Details

analyze88.0ms (2.4%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.6%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
82%	18%	0.1%	10
87.8%	12.1%	0.1%	11
90.7%	9.2%	0.1%	12
93.8%	6.1%	0.1%	13
95.3%	4.6%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample14.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify166.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	12
1	8	12

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: 28.4b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
26.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64_1821` `add-log-exp_binary64_1838`
3×	`pow1_binary64_1860` `add-cube-cbrt_binary64_1834` `sqrt-prod_binary64_1815` `*-un-lft-identity_binary64_1799`
2×	`sqrt-div_binary64_1816` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837` `flip3-+_binary64_1802` `flip-+_binary64_1773`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `pow1/2_binary64_1879` `sqrt-pow1_binary64_1817` `rem-sqrt-square_binary64_1812`

Counts

2 → 26

Calls

2 calls:

5.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series83.0ms (2.3%)

Counts

2 → 6

Calls

2 calls:

47.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
36.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify100.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4855	443
1	4855	443

prune43.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Merged error: 5.7b

Counts

33 → 5

Compiler

Compiled 650 to 266 computations (59.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.3b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
27.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1821`
14×	`cbrt-prod_binary64_1830` `sqrt-prod_binary64_1815`
12×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
9×	`associate-r_binary64_1739`
8×	`cbrt-div_binary64_1831`
7×	`pow1_binary64_1860`
6×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
4×	`sqrt-div_binary64_1816` `add-log-exp_binary64_1838` `flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`pow1/3_binary64_1881` `unswap-sqr_binary64_1767` `associate-l_binary64_1740`
2×	`associate-*r/_binary64_1741` `sqrt-pow1_binary64_1817` `rem-sqrt-square_binary64_1812`
1×	`prod-exp_binary64_1848` `pow1/2_binary64_1879` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `pow-prod-down_binary64_1870`

Counts

4 → 74

Calls

4 calls:

12.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
5.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series612.0ms (16.8%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
137.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
133.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
123.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify81.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5176	2012

prune93.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	85	6	91

Merged error: 5.7b

Counts

91 → 6

Compiler

Compiled 2512 to 521 computations (79.3% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

27.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_1830`
8×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799` `cbrt-div_binary64_1831`
4×	`pow1_binary64_1860` `add-log-exp_binary64_1838` `pow1/3_binary64_1881` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837` `flip3-+_binary64_1802` `flip-+_binary64_1773`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series561.0ms (15.4%)

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
142.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
135.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
131.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify59.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5170	1172

prune87.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	64	6	70

Merged error: 5.7b

Counts

70 → 6

Compiler

Compiled 3125 to 444 computations (85.8% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
5.2b	(exp.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
27.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1821`
13×	`add-cube-cbrt_binary64_1834` `cbrt-prod_binary64_1830` `*-un-lft-identity_binary64_1799`
9×	`associate-r_binary64_1739`
8×	`sqrt-prod_binary64_1815` `cbrt-div_binary64_1831`
7×	`pow1_binary64_1860`
6×	`log-prod_binary64_1885` `exp-sum_binary64_1845` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
5×	`exp-prod_binary64_1851`
4×	`add-log-exp_binary64_1838` `flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`pow1/3_binary64_1881` `unswap-sqr_binary64_1767` `associate-l_binary64_1740`
2×	`exp-diff_binary64_1847` `sqrt-div_binary64_1816` `associate-*r/_binary64_1741` `log-pow_binary64_1888` `log-div_binary64_1886`
1×	`prod-exp_binary64_1848` `rem-exp-log_binary64_1839` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `pow-prod-down_binary64_1870`

Counts

4 → 75

Calls

4 calls:

10.0ms	(.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
6.0ms	(exp.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series629.0ms (17.3%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
159.0ms	(exp.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
143.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
123.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify71.0ms (2%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4907	1965
1	4907	1965

prune83.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	87	6	93

Merged error: 5.7b

Counts

93 → 6

Compiler

Compiled 2461 to 477 computations (80.6% saved)

regimes181.0ms (5%)

Compiler: Compiled 757 to 374 computations (50.6% saved)

bsearch38.0ms (1%)

Steps

Iters	Range		Point
6	1.3948084812813239e+141	1.8910934844984227e+142	1.4612703761687805e+141
3	1.7831301631946202e-231	2.240617041941604e-231	1.9260948128030526e-231
7	-4.722333936516526e-240	-4.0343909743503125e-242	-2.8536898573216425e-241
8	-1.0098857864866275e+86	-5.6058301387264536e+82	-9.967998367313345e+85

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	53
1	29	53

end0.0ms (0%)

sample504.0ms (13.9%)

Algorithm

1×

intervals

Results

241.0ms

8000×

body

128

valid

Compiler

Compiled 122 to 64 computations (47.5% saved)

Details

analyze88.0ms (2.4%)

sample14.0ms (0.4%)

simplify166.0ms (4.5%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite11.0ms (0.3%)

series83.0ms (2.3%)

simplify100.0ms (2.8%)

prune43.0ms (1.2%)

localize9.0ms (0.3%)

rewrite33.0ms (0.9%)

series612.0ms (16.8%)

simplify81.0ms (2.2%)

prune93.0ms (2.6%)

localize14.0ms (0.4%)

rewrite24.0ms (0.7%)

series561.0ms (15.4%)

simplify59.0ms (1.6%)

prune87.0ms (2.4%)

localize13.0ms (0.4%)

rewrite33.0ms (0.9%)

series629.0ms (17.3%)

simplify71.0ms (2%)

prune83.0ms (2.3%)

regimes181.0ms (5%)

bsearch38.0ms (1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample504.0ms (13.9%)

Profiling