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%)

Symmetry

(sort re im)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify6.0ms (0.1%)

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

prune5.0ms (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))

series32.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

32.0ms

(/.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))

simplify85.0ms (1.7%)

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

prune58.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Error

0.1b

Counts

72 → 10

Alt Table

Status	Error	Program
	14.6b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 10) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	14.8b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.5b	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
	14.8b	(expm1.f64 (log1p.f64 (/.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))))
	14.6b	(*.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))))
	0.6b	(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))))
	1.3b	(.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))))
	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))))

Compiler

Compiled 1870 to 1253 computations (33% saved)

localize9.0ms (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)))

series147.0ms (2.9%)

Counts

2 → 48

Calls

2 calls:

111.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))
35.0ms	(*.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:

18.0ms	(*.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)))

simplify282.0ms (5.6%)

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

prune214.0ms (4.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	227	9	236
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	233	13	246

Error

Counts

246 → 13

Alt Table

Status	Error	Program
	14.5b	(.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)))))
	14.6b	(*.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))))
	1.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))) (*.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (log.f64 10)))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))
	0.5b	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
	14.8b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.6b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (/.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))))))
	1.3b	(.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 (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))))
	0.4b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (sqrt.f64 (log.f64 10)))))
	1.7b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (sqrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))) (sqrt.f64 (log.f64 10))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (sqrt.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))))))
	0.6b	(/.f64 (*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10)))

Compiler

Compiled 6828 to 5142 computations (24.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (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))))))
✓	1.0b	(/.f64 1 (log.f64 10))
✓	3.9b	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))

series421.0ms (8.4%)

Counts

4 → 72

Calls

4 calls:

264.0ms	(log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))))
93.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
63.0ms	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))
0.0ms	(/.f64 1 (log.f64 10))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
46×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`

Counts

4 → 159

Calls

4 calls:

9.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
3.0ms	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))
2.0ms	(/.f64 1 (log.f64 10))
2.0ms	(log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))))

simplify266.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

376×	`associate-r_binary64`
343×	`fma-def_binary64`
323×	`associate-l_binary64`
316×	`fma-neg_binary64`
249×	`associate-/l*_binary64`

Counts

231 → 330

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	461	8758
1	1388	8271
2	4791	8090
3	4700	7998
4	4922	7994
5	5033	7994

prune434.0ms (8.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	326	4	330
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	335	8	343

Error

Counts

343 → 8

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))) (*.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (log.f64 10)))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))
	14.8b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.3b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))) (log.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))))
	0.3b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))
	1.7b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (sqrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))) (sqrt.f64 (log.f64 10))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (sqrt.f64 (log.f64 10)))))
	0.6b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10))) 3))
	0.6b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))
▶	0.2b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10)))))

Compiler

Compiled 12069 to 10140 computations (16% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	1.0b	(/.f64 1 (log.f64 10))
✓	4.4b	(pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))))

series59.0ms (1.2%)

Counts

1 → 24

Calls

1 calls:

59.0ms

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

rewrite176.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

217×	`times-frac_binary64`
188×	`sqrt-prod_binary64`
137×	`pow-unpow_binary64`
104×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`

Counts

1 → 154

Calls

1 calls:

10.0ms

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

simplify191.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

476×	`cancel-sign-sub-inv_binary64`
312×	`times-frac_binary64`
268×	`associate-/l*_binary64`
263×	`associate-/r*_binary64`
220×	`pow-sqr_binary64`

Counts

178 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	5554
1	1029	5525
2	4034	5409
3	4714	5409
4	4825	5409
5	4829	5409

prune251.0ms (5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	205	8	213

Error

Counts

213 → 8

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))) (*.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (log.f64 10)))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))
	14.8b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	0.3b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))) (log.f64 (cbrt.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))))
	0.3b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))
	1.7b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (sqrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))) (sqrt.f64 (log.f64 10))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (sqrt.f64 (log.f64 10)))))
	0.6b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10))) 3))
	0.6b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))
✓	0.2b	(log.f64 (pow.f64 (hypot.f64 re im) (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10)))))

Compiler

Compiled 7187 to 6187 computations (13.9% saved)

regimes1.0s (20%)

Accuracy

Total 0.1b remaining (83.6%)

Threshold costs 0.1b (83.6%)

Counts

113 → 1

Compiler

Compiled 18718 to 15300 computations (18.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	16	26
2	15	26

end177.0ms (3.5%)

Remove: (sort re im)
Compiler: Compiled 258 to 221 computations (14.3% saved)

Details

analyze5.0ms (0.1%)

sample1.1s (22%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series32.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify85.0ms (1.7%)

prune58.0ms (1.2%)

localize9.0ms (0.2%)

series147.0ms (2.9%)

rewrite36.0ms (0.7%)

simplify282.0ms (5.6%)

prune214.0ms (4.2%)

localize14.0ms (0.3%)

series421.0ms (8.4%)

rewrite27.0ms (0.5%)

simplify266.0ms (5.3%)

prune434.0ms (8.6%)

localize12.0ms (0.2%)

series59.0ms (1.2%)

rewrite176.0ms (3.5%)

simplify191.0ms (3.8%)

prune251.0ms (5%)

regimes1.0s (20%)

simplify2.0ms (0%)

end177.0ms (3.5%)

Profiling