Details

analyze733.0ms (10.7%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 32 to 21 computations (34.4% saved)

sample60.0ms (0.9%)

Algorithm

1×

intervals

Results

33.0ms	256×	body	128	valid
4.0ms	39×	body	128	nan

Compiler

Compiled 66 to 44 computations (33.3% saved)

simplify100.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
620×	`associate-/l/_binary64`
557×	`cube-prod_binary64`
533×	`sqr-pow_binary64`
502×	`pow-sqr_binary64`

Counts

1 → 1

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	22
1	28	21
2	34	21
3	45	14
4	62	11
5	65	11
6	176	11
7	479	11
8	769	11
9	839	11
10	1233	11
11	1523	11
12	2341	11
13	3455	11
14	4399	11
15	4874	11
16	4872	11

prune4.0ms (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

Error

0.3b

Counts

2 → 2

Alt Table

Status	Error	Program
	32.0b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
▶	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Status

Error

Program

32.0b

(/.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 base)) (*.f64 (atan2.f64 im re) 0)) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))

▶

0.4b

(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Compiler

Compiled 92 to 61 computations (33.7% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

15×	`pow1_binary64`
11×	`log-pow_binary64`
7×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
5×	`add-cube-cbrt_binary64`

Counts

1 → 46

Calls

1 calls:

13.0ms

(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Compiler

Compiled 485 to 111 computations (77.1% saved)

series79.0ms (1.2%)

Error

0.3b

Counts

1 → 19

Calls

1 calls:

67.0ms

(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Compiler

Compiled 978 to 695 computations (28.9% saved)

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

659×	`fma-neg_binary64`
616×	`fma-def_binary64`
614×	`times-frac_binary64`
610×	`div-exp_binary64`
316×	`associate-/l*_binary64`

Counts

65 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	1025
1	257	939
2	738	912
3	2716	894
4	4475	894
5	5588	894

prune33.0ms (0.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	37	9	46
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	38	10	48

Error

0.0b

Counts

48 → 10

Alt Table

Status	Error	Program
	32.0b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
▶	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 im re))))
	31.9b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	0.9b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
	0.7b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	31.9b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	16.9b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)))) 1)
	1.7b	(log.f64 (+.f64 1 (expm1.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)))))

Compiler

Compiled 763 to 344 computations (54.9% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 im re))))
0.3b	(/.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))

rewrite87.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

21×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`
16×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
11×	`log-pow_binary64`

Counts

2 → 98

Calls

2 calls:

14.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 im re))))
12.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))

Compiler

Compiled 1253 to 397 computations (68.3% saved)

series220.0ms (3.2%)

Error

0.0b

Counts

2 → 40

Calls

2 calls:

116.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))
70.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 im re))))

Compiler

Compiled 3083 to 2249 computations (27.1% saved)

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-def_binary64`
319×	`times-frac_binary64`
307×	`cancel-sign-sub-inv_binary64`
255×	`unswap-sqr_binary64`
247×	`associate-/l*_binary64`

Counts

138 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	2951
1	790	2563
2	3171	2512
3	5033	2512

prune61.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	98	12	110

Error

0.0b

Counts

110 → 12

Alt Table

Status	Error	Program
	1.1b	(/.f64 1 (log1p.f64 (expm1.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	0.9b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
▶	0.6b	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
	31.8b	(/.f64 1 (exp.f64 (log.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	0.7b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	0.7b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 3)))
	32.0b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	1.4b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))))
	31.9b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	16.9b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)))) 1)
	1.4b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))

Compiler

Compiled 1926 to 889 computations (53.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (log.f64 (hypot.f64 re im)))
0.3b	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))))
0.4b	(log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im)))))
0.5b	(pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))

rewrite184.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

37×	`add-cube-cbrt_binary64`
21×	`pow1_binary64`
20×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

4 → 174

Calls

4 calls:

13.0ms	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))))
13.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))
13.0ms	(pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))
10.0ms	(log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im)))))

Compiler

Compiled 2538 to 1454 computations (42.7% saved)

series768.0ms (11.2%)

Error

0.0b

Counts

4 → 77

Calls

4 calls:

230.0ms	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))))
204.0ms	(pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))
197.0ms	(log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im)))))
57.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))

Compiler

Compiled 10790 to 7845 computations (27.3% saved)

simplify197.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

840×	`associate-/l*_binary64`
524×	`fma-def_binary64`
211×	`*-commutative_binary64`
109×	`unswap-sqr_binary64`
106×	`cancel-sign-sub-inv_binary64`

Counts

251 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	661	8006
1	2191	7421
2	4651	7385
3	4973	7385

prune130.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	149	5	154
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	154	12	166

Error

Counts

166 → 12

Alt Table

Status	Error	Program
	0.7b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 3)))
	0.9b	(/.f64 1 (log.f64 (pow.f64 base (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 (hypot.f64 re im))) 3)))))
	32.0b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	1.4b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))))
	31.9b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	0.9b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	0.7b	(cbrt.f64 (/.f64 1 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 3)))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) 3))
▶	0.7b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	16.9b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)))) 1)
	1.1b	(/.f64 1 (log.f64 (.f64 (cbrt.f64 (pow.f64 base (.f64 2 (/.f64 1 (log.f64 (hypot.f64 re im)))))) (cbrt.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))))))
	0.7b	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (cbrt.f64 (pow.f64 (log.f64 (hypot.f64 re im)) 3))))))

Compiler

Compiled 4872 to 2511 computations (48.5% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.3b	(/.f64 1 (log.f64 base))
0.5b	(pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base)))
0.5b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))

rewrite125.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

27×	`add-cube-cbrt_binary64`
17×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64`

Counts

3 → 124

Calls

3 calls:

13.0ms	(/.f64 1 (log.f64 base))
11.0ms	(pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base)))
10.0ms	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))

Compiler

Compiled 1658 to 852 computations (48.6% saved)

series240.0ms (3.5%)

Error

Counts

3 → 41

Calls

3 calls:

100.0ms	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
96.0ms	(pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base)))
10.0ms	(/.f64 1 (log.f64 base))

Compiler

Compiled 3064 to 2148 computations (29.9% saved)

simplify157.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1024×	`fma-def_binary64`
312×	`fma-neg_binary64`
246×	`times-frac_binary64`
239×	`associate-/r*_binary64`
237×	`cancel-sign-sub-inv_binary64`

Counts

165 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	3116
1	672	2870
2	2704	2591
3	4022	2587
4	4826	2587
5	4854	2587

prune58.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	106	11	117

Error

Counts

117 → 11

Alt Table

Status	Error	Program
	0.7b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 3)))
	0.9b	(/.f64 1 (log.f64 (pow.f64 base (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 (hypot.f64 re im))) 3)))))
	0.4b	(*.f64 (/.f64 1 (log.f64 base)) (log.f64 (hypot.f64 re im)))
	0.9b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 2)) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	1.4b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 im re)))))
	31.9b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	0.7b	(cbrt.f64 (/.f64 1 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 3)))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) 3))
	0.7b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	16.9b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)))) 1)
	1.1b	(/.f64 1 (log.f64 (.f64 (cbrt.f64 (pow.f64 base (.f64 2 (/.f64 1 (log.f64 (hypot.f64 re im)))))) (cbrt.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))))))

Compiler

Compiled 1476 to 625 computations (57.7% saved)

regimes1.7s (24.4%)

Accuracy

Total 0.3b remaining (91.6%)

Threshold costs 0.3b (91.6%)

Compiler

Compiled 21026 to 15396 computations (26.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`+-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	11	11
2	11	11

end6.0ms (0.1%)

Remove: (sort re im)
Compiler: Compiled 30 to 21 computations (30% saved)

sample1.7s (24.4%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
126.0ms	1087×	body	128	nan

Compiler

Compiled 245 to 166 computations (32.2% saved)

Details

analyze733.0ms (10.7%)

sample60.0ms (0.9%)

simplify100.0ms (1.5%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

rewrite47.0ms (0.7%)

series79.0ms (1.2%)

simplify79.0ms (1.2%)

prune33.0ms (0.5%)

localize9.0ms (0.1%)

rewrite87.0ms (1.3%)

series220.0ms (3.2%)

simplify90.0ms (1.3%)

prune61.0ms (0.9%)

localize11.0ms (0.2%)

rewrite184.0ms (2.7%)

series768.0ms (11.2%)

simplify197.0ms (2.9%)

prune130.0ms (1.9%)

localize14.0ms (0.2%)

rewrite125.0ms (1.8%)

series240.0ms (3.5%)

simplify157.0ms (2.3%)

prune58.0ms (0.9%)

regimes1.7s (24.4%)

simplify3.0ms (0%)

end6.0ms (0.1%)

sample1.7s (24.4%)

Profiling