Details

analyze24.0ms (0.5%)

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)

sample36.0ms (0.8%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 31 to 23 computations (25.8% saved)

simplify7.0ms (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

prune4.0ms (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))

series36.0ms (0.8%)

Counts

1 → 24

Calls

1 calls:

35.0ms

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

rewrite6.0ms (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:

4.0ms

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

simplify84.0ms (1.9%)

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

prune62.0ms (1.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	58	13	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	14	72

Error

0.1b

Counts

72 → 14

Alt Table

Status	Error	Program
	18.4b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 10) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	18.6b	(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))))
	18.4b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	18.3b	(*.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	(/.f64 (log.f64 (hypot.f64 re im)) (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 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3))
	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))))
	18.5b	(*.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10))) (/.f64 (sqrt.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))))
	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))))
	1.3b	(.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))))

Compiler

Compiled 1999 to 1334 computations (33.3% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.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)))

series78.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

41.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))
37.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))

rewrite41.0ms (0.9%)

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:

21.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
4.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

simplify254.0ms (5.8%)

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

prune215.0ms (4.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	231	5	236
Fresh	8	4	12
Picked	1	0	1
Done	0	1	1
Total	240	10	250

Error

Counts

250 → 10

Alt Table

Status	Error	Program
	0.6b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))) 3)))
	18.3b	(*.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))))
▶	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
	1.8b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.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)))))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (sqrt.f64 (log.f64 10)))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3))
	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 (/.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))))
	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))))

Compiler

Compiled 6719 to 5031 computations (25.1% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.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))))

series176.0ms (4%)

Counts

3 → 48

Calls

3 calls:

104.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
72.0ms	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))
0.0ms	(/.f64 1 (log.f64 10))

rewrite27.0ms (0.6%)

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:

10.0ms	(*.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))))
3.0ms	(/.f64 1 (log.f64 10))

simplify157.0ms (3.6%)

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

prune307.0ms (7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	5	3	8
Picked	0	1	1
Done	1	0	1
Total	264	8	272

Error

Counts

272 → 8

Alt Table

Status	Error	Program
	18.3b	(*.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))))
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
	0.3b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))
	0.6b	(+.f64 (/.f64 (log.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (/.f64 1 (log.f64 10))))) (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (/.f64 1 (log.f64 10))))) (sqrt.f64 (log.f64 10))))
	18.6b	(exp.f64 (log.f64 (*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))))
▶	0.2b	(log.f64 (pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (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))))
	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))))

Compiler

Compiled 9960 to 8338 computations (16.3% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10)))))
	1.0b	(/.f64 1 (log.f64 10))
✓	3.4b	(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))))

series284.0ms (6.5%)

Counts

2 → 48

Calls

2 calls:

150.0ms

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

134.0ms

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

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 73

Calls

2 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))))

3.0ms

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

simplify199.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

360×	`times-frac_binary64`
302×	`associate-/r*_binary64`
294×	`associate-/l*_binary64`
261×	`fma-neg_binary64`
199×	`associate-*r/_binary64`

Counts

121 → 185

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	347	6065
1	1138	5819
2	4617	5819
3	4994	5819
4	4991	5819
5	4998	5819

prune382.0ms (8.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	306	1	307
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	307	8	315

Error

Counts

315 → 8

Alt Table

Status	Error	Program
	18.3b	(*.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))))
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
	0.3b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))
	18.6b	(exp.f64 (log.f64 (/.f64 (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))) (sqrt.f64 (log.f64 10)))))
	0.6b	(+.f64 (/.f64 (log.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (/.f64 1 (log.f64 10))))) (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (/.f64 1 (log.f64 10))))) (sqrt.f64 (log.f64 10))))
✓	0.2b	(log.f64 (pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (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))))
	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))))

Compiler

Compiled 13187 to 11128 computations (15.6% saved)

regimes907.0ms (20.8%)

Accuracy

Total 0.1b remaining (81.7%)

Threshold costs 0.1b (81.7%)

Counts

106 → 1

Compiler

Compiled 18161 to 14552 computations (19.9% saved)

simplify2.0ms (0.1%)

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

end7.0ms (0.2%)

Remove: (sort re im)
Compiler: Compiled 54 to 48 computations (11.1% saved)

sample1.0s (23.3%)

Algorithm

1×

intervals

Results

637.0ms

8000×

body

128

valid

Compiler

Compiled 215 to 165 computations (23.3% saved)

Details

analyze24.0ms (0.5%)

sample36.0ms (0.8%)

simplify7.0ms (0.2%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series36.0ms (0.8%)

rewrite6.0ms (0.1%)

simplify84.0ms (1.9%)

prune62.0ms (1.4%)

localize10.0ms (0.2%)

series78.0ms (1.8%)

rewrite41.0ms (0.9%)

simplify254.0ms (5.8%)

prune215.0ms (4.9%)

localize13.0ms (0.3%)

series176.0ms (4%)

rewrite27.0ms (0.6%)

simplify157.0ms (3.6%)

prune307.0ms (7%)

localize15.0ms (0.3%)

series284.0ms (6.5%)

rewrite13.0ms (0.3%)

simplify199.0ms (4.6%)

prune382.0ms (8.7%)

regimes907.0ms (20.8%)

simplify2.0ms (0.1%)

end7.0ms (0.2%)

sample1.0s (23.3%)

Profiling