Details

analyze460.0ms (15.6%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
15.6%	84.3%	0.1%	6
25%	74.9%	0.1%	7
39.8%	60.1%	0.1%	8
49.2%	50.7%	0.1%	9
58.3%	41.6%	0.1%	10
64.2%	35.7%	0.1%	11
69.2%	30.7%	0.1%	12
72.4%	27.5%	0.1%	13
72.4%	27.5%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample911.0ms (30.9%)

Results

863.0ms

8256×

body

128

valid

Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

prune2.0ms (0.1%)

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 (0.2%)

Local error

Found 1 expressions with local error:

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

series56.0ms (1.9%)

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 (3.7%)

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

prune27.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	25	7	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	7	33

Error

0.0b

Counts

33 → 7

Alt Table

Status	Error	Program
	0.9b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))
	10.0b	(log.f64 (exp.f64 (/.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)))
	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))))
	5.2b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))
▶	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)))

Compiler

Compiled 629 to 385 computations (38.8% saved)

localize10.0ms (0.3%)

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))))
✓	0.7b	(expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))
	0.9b	(/.f64 (atan2.f64 im re) (log.f64 10))

series106.0ms (3.6%)

Counts

2 → 48

Calls

2 calls:

55.0ms	(expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))
51.0ms	(log1p.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))

rewrite1.0ms (0.1%)

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))))

simplify71.0ms (2.4%)

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 → 30

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	786
1	36	744
2	75	744
3	141	744
4	408	744
5	1794	744
6	3396	744
7	5040	744

prune37.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Error

0.0b

Counts

69 → 7

Alt Table

Status	Error	Program
	0.9b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))
	10.0b	(log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
▶	0.5b	(log1p.f64 (log1p.f64 (expm1.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))))
	1.0b	(/.f64 1 (/.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)))
	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))))
	5.2b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))

Compiler

Compiled 1086 to 713 computations (34.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(log1p.f64 (expm1.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))))
✓	0.4b	(log1p.f64 (log1p.f64 (expm1.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))))
	0.7b	(expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))
	0.9b	(/.f64 (atan2.f64 im re) (log.f64 10))

series109.0ms (3.7%)

Counts

2 → 48

Calls

2 calls:

56.0ms	(log1p.f64 (expm1.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))))
53.0ms	(log1p.f64 (log1p.f64 (expm1.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-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:

4.0ms	(log1p.f64 (expm1.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10)))))
0.0ms	(log1p.f64 (log1p.f64 (expm1.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))))

simplify71.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

70 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	837
1	41	755
2	67	749
3	129	749
4	384	749
5	1751	749
6	3386	749
7	5027	749

prune50.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	81	7	88

Error

0.0b

Counts

88 → 7

Alt Table

Status	Error	Program
▶	0.9b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))
	10.0b	(log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))
✓	0.5b	(log1p.f64 (log1p.f64 (expm1.f64 (expm1.f64 (/.f64 (atan2.f64 im re) (log.f64 10))))))
	1.0b	(/.f64 1 (/.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)))
	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))))
	5.2b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))

Compiler

Compiled 1476 to 1024 computations (30.6% saved)

localize8.0ms (0.3%)

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))))

series136.0ms (4.6%)

Counts

2 → 48

Calls

2 calls:

78.0ms	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))
57.0ms	(/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))

rewrite34.0ms (1.1%)

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:

17.0ms	(*.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)))

simplify240.0ms (8.2%)

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

prune125.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	153	5	158
Fresh	2	3	5
Picked	1	0	1
Done	1	0	1
Total	157	8	165

Error

0.0b

Counts

165 → 8

Alt Table

Status	Error	Program
	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)))
	1.3b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (*.f64 (cbrt.f64 (sqrt.f64 (log.f64 10))) (cbrt.f64 (sqrt.f64 (log.f64 10))))) (sqrt.f64 (log.f64 10))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (sqrt.f64 (log.f64 10)))))
	5.7b	(cbrt.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 (log.f64 10))) (/.f64 1 (sqrt.f64 (log.f64 10)))) (/.f64 1 (sqrt.f64 (log.f64 10)))) (.f64 (*.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10)))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 10))))))
	1.4b	(.f64 (/.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))))) (sqrt.f64 (log.f64 10))) (cbrt.f64 (/.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)))))
	5.2b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 10)) 3))
	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)))))
	1.0b	(/.f64 1 (/.f64 (log.f64 10) (atan2.f64 im re)))

Compiler

Compiled 3667 to 2769 computations (24.5% saved)

regimes172.0ms (5.8%)

Accuracy

Total 0.5b remaining (94.1%)

Threshold costs 0.5b (94.1%)

Counts

46 → 1

Compiler

Compiled 3622 to 2774 computations (23.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	11	17

end181.0ms (6.1%)

Compiler: Compiled 215 to 167 computations (22.3% saved)

Details

analyze460.0ms (15.6%)

sample911.0ms (30.9%)

simplify6.0ms (0.2%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series56.0ms (1.9%)

rewrite4.0ms (0.1%)

simplify109.0ms (3.7%)

prune27.0ms (0.9%)

localize10.0ms (0.3%)

series106.0ms (3.6%)

rewrite1.0ms (0.1%)

simplify71.0ms (2.4%)

prune37.0ms (1.3%)

localize11.0ms (0.4%)

series109.0ms (3.7%)

rewrite5.0ms (0.2%)

simplify71.0ms (2.4%)

prune50.0ms (1.7%)

localize8.0ms (0.3%)

series136.0ms (4.6%)

rewrite34.0ms (1.1%)

simplify240.0ms (8.2%)

prune125.0ms (4.2%)

regimes172.0ms (5.8%)

simplify2.0ms (0.1%)

end181.0ms (6.1%)

Profiling