Details

analyze26.0ms (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)

sample37.0ms (0.8%)

Algorithm

1×

intervals

Results

19.0ms

256×

body

128

valid

Compiler

Compiled 31 to 23 computations (25.8% saved)

simplify9.0ms (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 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))

rewrite6.0ms (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))
1.0ms	(hypot.f64 re im)

series51.0ms (1%)

Counts

2 → 48

Calls

2 calls:

38.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))
12.0ms	(hypot.f64 re im)

simplify93.0ms (1.9%)

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 → 154

Iterations

Useful iterations: 2 (0.0ms)

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

prune89.0ms (1.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	141	13	154
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	141	14	155

Error

0.1b

Counts

155 → 14

Alt Table

Status	Error	Program
	17.3b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 10) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	17.6b	(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))))
	14.2b	(log1p.f64 (expm1.f64 (/.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))))
	17.4b	(*.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))))
	0.8b	(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))))
✓	0.6b	(/.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))))
	1.2b	(/.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)))))
	17.6b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 10))))
	17.3b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))
	1.2b	(.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 2685 to 1838 computations (31.5% 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))))
✓	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

rewrite35.0ms (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))))
4.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))

series79.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

43.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10)))
36.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 10))))

simplify259.0ms (5.3%)

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 → 365

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

prune229.0ms (4.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	417	4	421
Fresh	6	6	12
Picked	1	0	1
Done	1	0	1
Total	425	10	435

Error

0.0b

Counts

435 → 10

Alt Table

Status	Error	Program
	0.7b	(.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))))))
	0.7b	(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))))
	0.6b	(/.f64 (*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (hypot.f64 re im))) (sqrt.f64 (log.f64 10)))
	17.6b	(expm1.f64 (log1p.f64 (/.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))))
▶	0.3b	(*.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 1 (/.f64 (log.f64 10) (log.f64 (hypot.f64 re im))))
	17.3b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))
	17.3b	(.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 (.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 7636 to 5736 computations (24.9% 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)))))
✓	0.2b	(*.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))
✓	3.8b	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))

rewrite29.0ms (0.6%)

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)))))

series313.0ms (6.4%)

Counts

4 → 72

Calls

4 calls:

159.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
87.0ms	(log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))))
67.0ms	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))
0.0ms	(/.f64 1 (log.f64 10))

simplify210.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

395×	`associate-r_binary64`
389×	`fma-def_binary64`
356×	`fma-neg_binary64`
347×	`associate-l_binary64`
245×	`associate-/l*_binary64`

Counts

231 → 414

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	462	9118
1	1361	8649
2	4949	8647
3	5250	8647

prune491.0ms (10%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	412	2	414
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	416	8	424

Error

Counts

424 → 8

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)))
	17.6b	(expm1.f64 (log1p.f64 (/.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	(.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))))))
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
	17.3b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))
	1.2b	(.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))))
▶	0.2b	(log.f64 (pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10)))))

Compiler

Compiled 12685 to 10625 computations (16.2% saved)

localize17.0ms (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))
✓	3.3b	(pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10))))
	3.8b	(pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (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)))))

series311.0ms (6.3%)

Counts

2 → 48

Calls

2 calls:

181.0ms

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

130.0ms

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

simplify166.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

367×	`times-frac_binary64`
298×	`associate-/r*_binary64`
296×	`associate-/l*_binary64`
227×	`fma-def_binary64`
209×	`fma-neg_binary64`

Counts

121 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	357	7221
1	1148	6907
2	4800	6905
3	4974	6905

prune435.0ms (8.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	375	0	375
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	375	8	383

Error

Counts

383 → 8

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)))
	17.6b	(expm1.f64 (log1p.f64 (/.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	(.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))))))
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10))))))
	17.3b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (log.f64 10)))
	1.2b	(.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))))
✓	0.2b	(log.f64 (pow.f64 (pow.f64 (hypot.f64 re im) (sqrt.f64 (/.f64 1 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10)))))

Compiler

Compiled 14342 to 12307 computations (14.2% saved)

regimes979.0ms (19.9%)

Accuracy

Total 0.1b remaining (85.9%)

Threshold costs 0.1b (85.9%)

Compiler

Compiled 16447 to 13616 computations (17.2% saved)

simplify3.0ms (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

end8.0ms (0.2%)

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

sample990.0ms (20.1%)

Algorithm

1×

intervals

Results

592.0ms

8000×

body

128

valid

Compiler

Compiled 204 to 151 computations (26% saved)

Details

analyze26.0ms (0.5%)

sample37.0ms (0.8%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

rewrite6.0ms (0.1%)

series51.0ms (1%)

simplify93.0ms (1.9%)

prune89.0ms (1.8%)

localize11.0ms (0.2%)

rewrite35.0ms (0.7%)

series79.0ms (1.6%)

simplify259.0ms (5.3%)

prune229.0ms (4.7%)

localize14.0ms (0.3%)

rewrite29.0ms (0.6%)

series313.0ms (6.4%)

simplify210.0ms (4.3%)

prune491.0ms (10%)

localize17.0ms (0.3%)

rewrite13.0ms (0.3%)

series311.0ms (6.3%)

simplify166.0ms (3.4%)

prune435.0ms (8.9%)

regimes979.0ms (19.9%)

simplify3.0ms (0.1%)

end8.0ms (0.2%)

sample990.0ms (20.1%)

Profiling