	(exp.f64 (*.f64 a x))

series71.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

50.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
20.0ms	(exp.f64 (*.f64 a x))

simplify86.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4989	393
1	4989	393

prune30.0ms (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	29	4	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	4	34

Merged error: 4.0b

Counts

34 → 4

Compiler

Compiled 403 to 203 computations (49.6% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.2b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
5.3b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
6.5b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
9.7b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `prod-exp_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64`
4×	`associate-*r/_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64`
1×	`pow-to-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 78

Calls

4 calls:

12.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
9.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
8.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
7.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))

series517.0ms (13.9%)

Counts

4 → 12

Calls

4 calls:

182.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
168.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
89.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
77.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify66.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4981	1910
1	4981	1910

prune111.0ms (3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Merged error: 0.1b

Counts

94 → 3

Compiler

Compiled 2294 to 1355 computations (40.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 x 1/6)
0.4b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
2.9b	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
6.5b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite47.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
17×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
12×	`associate-*r/_binary64` `add-sqr-sqrt_binary64`
10×	`associate-l_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-r_binary64`
4×	`add-log-exp_binary64` `insert-posit16` `*-commutative_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`unswap-sqr_binary64`

Counts

4 → 106

Calls

4 calls:

15.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
12.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
9.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
4.0ms	(*.f64 x 1/6)

series382.0ms (10.3%)

Counts

4 → 12

Calls

4 calls:

150.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
140.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
69.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
22.0ms	(*.f64 x 1/6)

simplify69.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5101	2173

prune123.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	118	3	121

Merged error: 0.1b

Counts

121 → 3

Compiler

Compiled 2813 to 1506 computations (46.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 x 1/6)
0.4b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
0.5b	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
8.5b	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64` `add-exp-log_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
9×	`log-prod_binary64`
6×	`associate-r_binary64` `unpow-prod-down_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `unpow-prod-up_binary64` `associate-l_binary64` `prod-exp_binary64` `insert-posit16`
3×	`rem-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `exp-prod_binary64`
2×	`pow-to-exp_binary64` `associate-r/_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `pow-exp_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `pow-unpow_binary64` `log-pow_binary64` `flip-+_binary64`

Counts

4 → 85

Calls

4 calls:

10.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
5.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))
5.0ms	(*.f64 x 1/6)
4.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))

series400.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
105.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))
74.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
22.0ms	(*.f64 x 1/6)

simplify130.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4998	1779
1	4998	1779

prune105.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	97	3	100

Merged error: 0.1b

Counts

100 → 3

Compiler

Compiled 2305 to 1311 computations (43.1% saved)

regimes130.0ms (3.5%)

Compiler: Compiled 265 to 214 computations (19.2% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	43	51
1	43	51

end0.0ms (0%)

sample1.1s (30.3%)

Algorithm

1×

intervals

Results

497.0ms	2708×	body	1280	valid
159.0ms	1316×	body	640	valid
81.0ms	2772×	body	80	valid
73.0ms	804×	body	320	valid
23.0ms	400×	body	160	valid
4.0ms	144×	body	80	invalid

Compiler

Compiled 120 to 87 computations (27.5% saved)

Details

analyze46.0ms (1.2%)

sample33.0ms (0.9%)

simplify114.0ms (3.1%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite8.0ms (0.2%)

series71.0ms (1.9%)

simplify86.0ms (2.3%)

prune30.0ms (0.8%)

localize14.0ms (0.4%)

rewrite38.0ms (1%)

series517.0ms (13.9%)

simplify66.0ms (1.8%)

prune111.0ms (3%)

localize12.0ms (0.3%)

rewrite47.0ms (1.3%)

series382.0ms (10.3%)

simplify69.0ms (1.9%)

prune123.0ms (3.3%)

localize13.0ms (0.3%)

rewrite27.0ms (0.7%)

series400.0ms (10.8%)

simplify130.0ms (3.5%)

prune105.0ms (2.8%)

regimes130.0ms (3.5%)

bsearch1.0ms (0%)

simplify7.0ms (0.2%)

end0.0ms (0%)

sample1.1s (30.3%)

Profiling