Details

analyze488.0ms (12.1%)

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)

sample1.9s (46.7%)

Results

870.0ms	6351×	body	128	valid
383.0ms	633×	body	2048	valid
311.0ms	497×	body	4096	valid
168.0ms	407×	body	1024	valid
75.0ms	237×	body	512	valid
31.0ms	131×	body	256	valid

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify26.0ms (0.6%)

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`

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

Stop Event

1×

saturated

Counts

1 → 2

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

14.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	41.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.2b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	1.6b	(-.f64 (hypot.f64 re im) re)

series71.0ms (1.8%)

Counts

3 → 56

Calls

3 calls:

31.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
30.0ms	(hypot.f64 re im)
10.0ms	(-.f64 (hypot.f64 re im) re)

rewrite52.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

811×	`log1p-expm1-u_binary64`
811×	`expm1-log1p-u_binary64`
410×	`prod-diff_binary64`
93×	`egg-rr`
85×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 93

Calls

3 calls:

51.0ms	(hypot.f64 re im)
51.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
51.0ms	(-.f64 (hypot.f64 re im) re)

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`

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

149 → 165

prune112.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	160	5	165
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	161	6	167

Error

0.1b

Counts

167 → 6

Alt Table

Status	Error	Program
✓	14.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	52.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	51.9b	(.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 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2))) (.f64 1/256 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (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)))))
	46.4b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
▶	31.4b	(.f64 1/2 (-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/2 (.f64 (*.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im))))))
	54.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (fma.f64 1/2 (/.f64 (.f64 im im) re) (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))))))))

Compiler

Compiled 3740 to 2567 computations (31.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 im))
✓	0.3b	(.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))
✓	0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
✓	0.5b	(*.f64 (sqrt.f64 2) re)

series30.0ms (0.7%)

Counts

4 → 0

Calls

4 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))
6.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
4.0ms	(*.f64 (sqrt.f64 2) re)
4.0ms	(sqrt.f64 (/.f64 1 im))

rewrite53.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

535×	`log-prod_binary64`
270×	`pow2_binary64`
217×	`pow-unpow_binary64`
192×	`pow1/3_binary64`
187×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	32
1	238	27
2	2505	27
3	5229	27

Stop Event

1×	node limit

Counts

4 → 98

Calls

4 calls:

51.0ms	(sqrt.f64 (/.f64 1 im))
51.0ms	(.f64 (.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im)))
51.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
51.0ms	(*.f64 (sqrt.f64 2) re)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

Stop Event

1×

saturated

Counts

98 → 98

prune77.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	98	6	104

Error

0.1b

Counts

104 → 6

Alt Table

Status	Error	Program
✓	14.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	52.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	51.9b	(.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 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2))) (.f64 1/256 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (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)))))
▶	46.4b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	31.4b	(.f64 1/2 (-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/2 (.f64 (*.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im))))))
	54.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (fma.f64 1/2 (/.f64 (.f64 im im) re) (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))))))))

Compiler

Compiled 2442 to 1979 computations (19% 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)))
✓	0.5b	(*.f64 (sqrt.f64 2) im)
✓	0.6b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))

series39.0ms (1%)

Counts

4 → 0

Calls

4 calls:

25.0ms	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
8.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))
4.0ms	(sqrt.f64 (/.f64 1 re))
3.0ms	(*.f64 (sqrt.f64 2) im)

rewrite49.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

915×	`log1p-expm1-u_binary64`
915×	`expm1-log1p-u_binary64`
117×	`add-sqr-sqrt_binary64`
111×	`add-log-exp_binary64`
110×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 74

Calls

4 calls:

48.0ms	(sqrt.f64 (/.f64 1 re))
48.0ms	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
48.0ms	(*.f64 (sqrt.f64 2) im)
48.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

Stop Event

1×

saturated

Counts

74 → 74

prune50.0ms (1.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	69	5	74
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	70	10	80

Error

0.1b

Counts

80 → 10

Alt Table

Status	Error	Program
✓	14.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	52.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	46.5b	(*.f64 1/2 (pow.f64 (cbrt.f64 (/.f64 im (sqrt.f64 re))) 3))
▶	46.3b	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))
	47.3b	(.f64 1/2 (.f64 (exp.f64 (log.f64 im)) (sqrt.f64 (/.f64 1 re))))
	51.9b	(.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 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2))) (.f64 1/256 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (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)))))
	46.3b	(.f64 1/2 (.f64 (pow.f64 im 1) (sqrt.f64 (/.f64 1 re))))
✓	31.4b	(.f64 1/2 (-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/2 (.f64 (*.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im))))))
	54.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (fma.f64 1/2 (/.f64 (.f64 im im) re) (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))))))))
	52.2b	(.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))))))

Compiler

Compiled 1425 to 1166 computations (18.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series18.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

18.0ms

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

rewrite39.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

496×	`log1p-expm1-u_binary64`
496×	`expm1-log1p-u_binary64`
399×	`unpow-prod-down_binary64`
262×	`log-prod_binary64`
136×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 66

Calls

1 calls:

38.0ms

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

78 → 67

prune35.0ms (0.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	4	3	7
Picked	0	1	1
Done	0	2	2
Total	68	9	77

Error

0.1b

Counts

77 → 9

Alt Table

Status	Error	Program
	52.4b	(.f64 1/2 (sqrt.f64 (/.f64 (.f64 im im) re)))
	47.3b	(.f64 1/2 (.f64 (exp.f64 (log.f64 im)) (sqrt.f64 (/.f64 1 re))))
	46.3b	(.f64 1/2 (.f64 (/.f64 (sqrt.f64 im) 1) (/.f64 (sqrt.f64 im) (sqrt.f64 re))))
	51.9b	(.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 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2))) (.f64 1/256 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (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)))))
	46.3b	(.f64 1/2 (.f64 im (pow.f64 re -1/2)))
✓	31.4b	(.f64 1/2 (-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im)) (.f64 1/2 (.f64 (*.f64 (sqrt.f64 2) re) (sqrt.f64 (/.f64 1 im))))))
✓	14.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
✓	46.3b	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))
	54.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (fma.f64 1/2 (/.f64 (.f64 im im) re) (.f64 1/16 (/.f64 (pow.f64 im 6) (pow.f64 re 5))))))))

Compiler

Compiled 1074 to 622 computations (42.1% saved)

regimes738.0ms (18.2%)

Accuracy

Total 5.9b remaining (98.6%)

Threshold costs 0b (0%)

Counts

55 → 2

Compiler

Compiled 6566 to 5210 computations (20.7% saved)

bsearch2.0ms (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

Stop Event

1×

saturated

end152.0ms (3.8%)

Compiler: Compiled 246 to 193 computations (21.5% 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

analyze488.0ms (12.1%)

sample1.9s (46.7%)

simplify26.0ms (0.6%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series71.0ms (1.8%)

rewrite52.0ms (1.3%)

simplify68.0ms (1.7%)

prune112.0ms (2.8%)

localize11.0ms (0.3%)

series30.0ms (0.7%)

rewrite53.0ms (1.3%)

simplify7.0ms (0.2%)

prune77.0ms (1.9%)

localize9.0ms (0.2%)

series39.0ms (1%)

rewrite49.0ms (1.2%)

simplify6.0ms (0.1%)

prune50.0ms (1.2%)

localize5.0ms (0.1%)

series18.0ms (0.4%)

rewrite39.0ms (1%)

simplify7.0ms (0.2%)

prune35.0ms (0.9%)

regimes738.0ms (18.2%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end152.0ms (3.8%)

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