Details

analyze242.0ms (8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
74.9%	25%	0.1%	4
81.2%	18.7%	0.1%	5
81.2%	15.6%	3.2%	6
81.2%	15.6%	3.2%	7
81.2%	14%	4.8%	8
81.2%	14%	4.8%	9
81.2%	13.3%	5.6%	10
81.2%	13.3%	5.6%	11
81.2%	12.9%	6%	12
81.2%	12.9%	6%	13
81.2%	12.7%	6.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample69.0ms (2.3%)

Algorithm

1×

intervals

Results

15.0ms	45×	body	1024	valid
9.0ms	171×	body	128	valid
8.0ms	29×	body	1024	invalid
6.0ms	29×	body	512	valid
1.0ms	25×	body	128	invalid
1.0ms	11×	body	256	valid
1.0ms	8×	body	512	invalid
1.0ms	7×	body	256	invalid

Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (exp.f64 re) (sin.f64 im))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 re) (sin.f64 im))

series10.0ms (0.3%)

Counts

1 → 8

Calls

1 calls:

10.0ms

(*.f64 (exp.f64 re) (sin.f64 im))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

(*.f64 (exp.f64 re) (sin.f64 im))

simplify67.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

963×	`fma-neg_binary64`
601×	`cancel-sign-sub-inv_binary64`
423×	`unswap-sqr_binary64`
355×	`distribute-rgt-neg-in_binary64`
283×	`*-commutative_binary64`

Counts

28 → 44

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	69	408
1	185	370
2	527	349
3	1418	335
4	2537	333
5	4402	333
6	4955	333

prune27.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	4	45

Error

Counts

45 → 4

Alt Table

Status	Error	Program
	22.3b	(.f64 (sqrt.f64 (.f64 (exp.f64 re) (sin.f64 im))) (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))))
✓	0.0b	(*.f64 (exp.f64 re) (sin.f64 im))
▶	0.0b	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (sin.f64 im)))
	13.5b	(cbrt.f64 (.f64 (.f64 (.f64 (exp.f64 re) (exp.f64 re)) (exp.f64 re)) (.f64 (*.f64 (sin.f64 im) (sin.f64 im)) (sin.f64 im))))

Compiler

Compiled 602 to 234 computations (61.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 re))
✓	0.0b	(*.f64 (sqrt.f64 (exp.f64 re)) (sin.f64 im))
✓	0.0b	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (sin.f64 im)))

series26.0ms (0.9%)

Counts

3 → 36

Calls

3 calls:

13.0ms	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (sin.f64 im)))
11.0ms	(*.f64 (sqrt.f64 (exp.f64 re)) (sin.f64 im))
2.0ms	(sqrt.f64 (exp.f64 re))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
11×	`pow1_binary64`
10×	`sqrt-prod_binary64`
10×	`*-un-lft-identity_binary64`

Counts

3 → 65

Calls

3 calls:

9.0ms	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (sin.f64 im)))
5.0ms	(*.f64 (sqrt.f64 (exp.f64 re)) (sin.f64 im))
2.0ms	(sqrt.f64 (exp.f64 re))

simplify110.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

993×	`fma-neg_binary64`
487×	`fma-def_binary64`
379×	`cancel-sign-sub-inv_binary64`
348×	`distribute-rgt-neg-in_binary64`
327×	`*-commutative_binary64`

Counts

101 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	133	1314
1	341	1214
2	1023	1155
3	2037	1121
4	3496	1113
5	4621	1113
6	4936	1113
7	4892	1113

prune96.0ms (3.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	153	4	157

Error

Counts

157 → 4

Alt Table

Status	Error	Program
	22.3b	(.f64 (sqrt.f64 (.f64 (exp.f64 re) (sin.f64 im))) (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))))
✓	0.0b	(*.f64 (exp.f64 re) (sin.f64 im))
✓	0.0b	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (sin.f64 im)))
▶	13.5b	(.f64 (sqrt.f64 (exp.f64 re)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re))) 3)))

Compiler

Compiled 2418 to 743 computations (69.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re)))
✓	0.0b	(.f64 (sqrt.f64 (exp.f64 re)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re))) 3)))
✓	0.3b	(pow.f64 (*.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re))) 3)
✓	13.5b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re))) 3))

series60.0ms (2%)

Counts

4 → 96

Calls

4 calls:

31.0ms	(pow.f64 (*.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re))) 3)
11.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re))) 3))
10.0ms	(*.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re)))
8.0ms	(.f64 (sqrt.f64 (exp.f64 re)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re))) 3)))

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
20×	`cbrt-prod_binary64`
17×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 103

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 (exp.f64 re)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re))) 3)))
5.0ms	(*.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re)))
5.0ms	(pow.f64 (*.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re))) 3)
2.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re))) 3))

simplify109.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

851×	`fma-def_binary64`
531×	`fma-neg_binary64`
260×	`associate-r_binary64`
231×	`cancel-sign-sub-inv_binary64`
214×	`associate-l_binary64`

Counts

199 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	3371
1	473	3176
2	1691	2927
3	3873	2829
4	4931	2829

prune109.0ms (3.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	183	4	187

Error

Counts

187 → 4

Alt Table

Status	Error	Program
▶	22.3b	(.f64 (sqrt.f64 (.f64 (exp.f64 re) (sin.f64 im))) (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))))
✓	0.0b	(*.f64 (exp.f64 re) (sin.f64 im))
✓	0.0b	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (sin.f64 im)))
✓	13.5b	(.f64 (sqrt.f64 (exp.f64 re)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re))) 3)))

Compiler

Compiled 3657 to 1394 computations (61.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (exp.f64 re) (sin.f64 im))
✓	0.2b	(.f64 (sqrt.f64 (.f64 (exp.f64 re) (sin.f64 im))) (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))))
✓	0.3b	(sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im)))

series25.0ms (0.8%)

Counts

2 → 28

Calls

2 calls:

15.0ms	(sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im)))
9.0ms	(.f64 (sqrt.f64 (.f64 (exp.f64 re) (sin.f64 im))) (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))))

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`pow1_binary64`
30×	`sqrt-pow1_binary64`
21×	`pow-prod-down_binary64`
11×	`pow1/2_binary64`
10×	`pow-prod-up_binary64`

Counts

2 → 64

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 (.f64 (exp.f64 re) (sin.f64 im))) (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))))
3.0ms	(sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im)))

simplify106.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

632×	`fma-neg_binary64`
617×	`associate-r_binary64`
461×	`unswap-sqr_binary64`
382×	`cancel-sign-sub-inv_binary64`
337×	`fma-def_binary64`

Counts

92 → 98

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	96	1107
1	234	1015
2	763	948
3	2367	899
4	4251	830
5	4844	830
6	4987	830
7	4920	830

prune105.0ms (3.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	212	4	216

Error

Counts

216 → 4

Alt Table

Status	Error	Program
✓	22.3b	(.f64 (sqrt.f64 (.f64 (exp.f64 re) (sin.f64 im))) (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))))
✓	0.0b	(*.f64 (exp.f64 re) (sin.f64 im))
✓	0.0b	(.f64 (sqrt.f64 (exp.f64 re)) (.f64 (sqrt.f64 (exp.f64 re)) (sin.f64 im)))
✓	13.5b	(.f64 (sqrt.f64 (exp.f64 re)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 im) (sqrt.f64 (exp.f64 re))) 3)))

Compiler

Compiled 3830 to 907 computations (76.3% saved)

regimes145.0ms (4.8%)

Accuracy

Total 0.0b remaining (44.6%)

Threshold costs 0.0b (44.6%)

Counts

33 → 1

Compiler

Compiled 1987 to 1300 computations (34.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

end0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

sample1.6s (53.7%)

Algorithm

1×

intervals

Results

471.0ms	1342×	body	1024	valid
324.0ms	5664×	body	128	valid
189.0ms	643×	body	1024	invalid
123.0ms	686×	body	512	valid
49.0ms	317×	body	512	invalid
48.0ms	911×	body	128	invalid
36.0ms	306×	body	256	valid
18.0ms	174×	body	256	invalid
2.0ms	2×	body	2048	valid

Compiler

Compiled 66 to 42 computations (36.4% saved)

Details

analyze242.0ms (8%)

sample69.0ms (2.3%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series10.0ms (0.3%)

rewrite5.0ms (0.2%)

simplify67.0ms (2.2%)

prune27.0ms (0.9%)

localize6.0ms (0.2%)

series26.0ms (0.9%)

rewrite18.0ms (0.6%)

simplify110.0ms (3.6%)

prune96.0ms (3.2%)

localize11.0ms (0.3%)

series60.0ms (2%)

rewrite26.0ms (0.9%)

simplify109.0ms (3.6%)

prune109.0ms (3.6%)

localize6.0ms (0.2%)

series25.0ms (0.8%)

rewrite17.0ms (0.6%)

simplify106.0ms (3.5%)

prune105.0ms (3.5%)

regimes145.0ms (4.8%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.6s (53.7%)

Profiling