Details

analyze5.0ms (0.1%)

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
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.1s (22.9%)

Symmetry

(sort re im)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`hypot-def_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	11
1	14	11
2	16	11
3	16	11

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

Compiler

Compiled 39 to 29 computations (25.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

series27.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

26.0ms

(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`times-frac_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

1 → 38

Calls

1 calls:

3.0ms

(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

simplify82.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

556×	`associate-/l/_binary64`
403×	`associate-/r/_binary64`
315×	`times-frac_binary64`
236×	`associate-/l*_binary64`
233×	`sub-neg_binary64`

Counts

62 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1669
1	331	1611
2	852	1567
3	2813	1547
4	4895	1547
5	5033	1547

prune61.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Error

0.1b

Counts

72 → 12

Alt Table

Status	Error	Program
	18.3b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 10))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10))))
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 10))))
	1.2b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))
▶	0.5b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
	18.1b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.7b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 10) (log.f64 10)) (log.f64 10))))
	1.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	18.0b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 10) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	0.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	18.4b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.6b	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))

Compiler

Compiled 1976 to 1311 computations (33.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
✓	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

series54.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

27.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))
26.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`times-frac_binary64`
96×	`add-sqr-sqrt_binary64`
59×	`sqrt-prod_binary64`
56×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

2 → 151

Calls

2 calls:

19.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
3.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

simplify216.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-def_binary64`
563×	`associate-/r*_binary64`
405×	`fma-neg_binary64`
308×	`associate-/l/_binary64`
218×	`cancel-sign-sub-inv_binary64`

Counts

199 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	5977
1	731	5300
2	2185	5063
3	4589	5035
4	4992	5035
5	4986	5035
6	4960	5035

prune212.0ms (4.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	228	8	236
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	235	13	248

Error

0.0b

Counts

248 → 13

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 10))))
	0.6b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (cbrt.f64 (.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
	18.0b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))
	0.6b	(/.f64 (*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10)))
	0.6b	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
	1.2b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (*.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))
	0.7b	(cbrt.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 1 (sqrt.f64 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 10))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10))))
▶	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
	0.4b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (sqrt.f64 (log.f64 10)))))
	18.0b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) 1)) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10))))
	1.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))

Compiler

Compiled 6902 to 5162 computations (25.2% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
✓	1.0b	(/.f64 1 (log.f64 10))
✓	3.9b	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))

series119.0ms (2.4%)

Counts

3 → 48

Calls

3 calls:

71.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
48.0ms	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))
0.0ms	(/.f64 1 (log.f64 10))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`

Counts

3 → 139

Calls

3 calls:

8.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
5.0ms	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))
2.0ms	(/.f64 1 (log.f64 10))

simplify152.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

343×	`associate-r_binary64`
295×	`fma-neg_binary64`
291×	`associate-l_binary64`
257×	`fma-def_binary64`
243×	`associate-/l*_binary64`

Counts

187 → 262

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	413	7156
1	1220	6771
2	4788	6769
3	5016	6769

prune332.0ms (6.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	269	6	275

Error

Counts

275 → 6

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 10))))
	0.6b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (cbrt.f64 (.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 10))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10))))
	0.4b	(+.f64 (.f64 (log.f64 (pow.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (sqrt.f64 (/.f64 1 (log.f64 10))))) (/.f64 1 (sqrt.f64 (log.f64 10)))) (*.f64 (log.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) (sqrt.f64 (/.f64 1 (log.f64 10))))) (/.f64 1 (sqrt.f64 (log.f64 10)))))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (*.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (log.f64 (hypot.f64 re im)))))
▶	0.1b	(log.f64 (pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10)))))

Compiler

Compiled 9972 to 8340 computations (16.4% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	1.0b	(/.f64 1 (log.f64 10))
✓	3.3b	(pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10))))
	3.9b	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))

series95.0ms (1.9%)

Counts

1 → 24

Calls

1 calls:

94.0ms

(pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10))))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`pow-unpow_binary64`
21×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`

Counts

1 → 47

Calls

1 calls:

5.0ms

(pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10))))

simplify96.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

504×	`cancel-sign-sub-inv_binary64`
336×	`times-frac_binary64`
282×	`associate-/l*_binary64`
272×	`associate-/r*_binary64`
215×	`unswap-sqr_binary64`

Counts

71 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	282	4070
1	948	4018
2	4007	3898
3	5429	3898

prune319.0ms (6.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	220	6	226

Error

Counts

226 → 6

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 10))))
	0.6b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (cbrt.f64 (.f64 (*.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (sqrt.f64 (log.f64 10))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10))))
	0.4b	(+.f64 (.f64 (log.f64 (pow.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (sqrt.f64 (/.f64 1 (log.f64 10))))) (/.f64 1 (sqrt.f64 (log.f64 10)))) (*.f64 (log.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) (sqrt.f64 (/.f64 1 (log.f64 10))))) (/.f64 1 (sqrt.f64 (log.f64 10)))))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (*.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (log.f64 (hypot.f64 re im)))))
✓	0.1b	(log.f64 (pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10)))))

Compiler

Compiled 10682 to 9130 computations (14.5% saved)

regimes1.8s (35.9%)

Accuracy

Total 0.1b remaining (80.1%)

Threshold costs 0.1b (80.1%)

Counts

178 → 1

Compiler

Compiled 32366 to 27254 computations (15.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	30
1	18	30
2	17	30

end149.0ms (3%)

Remove: (sort re im)
Compiler: Compiled 259 to 203 computations (21.6% saved)

Details

analyze5.0ms (0.1%)

sample1.1s (22.9%)

simplify11.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series27.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify82.0ms (1.6%)

prune61.0ms (1.2%)

localize10.0ms (0.2%)

series54.0ms (1.1%)

rewrite36.0ms (0.7%)

simplify216.0ms (4.3%)

prune212.0ms (4.3%)

localize14.0ms (0.3%)

series119.0ms (2.4%)

rewrite25.0ms (0.5%)

simplify152.0ms (3.1%)

prune332.0ms (6.7%)

localize15.0ms (0.3%)

series95.0ms (1.9%)

rewrite9.0ms (0.2%)

simplify96.0ms (1.9%)

prune319.0ms (6.4%)

regimes1.8s (35.9%)

simplify2.0ms (0%)

end149.0ms (3%)

Profiling