Details

analyze4.0ms (0%)

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)

sample924.0ms (10.8%)

Results

898.0ms

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

prune3.0ms (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

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(/.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
✓	0.8b	(/.f64 (atan2.f64 im re) (log.f64 10))

series54.0ms (0.6%)

Counts

1 → 0

Calls

1 calls:

53.0ms

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

rewrite4.0ms (0%)

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))

simplify115.0ms (1.3%)

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

prune26.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	26	6	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	7	33

Error

0.1b

Counts

33 → 7

Alt Table

Status	Error	Program
▶	1.0b	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))
	28.7b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 10)))
	2.0b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	28.2b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
	7.9b	(cbrt.f64 (.f64 (.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) (/.f64 (atan2.f64 im re) (log.f64 10))) (/.f64 (atan2.f64 im re) (log.f64 10))))
✓	0.8b	(/.f64 (atan2.f64 im re) (log.f64 10))
	28.7b	(/.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (log.f64 10) (sqrt.f64 (atan2.f64 im re))))

Compiler

Compiled 631 to 367 computations (41.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))
✓	0.9b	(/.f64 (log.f64 10) (atan2.f64 im re))

series98.0ms (1.2%)

Counts

2 → 24

Calls

2 calls:

51.0ms	(/.f64 (log.f64 10) (atan2.f64 im re))
47.0ms	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
60×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

2 → 123

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))
3.0ms	(/.f64 (log.f64 10) (atan2.f64 im re))

simplify212.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1150×	`fabs-mul_binary64`
912×	`fma-def_binary64`
471×	`unswap-sqr_binary64`
448×	`fma-neg_binary64`
383×	`associate-/l/_binary64`

Counts

147 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	2599
1	169	2355
2	393	2318
3	784	2318
4	1045	2318
5	1138	2318
6	1485	2318
7	1880	2318
8	2301	2318
9	3347	2318
10	4650	2318
11	4689	2318
12	4946	2318

prune86.0ms (1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	0	5	5
Picked	0	1	1
Done	1	0	1
Total	134	11	145

Error

0.0b

Counts

145 → 11

Alt Table

Status	Error	Program
	28.7b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 10)))
	31.0b	(/.f64 (/.f64 1 (sqrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))) (sqrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))
	7.9b	(cbrt.f64 (.f64 (.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) (/.f64 (atan2.f64 im re) (log.f64 10))) (/.f64 (atan2.f64 im re) (log.f64 10))))
	1.0b	(/.f64 1 (*.f64 (log.f64 10) (/.f64 1 (atan2.f64 im re))))
	28.7b	(/.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (log.f64 10) (sqrt.f64 (atan2.f64 im re))))
	1.0b	(/.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (sqrt.f64 (log.f64 10)) (atan2.f64 im re)))
✓	1.0b	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))
	0.7b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))
	2.0b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))
	28.2b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
▶	0.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))) (/.f64 1 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))

Compiler

Compiled 2758 to 1799 computations (34.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1 (*.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
✓	0.6b	(/.f64 1 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))
	0.9b	(/.f64 (log.f64 10) (atan2.f64 im re))
✓	3.9b	(cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))

series3.2s (37.9%)

Counts

3 → 72

Calls

3 calls:

1.4s

(/.f64 1 (*.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))

954.0ms

(/.f64 1 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))

893.0ms

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

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`times-frac_binary64`
80×	`cbrt-prod_binary64`
69×	`*-un-lft-identity_binary64`
69×	`add-sqr-sqrt_binary64`
69×	`add-cube-cbrt_binary64`

Counts

3 → 166

Calls

3 calls:

8.0ms

(/.f64 1 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))

8.0ms

(/.f64 1 (*.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))

2.0ms

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

simplify187.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

663×	`distribute-rgt-in_binary64`
656×	`fma-neg_binary64`
412×	`fma-def_binary64`
293×	`unswap-sqr_binary64`
278×	`*-commutative_binary64`

Counts

238 → 192

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	152	4788
1	225	4313
2	416	4280
3	1357	4130
4	2294	4031
5	4366	4031
6	4885	4031

prune474.0ms (5.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	346	3	349
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	351	9	360

Error

0.0b

Counts

360 → 9

Alt Table

Status	Error	Program
	0.7b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))
▶	0.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))) (/.f64 (/.f64 1 (cbrt.f64 (*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10))))) (cbrt.f64 (/.f64 (cbrt.f64 (log.f64 10)) (atan2.f64 im re)))))
	28.7b	(/.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (log.f64 10) (sqrt.f64 (atan2.f64 im re))))
	1.0b	(/.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (sqrt.f64 (log.f64 10)) (atan2.f64 im re)))
✓	1.0b	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))
	31.0b	(/.f64 (/.f64 1 (sqrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))) (sqrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))
	0.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (.f64 (cbrt.f64 (/.f64 1 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))))) (cbrt.f64 (/.f64 (log.f64 10) (cbrt.f64 (atan2.f64 im re))))))) (/.f64 1 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
	1.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))) (cbrt.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))))) (/.f64 1 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
	1.0b	(/.f64 1 (*.f64 (log.f64 10) (/.f64 1 (atan2.f64 im re))))

Compiler

Compiled 12511 to 8484 computations (32.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(cbrt.f64 (log.f64 10))
✓	1.6b	(*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))
	3.9b	(cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))
✓	4.2b	(cbrt.f64 (/.f64 (cbrt.f64 (log.f64 10)) (atan2.f64 im re)))

series1.0s (12.3%)

Counts

3 → 24

Calls

3 calls:

1.0s	(cbrt.f64 (/.f64 (cbrt.f64 (log.f64 10)) (atan2.f64 im re)))
0.0ms	(*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))
0.0ms	(cbrt.f64 (log.f64 10))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`

Counts

3 → 97

Calls

3 calls:

5.0ms	(*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))
3.0ms	(cbrt.f64 (/.f64 (cbrt.f64 (log.f64 10)) (atan2.f64 im re)))
1.0ms	(cbrt.f64 (log.f64 10))

simplify147.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-neg_binary64`
430×	`sqr-pow_binary64`
356×	`associate-/l*_binary64`
356×	`times-frac_binary64`
342×	`*-commutative_binary64`

Counts

121 → 110

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	122	2084
1	167	2046
2	354	1984
3	767	1966
4	2173	1780
5	2465	1780
6	3004	1780
7	4691	1780
8	4843	1780

prune333.0ms (3.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	199	10	209

Error

0.0b

Counts

209 → 10

Alt Table

Status	Error	Program
	0.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))) (/.f64 (/.f64 1 (cbrt.f64 (.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10))))) (.f64 (*.f64 (cbrt.f64 (cbrt.f64 (/.f64 (cbrt.f64 (log.f64 10)) (atan2.f64 im re)))) (cbrt.f64 (cbrt.f64 (/.f64 (cbrt.f64 (log.f64 10)) (atan2.f64 im re))))) (cbrt.f64 (cbrt.f64 (/.f64 (cbrt.f64 (log.f64 10)) (atan2.f64 im re)))))))
	0.7b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))
✓	0.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))) (/.f64 (/.f64 1 (cbrt.f64 (*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10))))) (cbrt.f64 (/.f64 (cbrt.f64 (log.f64 10)) (atan2.f64 im re)))))
	28.7b	(/.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (log.f64 10) (sqrt.f64 (atan2.f64 im re))))
	1.0b	(/.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (sqrt.f64 (log.f64 10)) (atan2.f64 im re)))
✓	1.0b	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))
	31.0b	(/.f64 (/.f64 1 (sqrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))) (sqrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))
	0.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (.f64 (cbrt.f64 (/.f64 1 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))))) (cbrt.f64 (/.f64 (log.f64 10) (cbrt.f64 (atan2.f64 im re))))))) (/.f64 1 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
	1.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))) (cbrt.f64 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re))))))) (/.f64 1 (cbrt.f64 (/.f64 (log.f64 10) (atan2.f64 im re)))))
	1.0b	(/.f64 1 (*.f64 (log.f64 10) (/.f64 1 (atan2.f64 im re))))

Compiler

Compiled 9057 to 6902 computations (23.8% saved)

regimes1.2s (14.2%)

Accuracy

Total 0.4b remaining (74.8%)

Threshold costs 0.4b (74.8%)

Counts

240 → 1

Compiler

Compiled 31188 to 23389 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	18	43
2	16	43

end245.0ms (2.9%)

Compiler: Compiled 344 to 251 computations (27% saved)

Details

analyze4.0ms (0%)

sample924.0ms (10.8%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series54.0ms (0.6%)

rewrite4.0ms (0%)

simplify115.0ms (1.3%)

prune26.0ms (0.3%)

localize6.0ms (0.1%)

series98.0ms (1.2%)

rewrite18.0ms (0.2%)

simplify212.0ms (2.5%)

prune86.0ms (1%)

localize12.0ms (0.1%)

series3.2s (37.9%)

rewrite36.0ms (0.4%)

simplify187.0ms (2.2%)

prune474.0ms (5.6%)

localize19.0ms (0.2%)

series1.0s (12.3%)

rewrite22.0ms (0.3%)

simplify147.0ms (1.7%)

prune333.0ms (3.9%)

regimes1.2s (14.2%)

simplify2.0ms (0%)

end245.0ms (2.9%)

Profiling