Details

analyze446.0ms (12.4%)

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)

sample1.7s (47.9%)

Results

768.0ms	6293×	body	128	valid
324.0ms	645×	body	2048	valid
320.0ms	537×	body	4096	valid
166.0ms	424×	body	1024	valid
81.0ms	239×	body	512	valid
29.0ms	118×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	25	15
2	29	15
3	31	15
4	31	15

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

11.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% 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 re (hypot.f64 re im))))
✓	0.5b	(+.f64 re (hypot.f64 re im))

series66.0ms (1.8%)

Counts

3 → 56

Calls

3 calls:

40.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
13.0ms	(hypot.f64 re im)
13.0ms	(+.f64 re (hypot.f64 re im))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

3 → 42

Calls

3 calls:

3.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
2.0ms	(+.f64 re (hypot.f64 re im))
0.0ms	(hypot.f64 re im)

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

615×	`fma-def_binary64`
531×	`fma-neg_binary64`
460×	`associate-r_binary64`
385×	`associate-l_binary64`
294×	`cancel-sign-sub-inv_binary64`

Counts

98 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	1829
1	514	1737
2	1465	1673
3	4990	1673
4	5308	1673

prune77.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	6	119

Error

7.9b

Counts

119 → 6

Alt Table

Status	Error	Program
	58.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	45.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
▶	11.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	14.9b	(.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 2623 to 1798 computations (31.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
	0.5b	(+.f64 re (hypot.f64 re im))

series45.0ms (1.2%)

Counts

1 → 8

Calls

1 calls:

45.0ms

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

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`sqrt-prod_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
6×	`associate-l_binary64`

Counts

1 → 36

Calls

1 calls:

7.0ms

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

simplify98.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-neg_binary64`
450×	`associate-r_binary64`
420×	`associate-l_binary64`
310×	`fma-def_binary64`
242×	`distribute-rgt-neg-in_binary64`

Counts

44 → 50

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	1011
1	313	991
2	914	951
3	3063	927
4	4881	923
5	5148	923

prune94.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	136	7	143

Error

7.9b

Counts

143 → 7

Alt Table

Status	Error	Program
	58.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	45.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	11.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	58.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2))))
▶	14.9b	(.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 3082 to 2060 computations (33.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))
	0.2b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
	0.5b	(+.f64 re (hypot.f64 re im))
✓	3.9b	(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))

series101.0ms (2.8%)

Counts

2 → 16

Calls

2 calls:

59.0ms	(log.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))
42.0ms	(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64`
8×	`log-prod_binary64`
8×	`log-pow_binary64`
7×	`exp-prod_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 43

Calls

2 calls:

5.0ms	(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))
4.0ms	(log.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))

simplify83.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
491×	`associate-l_binary64`
463×	`associate-/r*_binary64`
414×	`associate-/l*_binary64`
276×	`cancel-sign-sub-inv_binary64`

Counts

59 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	1617
1	471	1406
2	1470	1301
3	4824	1301
4	4993	1301
5	4930	1301

prune102.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	163	8	171

Error

7.9b

Counts

171 → 8

Alt Table

Status	Error	Program
	58.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	45.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	11.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	58.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	48.7b	(.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (.f64 2 im)))))
▶	15.3b	(.f64 1/2 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))

Compiler

Compiled 4077 to 2813 computations (31% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))
	0.2b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
	0.5b	(+.f64 re (hypot.f64 re im))
✓	4.2b	(pow.f64 (E.f64) (log.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))

series79.0ms (2.2%)

Counts

1 → 8

Calls

1 calls:

79.0ms

(pow.f64 (E.f64) (log.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow-unpow_binary64`
6×	`pow1_binary64`
4×	`log-pow_binary64`
4×	`unpow-prod-up_binary64`
4×	`log-prod_binary64`

Counts

1 → 30

Calls

1 calls:

19.0ms

(pow.f64 (E.f64) (log.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))

simplify92.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

506×	`fma-neg_binary64`
393×	`associate-r_binary64`
348×	`times-frac_binary64`
343×	`associate-l_binary64`
342×	`fma-def_binary64`

Counts

38 → 48

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	1136
1	383	1063
2	1014	1023
3	3580	1023
4	4926	1023
5	4988	1023
6	4941	1023

prune107.0ms (3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	163	9	172

Error

7.9b

Counts

172 → 9

Alt Table

Status	Error	Program
	58.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	45.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	11.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	46.8b	(.f64 1/2 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (.f64 2 (neg.f64 im))))))
	29.6b	(.f64 1/2 (cbrt.f64 (pow.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))) 3)))
	58.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	48.7b	(.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (.f64 2 im)))))

Compiler

Compiled 4236 to 2812 computations (33.6% saved)

regimes209.0ms (5.8%)

Accuracy

Total 6.1b remaining (45.5%)

Threshold costs 0b (0%)

Counts

32 → 1

Compiler

Compiled 2902 to 2401 computations (17.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	13	15
2	13	15

end106.0ms (2.9%)

Compiler: Compiled 135 to 111 computations (17.8% saved)

Details

analyze446.0ms (12.4%)

sample1.7s (47.9%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series66.0ms (1.8%)

rewrite7.0ms (0.2%)

simplify75.0ms (2.1%)

prune77.0ms (2.1%)

localize7.0ms (0.2%)

series45.0ms (1.2%)

rewrite9.0ms (0.2%)

simplify98.0ms (2.7%)

prune94.0ms (2.6%)

localize10.0ms (0.3%)

series101.0ms (2.8%)

rewrite11.0ms (0.3%)

simplify83.0ms (2.3%)

prune102.0ms (2.8%)

localize11.0ms (0.3%)

series79.0ms (2.2%)

rewrite21.0ms (0.6%)

simplify92.0ms (2.6%)

prune107.0ms (3%)

regimes209.0ms (5.8%)

simplify2.0ms (0%)

end106.0ms (2.9%)

Profiling