Details

analyze254.0ms (2.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
3.1%	3.1%	93.8%	2
3.1%	3.1%	93.8%	3
4.7%	1.6%	93.8%	4
4.7%	1.6%	93.8%	5
5.5%	0.8%	93.8%	6
5.5%	0.8%	93.8%	7
5.8%	0.4%	93.8%	8
5.8%	0.4%	93.8%	9
6%	0.2%	93.8%	10
6%	0.2%	93.8%	11
6.1%	0.1%	93.8%	12
6.1%	0.1%	93.8%	13
6.2%	0%	93.8%	14

Compiler

Compiled 36 to 30 computations (16.7% saved)

sample81.0ms (0.7%)

Algorithm

1×

intervals

Results

61.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 59 to 51 computations (13.6% saved)

simplify127.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

909×	`cube-prod_binary64`
818×	`unswap-sqr_binary64`
698×	`fabs-mul_binary64`
671×	`sqr-pow_binary64`
541×	`cube-mult_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	24
1	38	24
2	63	24
3	101	24
4	203	24
5	528	24
6	667	24
7	856	24
8	1442	24
9	1481	24
10	1512	24
11	1576	24
12	1582	24
13	1854	24
14	2077	24
15	2498	24
16	3106	24
17	3604	24
18	4037	24
19	4445	24
20	4754	24
21	4859	24

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)

Compiler

Compiled 78 to 68 computations (12.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.1b	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
✓	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))

series985.0ms (8.5%)

Counts

4 → 60

Calls

4 calls:

549.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)
267.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
166.0ms	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-exp-log_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`prod-exp_binary64`
16×	`*-un-lft-identity_binary64`
14×	`associate-l_binary64`

Counts

4 → 107

Calls

4 calls:

8.0ms	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
8.0ms	(.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))
4.0ms	(.f64 (.f64 2 (PI.f64)) u2)
3.0ms	(pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)

simplify150.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

411×	`unswap-sqr_binary64`
378×	`cancel-sign-sub-inv_binary64`
371×	`fma-def_binary64`
332×	`fma-neg_binary64`
234×	`associate-l_binary64`

Counts

167 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	2863
1	473	2660
2	1532	2604
3	3218	2602
4	4807	2602
5	4998	2602
6	4924	2602

prune208.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	167	6	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	168	6	174

Error

Counts

174 → 6

Alt Table

Status	Error	Program
	0.6b	(+.f64 (.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 6)) (.f64 (log.f64 (.f64 -2 (log.f64 u1))) 1/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.5b	(+.f64 (.f64 (.f64 (.f64 1/6 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	1.2b	(+.f64 (.f64 (.f64 (.f64 1/6 (.f64 (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cbrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.4b	(/.f64 (fma.f64 (.f64 -1/18 (log.f64 u1)) (.f64 (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) -1/4) (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) -1/2))
	0.4b	(+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
▶	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)

Compiler

Compiled 4752 to 3773 computations (20.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
✓	0.3b	(*.f64 u2 (PI.f64))
✓	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
✓	0.4b	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))))

series448.0ms (3.9%)

Counts

4 → 68

Calls

4 calls:

241.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))))
182.0ms	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
23.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
2.0ms	(*.f64 u2 (PI.f64))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-prod_binary64`
18×	`associate-l_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`

Counts

4 → 86

Calls

4 calls:

8.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))))
4.0ms	(*.f64 u2 (PI.f64))
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
0.0ms	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)

simplify134.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-neg_binary64`
515×	`*-commutative_binary64`
379×	`distribute-rgt-neg-in_binary64`
347×	`distribute-lft-neg-in_binary64`
263×	`fma-def_binary64`

Counts

154 → 143

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	180	3395
1	401	3209
2	1225	3115
3	2639	3096
4	4926	3094
5	5120	3094

prune144.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	143	6	149

Error

Counts

149 → 6

Alt Table

Status	Error	Program
	0.6b	(+.f64 (.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 6)) (.f64 (log.f64 (.f64 -2 (log.f64 u1))) 1/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.5b	(+.f64 (.f64 (.f64 (.f64 1/6 (pow.f64 (.f64 -2 (log.f64 u1)) 1/4)) (sqrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	1.2b	(+.f64 (.f64 (.f64 (.f64 1/6 (.f64 (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cbrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cbrt.f64 (pow.f64 (.f64 -2 (log.f64 u1)) 1/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.4b	(/.f64 (fma.f64 (.f64 -1/18 (log.f64 u1)) (.f64 (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) -1/4) (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) -1/2))
▶	0.4b	(+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
✓	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)

Compiler

Compiled 3823 to 2356 computations (38.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.3b	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))

series85.0ms (0.7%)

Counts

3 → 28

Calls

3 calls:

32.0ms	(.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
28.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
26.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`pow1_binary64`
20×	`associate-l_binary64`
19×	`sqrt-prod_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`pow-prod-down_binary64`

Counts

3 → 80

Calls

3 calls:

10.0ms	(.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (sqrt.f64 1/6)))
6.0ms	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))
3.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))

simplify119.0ms (1%)

Algorithm

1×	egg-herbie

Rules

756×	`fma-def_binary64`
520×	`fma-neg_binary64`
211×	`associate-*r/_binary64`
193×	`*-commutative_binary64`
190×	`associate-*l/_binary64`

Counts

108 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1729
1	192	1553
2	492	1483
3	638	1433
4	845	1433
5	1727	1433
6	4099	1433
7	4992	1433
8	4838	1433

prune263.0ms (2.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	149	5	154

Error

Counts

154 → 5

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.6b	(+.f64 (.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 6)) (.f64 (log.f64 (.f64 -2 (log.f64 u1))) 1/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.4b	(/.f64 (fma.f64 (.f64 -1/18 (log.f64 u1)) (.f64 (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) -1/4) (fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) -1/2))
✓	0.4b	(+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
✓	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)

Compiler

Compiled 4180 to 3450 computations (17.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.2b	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
	0.3b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

series210.0ms (1.8%)

Counts

3 → 48

Calls

3 calls:

165.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
23.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))
21.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
6×	`pow-prod-down_binary64`
5×	`add-log-exp_binary64`

Counts

3 → 48

Calls

3 calls:

6.0ms	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
4.0ms	(.f64 (.f64 -2 (log.f64 u1)) 1/36)
3.0ms	(sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36))

simplify150.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

447×	`cancel-sign-sub-inv_binary64`
388×	`*-commutative_binary64`
282×	`fma-neg_binary64`
255×	`sub-neg_binary64`
233×	`fma-def_binary64`

Counts

96 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	1711
1	334	1481
2	952	1440
3	1986	1426
4	3949	1426
5	4787	1426
6	4952	1426
7	4981	1426
8	4786	1426

prune146.0ms (1.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	120	5	125

Error

Counts

125 → 5

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 (log.f64 u1)) 1/36)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
	0.6b	(+.f64 (.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 6)) (.f64 (log.f64 (.f64 -2 (log.f64 u1))) 1/2))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
✓	0.4b	(+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 6)) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (sqrt.f64 1/6))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2))) 1/2)
✓	0.4b	(fma.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (sqrt.f64 2) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))) 1/2)
	0.4b	(/.f64 (fma.f64 (.f64 -1/18 (log.f64 u1)) (.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))) -1/4) (fma.f64 (sqrt.f64 (.f64 -1/18 (log.f64 u1))) (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) -1/2))

Compiler

Compiled 2750 to 2060 computations (25.1% saved)

regimes4.7s (40.9%)

Accuracy

Total 0.2b remaining (95.4%)

Threshold costs 0.2b (95.4%)

Counts

223 → 1

Compiler

Compiled 56131 to 49217 computations (12.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	23	26
2	23	26

end1.0ms (0%)

Compiler: Compiled 18 to 16 computations (11.1% saved)

sample3.2s (27.4%)

Algorithm

1×

intervals

Results

1.9s	8000×	body	128	valid
462.0ms	8000×	pre	128	true

Compiler

Compiled 175 to 149 computations (14.9% saved)

Details

analyze254.0ms (2.2%)

sample81.0ms (0.7%)

simplify127.0ms (1.1%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series985.0ms (8.5%)

rewrite29.0ms (0.3%)

simplify150.0ms (1.3%)

prune208.0ms (1.8%)

localize12.0ms (0.1%)

series448.0ms (3.9%)

rewrite18.0ms (0.2%)

simplify134.0ms (1.2%)

prune144.0ms (1.2%)

localize15.0ms (0.1%)

series85.0ms (0.7%)

rewrite29.0ms (0.3%)

simplify119.0ms (1%)

prune263.0ms (2.3%)

localize11.0ms (0.1%)

series210.0ms (1.8%)

rewrite15.0ms (0.1%)

simplify150.0ms (1.3%)

prune146.0ms (1.3%)

regimes4.7s (40.9%)

simplify5.0ms (0%)

end1.0ms (0%)

sample3.2s (27.4%)

Profiling