Details

analyze20.0ms (0.3%)

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)

sample19.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify9.0ms (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

0.8b

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)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.8b	(/.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))

series405.0ms (6.9%)

Counts

1 → 0

Calls

1 calls:

405.0ms

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

simplify124.0ms (2.1%)

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 → 44

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 (0.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	38	6	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	6	45

Error

0.1b

Counts

45 → 6

Alt Table

Status	Error	Program
	9.0b	(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	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
	1.0b	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))
	0.8b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))
	27.8b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 10)))
	1.9b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))

Compiler

Compiled 611 to 363 computations (40.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
✓	0.6b	(expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))
	0.8b	(/.f64 (atan2.f64 im re) (log.f64 10))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))
0.0ms	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))

series1.7s (29.5%)

Counts

2 → 48

Calls

2 calls:

1.3s	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
471.0ms	(expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

932×	`unsub-neg_binary64`
460×	`distribute-neg-out_binary64`
355×	`distribute-rgt-in_binary64`
295×	`distribute-lft-in_binary64`
290×	`sub-neg_binary64`

Counts

70 → 128

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	786
1	37	744
2	76	744
3	142	744
4	409	744
5	1795	744
6	3402	744
7	5055	744

prune38.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	172	6	178

Error

0.1b

Counts

178 → 6

Alt Table

Status	Error	Program
	9.0b	(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	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
	1.0b	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))
▶	0.8b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))
	27.8b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 10)))
	1.9b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 10)))

Compiler

Compiled 1018 to 655 computations (35.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))
✓	0.7b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))

rewrite29.0ms (0.5%)

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:

16.0ms	(*.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)))

series850.0ms (14.4%)

Counts

2 → 48

Calls

2 calls:

451.0ms	(/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))
399.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))

simplify265.0ms (4.5%)

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 → 316

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

prune114.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	310	6	316
Fresh	1	3	4
Picked	1	0	1
Done	1	0	1
Total	313	9	322

Error

0.0b

Counts

322 → 9

Alt Table

Status	Error	Program
	1.9b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (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)))))
	9.0b	(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))))
	27.5b	(.f64 (/.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (sqrt.f64 (log.f64 10))) (.f64 (cbrt.f64 (sqrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (sqrt.f64 (log.f64 10)))))
	27.6b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (sqrt.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))) (sqrt.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))))
	27.8b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 10)))
	0.8b	(/.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)))))
	1.1b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (*.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))))))

Compiler

Compiled 3876 to 2924 computations (24.6% saved)

localize10.0ms (0.2%)

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))))
✓	0.7b	(.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))

rewrite28.0ms (0.5%)

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:

11.0ms	(.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))))
2.0ms	(/.f64 1 (log.f64 10))

series822.0ms (13.9%)

Counts

3 → 24

Calls

3 calls:

425.0ms	(*.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10))))
397.0ms	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 10)))))
0.0ms	(/.f64 1 (log.f64 10))

simplify246.0ms (4.2%)

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 → 262

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

prune112.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	261	1	262
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	266	5	271

Error

0.0b

Counts

271 → 5

Alt Table

Status	Error	Program
	27.8b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.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)))
	0.8b	(/.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)))))
	1.1b	(.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (.f64 (*.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))))))

Compiler

Compiled 3584 to 2949 computations (17.7% saved)

regimes240.0ms (4.1%)

Accuracy

Total 0.1b remaining (86.9%)

Threshold costs 0.1b (86.9%)

Compiler

Compiled 3380 to 2630 computations (22.2% saved)

simplify3.0ms (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

end1.0ms (0%)

Compiler: Compiled 20 to 18 computations (10% saved)

sample682.0ms (11.6%)

Algorithm

1×

intervals

Results

358.0ms

8000×

body

128

valid

Compiler

Compiled 131 to 107 computations (18.3% saved)

Details

analyze20.0ms (0.3%)

sample19.0ms (0.3%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite4.0ms (0.1%)

series405.0ms (6.9%)

simplify124.0ms (2.1%)

prune26.0ms (0.4%)

localize8.0ms (0.1%)

rewrite2.0ms (0%)

series1.7s (29.5%)

simplify84.0ms (1.4%)

prune38.0ms (0.6%)

localize8.0ms (0.1%)

rewrite29.0ms (0.5%)

series850.0ms (14.4%)

simplify265.0ms (4.5%)

prune114.0ms (1.9%)

localize10.0ms (0.2%)

rewrite28.0ms (0.5%)

series822.0ms (13.9%)

simplify246.0ms (4.2%)

prune112.0ms (1.9%)

regimes240.0ms (4.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample682.0ms (11.6%)

Profiling