Details

analyze4.0ms (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
99.9%	0%	0.1%	3

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.4s (18.6%)

Symmetry

(sort re im)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify7.0ms (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

prune6.0ms (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)

localize8.0ms (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))

series56.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

43.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
13.0ms	(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)

simplify97.0ms (1.3%)

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

prune140.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	13	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	13	114

Error

0.1b

Counts

114 → 13

Alt Table

Status	Error	Program
	0.6b	(/.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.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))))
	16.3b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 10) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	16.7b	(exp.f64 (log.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))))
	1.5b	(.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)))
	16.3b	(*.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))))
	0.7b	(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))))
	0.6b	(/.f64 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
	16.6b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	16.3b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))

Compiler

Compiled 2714 to 1845 computations (32% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(*.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)))

series74.0ms (1%)

Counts

2 → 48

Calls

2 calls:

39.0ms	(/.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))))

rewrite44.0ms (0.6%)

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:

22.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))
5.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

simplify249.0ms (3.4%)

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

prune274.0ms (3.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	273	5	278
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	278	13	291

Error

0.0b

Counts

291 → 13

Alt Table

Status	Error	Program
	1.3b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.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))))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))))
	1.5b	(.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 (/.f64 1 (sqrt.f64 (log.f64 10))) (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))))))
	1.2b	(.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))))
	1.6b	(.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)))))
	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))))
	1.3b	(.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)))
	16.3b	(*.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))))
	0.7b	(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))))
	16.4b	(*.f64 (/.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))) (sqrt.f64 (log.f64 10))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))))
	16.7b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	16.3b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))

Compiler

Compiled 7838 to 5860 computations (25.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series258.0ms (3.5%)

Counts

3 → 48

Calls

3 calls:

183.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
75.0ms	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))
0.0ms	(/.f64 1 (log.f64 10))

rewrite25.0ms (0.3%)

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:

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

simplify263.0ms (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

prune576.0ms (7.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	301	3	304
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	309	8	317

Error

Counts

317 → 8

Alt Table

Status	Error	Program
	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))))
	1.6b	(.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)))))
	1.3b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.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))))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (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 (cbrt.f64 (log.f64 (hypot.f64 re im))) (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)))))
	0.2b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))
	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))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))))))

Compiler

Compiled 11120 to 9240 computations (16.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series188.0ms (2.6%)

Counts

1 → 24

Calls

1 calls:

188.0ms

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

rewrite15.0ms (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:

9.0ms

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

simplify107.0ms (1.5%)

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

prune724.0ms (9.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	262	8	270

Error

Counts

270 → 8

Alt Table

Status	Error	Program
	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))))
	1.6b	(.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)))))
	1.3b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.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))))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (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 (cbrt.f64 (log.f64 (hypot.f64 re im))) (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)))))
	0.2b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im)))
	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))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))))))

Compiler

Compiled 11798 to 10010 computations (15.2% saved)

regimes2.5s (34%)

Accuracy

Total 0.1b remaining (85.1%)

Threshold costs 0.1b (85.1%)

Counts

164 → 1

Compiler

Compiled 26304 to 21851 computations (16.9% saved)

simplify5.0ms (0.1%)

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

end292.0ms (4%)

Remove: (sort re im)
Compiler: Compiled 291 to 223 computations (23.4% saved)

Details

analyze4.0ms (0.1%)

sample1.4s (18.6%)

simplify7.0ms (0.1%)

prune6.0ms (0.1%)

localize8.0ms (0.1%)

series56.0ms (0.8%)

rewrite5.0ms (0.1%)

simplify97.0ms (1.3%)

prune140.0ms (1.9%)

localize11.0ms (0.2%)

series74.0ms (1%)

rewrite44.0ms (0.6%)

simplify249.0ms (3.4%)

prune274.0ms (3.8%)

localize13.0ms (0.2%)

series258.0ms (3.5%)

rewrite25.0ms (0.3%)

simplify263.0ms (3.6%)

prune576.0ms (7.9%)

localize17.0ms (0.2%)

series188.0ms (2.6%)

rewrite15.0ms (0.2%)

simplify107.0ms (1.5%)

prune724.0ms (9.9%)

regimes2.5s (34%)

simplify5.0ms (0.1%)

end292.0ms (4%)

Profiling