Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	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 9 to 7 computations (22.2% saved)

sample898.0ms (21.4%)

Results

869.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.9b	(/.f64 (atan2.f64 im re) (log.f64 10))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.9b	(/.f64 (atan2.f64 im re) (log.f64 10))

series57.0ms (1.3%)

Counts

1 → 0

Calls

1 calls:

56.0ms

(/.f64 (atan2.f64 im re) (log.f64 10))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 33

Calls

1 calls:

2.0ms

(/.f64 (atan2.f64 im re) (log.f64 10))

simplify109.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1288×	`associate-/l/_binary64`
1067×	`fma-neg_binary64`
979×	`fma-def_binary64`
677×	`unswap-sqr_binary64`
350×	`times-frac_binary64`

Counts

33 → 32

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	551
1	92	513
2	177	513
3	294	513
4	454	513
5	676	513
6	1686	513
7	2393	513
8	2851	513
9	3810	513
10	4033	513
11	4008	513
12	4982	513

prune29.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	26	6	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	6	33

Error

0.0b

Counts

33 → 6

Alt Table

Status	Error	Program
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
	6.3b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))
	2.0b	(/.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (log.f64 10) (cbrt.f64 (atan2.f64 im re))))
	1.1b	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))
▶	0.9b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))
	29.5b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 10)))

Compiler

Compiled 617 to 369 computations (40.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))
✓	0.8b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))

series106.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

56.0ms	(/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))
51.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-sqr-sqrt_binary64`
85×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
51×	`sqrt-prod_binary64`
46×	`add-cube-cbrt_binary64`

Counts

2 → 136

Calls

2 calls:

18.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))
3.0ms	(/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))

simplify368.0ms (8.8%)

Algorithm

1×	egg-herbie

Rules

765×	`fma-neg_binary64`
413×	`div-sub_binary64`
411×	`associate-/l*_binary64`
410×	`*-commutative_binary64`
326×	`sqr-pow_binary64`

Counts

184 → 158

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	132	3954
1	293	3396
2	887	3396
3	1945	3064
4	2127	3016
5	2461	3016
6	3273	3016
7	4164	3016
8	4684	2992
9	4970	2992
10	4687	2992

prune161.0ms (3.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	152	6	158
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	154	10	164

Error

0.0b

Counts

164 → 10

Alt Table

Status	Error	Program
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
	0.9b	(/.f64 (*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (atan2.f64 im re)) (sqrt.f64 (log.f64 10)))
▶	0.8b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10)))))
	2.0b	(/.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (log.f64 10) (cbrt.f64 (atan2.f64 im re))))
	2.3b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (sqrt.f64 (.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (sqrt.f64 (cbrt.f64 (log.f64 10)))))
	0.9b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))))
	6.3b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))
	1.1b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 1 (/.f64 (sqrt.f64 (log.f64 10)) (atan2.f64 im re))))
	1.0b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (*.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))))) (cbrt.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))))
	29.5b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 10)))

Compiler

Compiled 3898 to 2940 computations (24.6% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10))))
✓	0.8b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10)))))
✓	1.0b	(/.f64 1 (log.f64 10))

series139.0ms (3.3%)

Counts

3 → 24

Calls

3 calls:

83.0ms	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10)))))
56.0ms	(*.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10))))
0.0ms	(/.f64 1 (log.f64 10))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`times-frac_binary64`
45×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
31×	`sqrt-prod_binary64`

Counts

3 → 130

Calls

3 calls:

12.0ms	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10)))))
7.0ms	(*.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10))))
3.0ms	(/.f64 1 (log.f64 10))

simplify194.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

705×	`fma-def_binary64`
664×	`fabs-mul_binary64`
562×	`pow-sqr_binary64`
512×	`associate-/l/_binary64`
420×	`fma-neg_binary64`

Counts

154 → 163

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	121	2422
1	232	2177
2	672	2177
3	1381	1820
4	1601	1820
5	1819	1820
6	2233	1820
7	3083	1814
8	3992	1814
9	4454	1814
10	4922	1814
11	5022	1814

prune118.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	7	2	9
Picked	0	1	1
Done	0	0	0
Total	168	5	173

Error

Counts

173 → 5

Alt Table

Status	Error	Program
	0.9b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))))
✓	0.8b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10)))))
	0.9b	(*.f64 (/.f64 1 (sqrt.f64 1)) (/.f64 (atan2.f64 im re) (log.f64 10)))
▶	0.1b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) 3/2)))
	2.3b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (sqrt.f64 (.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (sqrt.f64 (cbrt.f64 (log.f64 10)))))

Compiler

Compiled 3716 to 3061 computations (17.6% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.8b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) 3/2)))
✓	0.9b	(*.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) 3/2))
	1.0b	(/.f64 1 (log.f64 10))

series1.1s (26.4%)

Counts

2 → 48

Calls

2 calls:

1.1s	(*.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) 3/2))
51.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) 3/2)))

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`sqrt-prod_binary64`
40×	`add-sqr-sqrt_binary64`
35×	`times-frac_binary64`
31×	`associate-l_binary64`
29×	`*-un-lft-identity_binary64`

Counts

2 → 93

Calls

2 calls:

16.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) 3/2)))
11.0ms	(*.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) 3/2))

simplify130.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

496×	`associate-/r*_binary64`
466×	`associate-/r/_binary64`
392×	`unswap-sqr_binary64`
389×	`associate-*l/_binary64`
285×	`*-commutative_binary64`

Counts

141 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	126	3107
1	240	2967
2	741	2955
3	1029	2955
4	1870	2955
5	4924	2955
6	4967	2955

prune141.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	3	0	3
Picked	0	1	1
Done	0	1	1
Total	158	4	162

Error

Counts

162 → 4

Alt Table

Status	Error	Program
	0.8b	(/.f64 (*.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) 3/2)) (sqrt.f64 (sqrt.f64 (log.f64 10))))
✓	0.8b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10)))))
✓	0.1b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (atan2.f64 im re) (pow.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) 3/2)))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (.f64 (cbrt.f64 (atan2.f64 im re)) (pow.f64 (sqrt.f64 (/.f64 1 (log.f64 10))) 3/2))))

Compiler

Compiled 4342 to 3737 computations (13.9% saved)

regimes378.0ms (9%)

Accuracy

Total 0.1b remaining (88%)

Threshold costs 0.1b (88%)

Counts

83 → 1

Compiler

Compiled 6687 to 5550 computations (17% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	29
1	20	29
2	19	29

end106.0ms (2.5%)

Compiler: Compiled 126 to 106 computations (15.9% saved)

Details

analyze5.0ms (0.1%)

sample898.0ms (21.4%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series57.0ms (1.3%)

rewrite4.0ms (0.1%)

simplify109.0ms (2.6%)

prune29.0ms (0.7%)

localize8.0ms (0.2%)

series106.0ms (2.5%)

rewrite35.0ms (0.8%)

simplify368.0ms (8.8%)

prune161.0ms (3.8%)

localize11.0ms (0.3%)

series139.0ms (3.3%)

rewrite32.0ms (0.8%)

simplify194.0ms (4.6%)

prune118.0ms (2.8%)

localize15.0ms (0.3%)

series1.1s (26.4%)

rewrite36.0ms (0.9%)

simplify130.0ms (3.1%)

prune141.0ms (3.3%)

regimes378.0ms (9%)

simplify2.0ms (0.1%)

end106.0ms (2.5%)

Profiling