Details

analyze528.0ms (13%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample2.0s (49.9%)

Results

892.0ms	6280×	body	128	valid
408.0ms	663×	body	2048	valid
336.0ms	519×	body	4096	valid
226.0ms	422×	body	1024	valid
79.0ms	239×	body	512	valid
31.0ms	133×	body	256	valid

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify37.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

203×	`fma-def_binary64`
142×	`fma-neg_binary64`
51×	`distribute-rgt-in_binary64`
42×	`cancel-sign-sub-inv_binary64`
28×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

11.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	35.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
▶	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	0.0b	(hypot.f64 re im)
✓	0.9b	(-.f64 (hypot.f64 re im) re)

series69.0ms (1.7%)

Counts

3 → 56

Calls

3 calls:

44.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
14.0ms	(-.f64 (hypot.f64 re im) re)
11.0ms	(hypot.f64 re im)

rewrite52.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

93× egg-rr

Counts

3 → 93

Calls

2 calls:

50.0ms	((-.f64 (hypot.f64 re im) re) (hypot.f64 re im) (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	172	23
2	2053	23
3	5735	23
0	0	0
1	0	0

simplify68.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-def_binary64`
559×	`fma-neg_binary64`
365×	`associate-/l*_binary64`
347×	`times-frac_binary64`
280×	`cancel-sign-sub-inv_binary64`

Counts

149 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	158	1505
1	489	1464
2	1585	1399
3	4793	1395
4	5057	1395

prune99.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	161	4	165
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	162	5	167

Error

0.1b

Counts

167 → 5

Alt Table

Status	Error	Program
	55.6b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (-.f64 (.f64 1/32 (/.f64 (.f64 (pow.f64 im 5) (sqrt.f64 2)) (sqrt.f64 1/2))) (.f64 1/256 (/.f64 (.f64 (pow.f64 im 5) (sqrt.f64 2)) (sqrt.f64 1/2)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16)))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	49.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
	56.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
▶	12.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))

Compiler

Compiled 3664 to 2505 computations (31.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)))
	0.0b	(hypot.f64 re im)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 re im)) 2)
✓	7.4b	(-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)

series88.0ms (2.2%)

Counts

3 → 40

Calls

3 calls:

45.0ms	(sqrt.f64 (*.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)))
29.0ms	(pow.f64 (sqrt.f64 (hypot.f64 re im)) 2)
14.0ms	(-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re)

rewrite58.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

113× egg-rr

Counts

3 → 113

Calls

2 calls:

55.0ms	((-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re) (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) (sqrt.f64 (*.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	196	23
2	2224	23
3	6156	23
0	0	0
1	0	0

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

595×	`fma-def_binary64`
425×	`fma-neg_binary64`
365×	`associate-/l*_binary64`
347×	`times-frac_binary64`
260×	`cancel-sign-sub-inv_binary64`

Counts

153 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	1177
1	460	1148
2	1497	1091
3	4902	1087
4	5086	1087

prune127.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	217	5	222

Error

0.1b

Counts

222 → 5

Alt Table

Status	Error	Program
	55.6b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (-.f64 (.f64 1/32 (/.f64 (.f64 (pow.f64 im 5) (sqrt.f64 2)) (sqrt.f64 1/2))) (.f64 1/256 (/.f64 (.f64 (pow.f64 im 5) (sqrt.f64 2)) (sqrt.f64 1/2)))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16)))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
▶	49.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
	56.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓	12.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))

Compiler

Compiled 4993 to 3226 computations (35.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 re))
✓	0.1b	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
✓	0.4b	(*.f64 (sqrt.f64 2) im)
✓	0.5b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))

series60.0ms (1.5%)

Counts

4 → 0

Calls

4 calls:

45.0ms	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
6.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))
5.0ms	(sqrt.f64 (/.f64 1 re))
4.0ms	(*.f64 (sqrt.f64 2) im)

rewrite80.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

75× egg-rr

Counts

4 → 74

Calls

2 calls:

79.0ms	((.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (.f64 (sqrt.f64 2) im) (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))) (sqrt.f64 (/.f64 1 re)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	258	17
2	2458	17
3	5506	17
0	0	0
1	0	0

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune45.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	67	7	74
Fresh	2	0	2
Picked	1	0	1
Done	0	2	2
Total	70	9	79

Error

0.0b

Counts

79 → 9

Alt Table

Status	Error	Program
	49.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (expm1.f64 (log1p.f64 (pow.f64 re -1/2)))))
	56.0b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 re -2))) (sqrt.f64 (/.f64 1 (cbrt.f64 re))))))
	58.3b	(*.f64 1/2 (cbrt.f64 (pow.f64 (/.f64 im (sqrt.f64 re)) 3)))
	49.5b	(*.f64 1/2 (pow.f64 (sqrt.f64 (/.f64 im (sqrt.f64 re))) 2))
▶	49.5b	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))
	49.6b	(.f64 1/2 (.f64 (pow.f64 (sqrt.f64 im) 2) (sqrt.f64 (/.f64 1 re))))
	49.5b	(.f64 1/2 (.f64 (pow.f64 im 1) (sqrt.f64 (/.f64 1 re))))
✓	12.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 1257 to 1022 computations (18.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 im (sqrt.f64 re))

series22.0ms (0.6%)

Counts

1 → 12

Calls

1 calls:

22.0ms

(/.f64 im (sqrt.f64 re))

rewrite41.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

66× egg-rr

Counts

1 → 66

Calls

2 calls:

39.0ms	((/.f64 im (sqrt.f64 re)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	103	6
2	1293	6
3	5017	6
0	0	0
1	0	0

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

78 → 67

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	108
1	10	108
2	9	108

prune30.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	4	2	6
Picked	1	0	1
Done	0	2	2
Total	70	6	76

Error

0.0b

Counts

76 → 6

Alt Table

Status	Error	Program
	49.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (expm1.f64 (log1p.f64 (pow.f64 re -1/2)))))
	49.5b	(.f64 1/2 (.f64 (sqrt.f64 im) (*.f64 (sqrt.f64 im) (pow.f64 re -1/2))))
	49.7b	(*.f64 1/2 (pow.f64 (/.f64 (sqrt.f64 re) im) -1))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	49.5b	(*.f64 1/2 (pow.f64 (sqrt.f64 (/.f64 im (sqrt.f64 re))) 2))
✓	12.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))

Compiler

Compiled 970 to 535 computations (44.8% saved)

regimes418.0ms (10.3%)

Accuracy

Total 6.2b remaining (97.2%)

Threshold costs 0b (0%)

Counts

36 → 2

Compiler

Compiled 3842 to 3160 computations (17.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	45
1	31	45
2	36	45
3	38	45
4	39	45
5	39	45

end89.0ms (2.2%)

Compiler: Compiled 142 to 106 computations (25.4% saved)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

Details

analyze528.0ms (13%)

sample2.0s (49.9%)

simplify37.0ms (0.9%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series69.0ms (1.7%)

rewrite52.0ms (1.3%)

simplify68.0ms (1.7%)

prune99.0ms (2.4%)

localize8.0ms (0.2%)

series88.0ms (2.2%)

rewrite58.0ms (1.4%)

simplify66.0ms (1.6%)

prune127.0ms (3.1%)

localize9.0ms (0.2%)

series60.0ms (1.5%)

rewrite80.0ms (2%)

simplify6.0ms (0.1%)

prune45.0ms (1.1%)

localize5.0ms (0.1%)

series22.0ms (0.6%)

rewrite41.0ms (1%)

simplify10.0ms (0.3%)

prune30.0ms (0.7%)

regimes418.0ms (10.3%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end89.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15