Details

analyze514.0ms (13.1%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample2.1s (54.2%)

Results

856.0ms	6262×	body	128	valid
410.0ms	552×	body	4096	valid
396.0ms	644×	body	2048	valid
179.0ms	429×	body	1024	valid
175.0ms	119×	body	256	valid
78.0ms	250×	body	512	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	25	15
2	34	15
3	36	15

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

10.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series175.0ms (4.4%)

Counts

2 → 32

Calls

2 calls:

165.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
9.0ms	(+.f64 re (hypot.f64 re im))

rewrite43.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

844×	`expm1-log1p-u_binary64`
589×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
86×	`log1p-expm1-u_binary64`
85×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	178	19
2	2341	19

Stop Event

1×	node limit

Counts

2 → 60

Calls

2 calls:

42.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
42.0ms	(+.f64 re (hypot.f64 re im))

simplify29.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-def_binary64`
387×	`associate-r_binary64`
306×	`associate-l_binary64`
236×	`cancel-sign-sub-inv_binary64`
223×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	860
1	345	810
2	1133	762

Stop Event

1×	node limit

Counts

92 → 105

prune84.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	100	5	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	100	6	106

Error

3.4b

Counts

106 → 6

Alt Table

Status	Error	Program
▶	10.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	55.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))))))
	53.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	45.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	10.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 2227 to 1505 computations (32.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
✓	0.0b	(sqrt.f64 (*.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)))
✓	0.4b	(pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)
	0.9b	(+.f64 re (hypot.f64 re im))

series93.0ms (2.4%)

Counts

3 → 24

Calls

3 calls:

40.0ms	(pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)
30.0ms	(sqrt.f64 (*.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)))
23.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))

rewrite56.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

868×	`expm1-log1p-u_binary64`
506×	`prod-diff_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`egg-rr`
91×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	215	28
2	2425	28

Stop Event

1×	node limit

Counts

3 → 92

Calls

3 calls:

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

simplify37.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

594×	`fma-def_binary64`
413×	`times-frac_binary64`
393×	`associate-l_binary64`
388×	`associate-/l*_binary64`
361×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	957
1	419	866
2	1447	795

Stop Event

1×	node limit

Counts

116 → 136

prune157.0ms (4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	201	6	207

Error

3.4b

Counts

207 → 6

Alt Table

Status	Error	Program
	55.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))))))
	53.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
✓	10.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 im) 2))))
▶	45.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	10.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 4475 to 2969 computations (33.7% saved)

localize5.0ms (0.1%)

prune8.0ms (0.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	2	2
Total	6	6

Error

3.4b

Counts

6 → 6

Alt Table

Status	Error	Program
	55.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))))))
	53.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
✓	10.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
▶	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 im) 2))))
✓	45.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	10.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 134 to 111 computations (17.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (sqrt.f64 im) 2)

series6.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

6.0ms

(pow.f64 (sqrt.f64 im) 2)

rewrite28.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

302×	`log1p-expm1-u_binary64`
302×	`expm1-log1p-u_binary64`
272×	`add-cbrt-cube_binary64`
266×	`add-log-exp_binary64`
265×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	1
1	103	1
2	893	1

Stop Event

1×	node limit

Counts

1 → 28

Calls

1 calls:

28.0ms

(pow.f64 (sqrt.f64 im) 2)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

28 → 28

prune25.0ms (0.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	27	7	34

Error

3.4b

Counts

34 → 7

Alt Table

Status	Error	Program
	55.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3))) (.f64 1/2 (/.f64 (pow.f64 im 2) re))))))
	53.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	42.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (sqrt.f64 (*.f64 im im)))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (pow.f64 im 5/6) (pow.f64 im 1/6)))))
✓	10.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
✓	45.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	10.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 419 to 329 computations (21.5% saved)

regimes367.0ms (9.3%)

Accuracy

Total 4.3b remaining (43.8%)

Threshold costs 0b (0%)

Counts

34 → 2

Compiler

Compiled 3445 to 2809 computations (18.5% saved)

bsearch1.0ms (0%)

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

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	53
1	35	53

Stop Event

1×

saturated

end134.0ms (3.4%)

Compiler: Compiled 173 to 133 computations (23.1% saved)

Details

analyze514.0ms (13.1%)

sample2.1s (54.2%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series175.0ms (4.4%)

rewrite43.0ms (1.1%)

simplify29.0ms (0.7%)

prune84.0ms (2.1%)

localize8.0ms (0.2%)

series93.0ms (2.4%)

rewrite56.0ms (1.4%)

simplify37.0ms (0.9%)

prune157.0ms (4%)

localize5.0ms (0.1%)

prune8.0ms (0.2%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite28.0ms (0.7%)

simplify10.0ms (0.3%)

prune25.0ms (0.6%)

regimes367.0ms (9.3%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end134.0ms (3.4%)

Profiling