Details

analyze541.0ms (9.8%)

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
25%	74.9%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
62.4%	31.2%	6.3%	7
62.4%	31.2%	6.3%	8
62.4%	28.1%	9.5%	9
62.4%	28.1%	9.5%	10
62.4%	26.5%	11%	11
62.4%	26.5%	11%	12
62.4%	25.8%	11.8%	13
62.4%	25.8%	11.8%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample113.0ms (2%)

Algorithm

1×

intervals

Results

30.0ms	54×	body	1024	valid
27.0ms	64×	body	1024	invalid
12.0ms	156×	body	128	valid
8.0ms	40×	body	512	invalid
8.0ms	105×	body	128	invalid
7.0ms	32×	body	512	valid
2.0ms	14×	body	256	valid
2.0ms	11×	body	256	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

778×	`unswap-sqr_binary64`
536×	`fma-def_binary64`
491×	`associate-/r*_binary64`
476×	`fabs-mul_binary64`
360×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	27	18
2	65	18
3	104	17
4	137	17
5	196	17
6	329	17
7	736	17
8	2242	17
9	2250	17
10	2619	17
11	4128	17
12	4563	17
13	5391	17

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 51 to 34 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 re)
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
✓	0.0b	(/.f64 1/2 (exp.f64 im))

series34.0ms (0.6%)

Counts

3 → 32

Calls

3 calls:

25.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
7.0ms	(/.f64 1/2 (exp.f64 im))
2.0ms	(sin.f64 re)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 60

Calls

3 calls:

3.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
3.0ms	(/.f64 1/2 (exp.f64 im))
1.0ms	(sin.f64 re)

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-neg_binary64`
504×	`associate-l_binary64`
496×	`fma-def_binary64`
446×	`associate-r_binary64`
324×	`times-frac_binary64`

Counts

92 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	1614
1	407	1481
2	1235	1465
3	4039	1461
4	5302	1461

prune81.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	4	107

Error

Counts

107 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
	0.5b	(fma.f64 1/2 (.f64 (.f64 im im) (sin.f64 re)) (sin.f64 re))
▶	0.0b	(+.f64 (.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re)) (*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))
	21.9b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)) 3))

Compiler

Compiled 2074 to 1135 computations (45.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re)) (*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))
✓	0.0b	(*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re))
✓	0.0b	(.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re))
	0.0b	(/.f64 1/2 (exp.f64 im))

series63.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

32.0ms	(+.f64 (.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re)) (*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))
19.0ms	(*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re))
13.0ms	(.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`associate-l_binary64`
13×	`add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 69

Calls

3 calls:

6.0ms	(*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re))
5.0ms	(+.f64 (.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re)) (*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))
5.0ms	(.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re))

simplify100.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

706×	`fma-neg_binary64`
425×	`cancel-sign-sub-inv_binary64`
247×	`associate-l_binary64`
223×	`associate-r_binary64`
200×	`times-frac_binary64`

Counts

141 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	205	2469
1	612	2347
2	2145	2307
3	4646	2303
4	5026	2303

prune133.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	195	3	198

Error

Counts

198 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
▶	0.0b	(fma.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re) (.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))
	21.9b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)) 3))

Compiler

Compiled 4512 to 2353 computations (47.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 re)
	0.0b	(*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re))
✓	0.0b	(fma.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re) (.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))
	0.0b	(/.f64 1/2 (exp.f64 im))

series30.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

30.0ms

(fma.f64 (*.f64 1/2 (exp.f64 im)) (sin.f64 re) (*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (*.f64 1/2 (exp.f64 im)) (sin.f64 re) (*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))

simplify66.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-neg_binary64`
376×	`fma-def_binary64`
290×	`times-frac_binary64`
258×	`distribute-rgt-in_binary64`
257×	`sub-neg_binary64`

Counts

34 → 36

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	928
1	225	754
2	670	746
3	2394	737
4	4799	737
5	5248	737

prune148.0ms (2.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	180	3	183

Error

Counts

183 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
✓	0.0b	(fma.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re) (.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))
▶	21.9b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)) 3))

Compiler

Compiled 3886 to 1976 computations (49.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))
	0.0b	(/.f64 1/2 (exp.f64 im))
✓	0.3b	(pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)) 3)
✓	21.9b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)) 3))

series122.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

70.0ms

(pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)) 3)

26.0ms

(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)) 3))

26.0ms

(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`cbrt-prod_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`

Counts

3 → 63

Calls

3 calls:

3.0ms

(*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re))

3.0ms

(pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)) 3)

2.0ms

(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)) 3))

simplify134.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

328×	`cancel-sign-sub-inv_binary64`
320×	`distribute-rgt-in_binary64`
214×	`fma-def_binary64`
195×	`log-prod_binary64`
194×	`exp-prod_binary64`

Counts

135 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	215	3527
1	549	3351
2	2280	3294
3	4671	3292
4	4980	3292

prune103.0ms (1.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	156	3	159

Error

Counts

159 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
✓	0.0b	(fma.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re) (.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))
✓	21.9b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))) (sin.f64 re)) 3))

Compiler

Compiled 4033 to 2464 computations (38.9% saved)

regimes149.0ms (2.7%)

Accuracy

Total 0.0b remaining (22.3%)

Threshold costs 0.0b (22.3%)

Counts

24 → 1

Compiler

Compiled 2305 to 1594 computations (30.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	12	22
2	12	22

end1.0ms (0%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

sample3.5s (62.7%)

Algorithm

1×

intervals

Results

981.0ms	1953×	body	1024	valid
764.0ms	2020×	body	1024	invalid
364.0ms	4509×	body	128	valid
248.0ms	1019×	body	512	valid
214.0ms	975×	body	512	invalid
211.0ms	2608×	body	128	invalid
85.0ms	510×	body	256	valid
67.0ms	446×	body	256	invalid
11.0ms	9×	body	2048	valid

Compiler

Compiled 78 to 55 computations (29.5% saved)

Details

analyze541.0ms (9.8%)

sample113.0ms (2%)

simplify89.0ms (1.6%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series34.0ms (0.6%)

rewrite9.0ms (0.2%)

simplify81.0ms (1.5%)

prune81.0ms (1.5%)

localize9.0ms (0.2%)

series63.0ms (1.1%)

rewrite19.0ms (0.3%)

simplify100.0ms (1.8%)

prune133.0ms (2.4%)

localize8.0ms (0.2%)

series30.0ms (0.5%)

rewrite1.0ms (0%)

simplify66.0ms (1.2%)

prune148.0ms (2.7%)

localize10.0ms (0.2%)

series122.0ms (2.2%)

rewrite10.0ms (0.2%)

simplify134.0ms (2.4%)

prune103.0ms (1.8%)

regimes149.0ms (2.7%)

simplify2.0ms (0%)

end1.0ms (0%)

sample3.5s (62.7%)

Profiling