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)

sample1.2s (26.4%)

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

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 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))

series37.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

27.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
10.0ms	(hypot.f64 re im)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

3.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
0.0ms	(hypot.f64 re im)

simplify77.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

783×	`times-frac_binary64`
715×	`fma-neg_binary64`
436×	`associate-/r*_binary64`
404×	`associate-/l*_binary64`
347×	`fma-def_binary64`

Counts

96 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2237
1	472	2152
2	1292	2092
3	4552	2092
4	5054	2092

prune83.0ms (1.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	101	12	113
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	13	114

Error

0.1b

Counts

114 → 13

Alt Table

Status	Error	Program
	0.6b	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
	19.2b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	19.0b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
▶	0.6b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
	19.0b	(*.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 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3))
	19.3b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	1.3b	(/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 10) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
	19.2b	(*.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))))
	1.4b	(.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 2663 to 1832 computations (31.2% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
✓	0.5b	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

series117.0ms (2.6%)

Counts

2 → 48

Calls

2 calls:

88.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
29.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

rewrite38.0ms (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:

18.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
6.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

simplify215.0ms (4.8%)

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

prune285.0ms (6.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	273	5	278
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	277	14	291

Error

0.0b

Counts

291 → 14

Alt Table

Status	Error	Program
	19.3b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	1.6b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (sqrt.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 (log.f64 10) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
▶	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))))))
	19.0b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))
	19.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
✓	0.6b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
	19.0b	(*.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 (pow.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10)) 3))
	0.6b	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
	19.0b	(.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)))))
	1.3b	(.f64 (/.f64 (.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))))) (sqrt.f64 (log.f64 10))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))

Compiler

Compiled 7763 to 5843 computations (24.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	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))
✓	3.7b	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))

series125.0ms (2.8%)

Counts

3 → 48

Calls

3 calls:

75.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
50.0ms	(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:

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))))
2.0ms	(/.f64 1 (log.f64 10))

simplify161.0ms (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

prune347.0ms (7.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	301	3	304
Fresh	10	2	12
Picked	0	1	1
Done	1	0	1
Total	312	6	318

Error

0.0b

Counts

318 → 6

Alt Table

Status	Error	Program
	0.3b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))
	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)))))
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
▶	0.1b	(log.f64 (pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10)))))
	19.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
	1.3b	(.f64 (/.f64 (.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))))) (sqrt.f64 (log.f64 10))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))

Compiler

Compiled 10974 to 9160 computations (16.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
	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))))
	3.7b	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))

series207.0ms (4.6%)

Counts

1 → 24

Calls

1 calls:

207.0ms

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

rewrite8.0ms (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))))

simplify124.0ms (2.8%)

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

prune440.0ms (9.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	262	6	268

Error

0.0b

Counts

268 → 6

Alt Table

Status	Error	Program
	0.3b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))
	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)))))
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
✓	0.1b	(log.f64 (pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10)))))
	19.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
	1.3b	(.f64 (/.f64 (.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))))) (sqrt.f64 (log.f64 10))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))

Compiler

Compiled 11734 to 9978 computations (15% saved)

regimes808.0ms (18%)

Accuracy

Total 0.1b remaining (88.1%)

Threshold costs 0.1b (88.1%)

Counts

93 → 1

Compiler

Compiled 15638 to 12819 computations (18% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	15	23
2	14	23

end135.0ms (3%)

Remove: (sort re im)
Compiler: Compiled 211 to 175 computations (17.1% saved)

Details

analyze5.0ms (0.1%)

sample1.2s (26.4%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series37.0ms (0.8%)

rewrite5.0ms (0.1%)

simplify77.0ms (1.7%)

prune83.0ms (1.9%)

localize11.0ms (0.2%)

series117.0ms (2.6%)

rewrite38.0ms (0.9%)

simplify215.0ms (4.8%)

prune285.0ms (6.4%)

localize13.0ms (0.3%)

series125.0ms (2.8%)

rewrite25.0ms (0.5%)

simplify161.0ms (3.6%)

prune347.0ms (7.7%)

localize15.0ms (0.3%)

series207.0ms (4.6%)

rewrite8.0ms (0.2%)

simplify124.0ms (2.8%)

prune440.0ms (9.8%)

regimes808.0ms (18%)

simplify2.0ms (0%)

end135.0ms (3%)

Profiling