Details

analyze261.0ms (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 30 to 26 computations (13.3% saved)

sample89.0ms (0.7%)

Algorithm

1×

intervals

Results

42.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 53 to 47 computations (11.3% saved)

simplify138.0ms (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

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

0.4b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 70 to 60 computations (14.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`

Counts

4 → 64

Calls

4 calls:

8.0ms	(.f64 (.f64 2 PI.f64) u2)
5.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)

series1.4s (10.6%)

Counts

4 → 52

Calls

4 calls:

530.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
483.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
381.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
11.0ms	(.f64 (.f64 2 PI.f64) u2)

simplify126.0ms (1%)

Algorithm

1×	egg-herbie

Rules

765×	`fma-def_binary64`
424×	`*-commutative_binary64`
391×	`unswap-sqr_binary64`
345×	`distribute-rgt-neg-in_binary64`
327×	`cancel-sign-sub-inv_binary64`

Counts

116 → 190

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	153	2049
1	322	1936
2	915	1852
3	1718	1796
4	3438	1796
5	4798	1796
6	4916	1796

prune112.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	182	8	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	183	8	191

Error

Counts

191 → 8

Alt Table

Status	Error	Program
	0.6b	(fma.f64 (cbrt.f64 (.f64 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.7b	(fma.f64 (exp.f64 (+.f64 (log.f64 1/6) (log.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.4b	(fma.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.6b	(fma.f64 (.f64 (.f64 1/6 (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
▶	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.9b	(.f64 (sqrt.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)) (sqrt.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)))
	0.6b	(fma.f64 (.f64 (sqrt.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (sqrt.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.3b	(fma.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)

Compiler

Compiled 2508 to 1909 computations (23.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
✓	0.2b	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
✓	0.2b	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))
	0.3b	(.f64 (.f64 2 PI.f64) u2)

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64`
15×	`pow-prod-down_binary64`
12×	`associate-l_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`sqrt-pow1_binary64`

Counts

2 → 56

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
6.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))

series441.0ms (3.3%)

Counts

2 → 24

Calls

2 calls:

223.0ms	(.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (*.f64 -2 (log.f64 u1)))))
217.0ms	(.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-neg_binary64`
311×	`*-commutative_binary64`
240×	`neg-mul-1_binary64`
239×	`associate-*r/_binary64`
218×	`associate-*l/_binary64`

Counts

80 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1130
1	170	1084
2	470	1084
3	633	1076
4	841	1076
5	1846	1076
6	3632	1076
7	4942	1076

prune313.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	220	4	224
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	225	7	232

Error

Counts

232 → 7

Alt Table

Status	Error	Program
	0.7b	(fma.f64 (exp.f64 (+.f64 (log.f64 1/6) (log.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.3b	(fma.f64 (.f64 (.f64 (sqrt.f64 1/6) (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 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
▶	0.2b	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.6b	(fma.f64 (cbrt.f64 (.f64 (.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.6b	(fma.f64 (expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)

Compiler

Compiled 3352 to 2692 computations (19.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
✓	0.1b	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))
	0.3b	(.f64 (.f64 2 PI.f64) u2)
✓	0.3b	(*.f64 (log.f64 u1) -1/18)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 44

Calls

3 calls:

3.0ms	(*.f64 (log.f64 u1) -1/18)
2.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))
0.0ms	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)

series891.0ms (6.7%)

Counts

3 → 48

Calls

3 calls:

428.0ms	(fma.f64 (sqrt.f64 (.f64 (log.f64 u1) -1/18)) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
259.0ms	(sqrt.f64 (*.f64 (log.f64 u1) -1/18))
202.0ms	(*.f64 (log.f64 u1) -1/18)

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

434×	`unswap-sqr_binary64`
386×	`fma-neg_binary64`
358×	`associate-l_binary64`
318×	`associate-r_binary64`
298×	`distribute-rgt-neg-in_binary64`

Counts

92 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1430
1	228	1354
2	584	1331
3	1842	1314
4	4046	1314
5	5285	1314

prune133.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	255	3	258
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	260	5	265

Error

Counts

265 → 5

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.4b	(fma.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
▶	0.2b	(fma.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.3b	(fma.f64 (sqrt.f64 (exp.f64 (log.f64 (.f64 -1/18 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.3b	(fma.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (.f64 (log.f64 u1) -1/18)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)

Compiler

Compiled 2246 to 1611 computations (28.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
✓	0.1b	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))
	0.3b	(.f64 (.f64 2 PI.f64) u2)
✓	2.7b	(pow.f64 u1 -1/18)

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
4×	`sqrt-prod_binary64`

Counts

3 → 45

Calls

3 calls:

2.0ms	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))
1.0ms	(pow.f64 u1 -1/18)
0.0ms	(fma.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)

series1.8s (13.8%)

Counts

3 → 44

Calls

3 calls:

1.0s	(fma.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
622.0ms	(sqrt.f64 (log.f64 (pow.f64 u1 -1/18)))
206.0ms	(pow.f64 u1 -1/18)

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

429×	`fma-neg_binary64`
311×	`associate-r_binary64`
306×	`unswap-sqr_binary64`
291×	`associate-l_binary64`
269×	`distribute-rgt-neg-in_binary64`

Counts

89 → 161

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	1397
1	233	1319
2	565	1286
3	2026	1260
4	4702	1221
5	4917	1221

prune114.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	349	0	349
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	349	5	354

Error

Counts

354 → 5

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 (log.f64 u1) -1/3))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.4b	(fma.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) 1/6) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
✓	0.2b	(fma.f64 (sqrt.f64 (log.f64 (pow.f64 u1 -1/18))) (cos.f64 (.f64 (.f64 2 PI.f64) u2)) 1/2)
	0.3b	(fma.f64 (sqrt.f64 (exp.f64 (log.f64 (.f64 -1/18 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)
	0.3b	(fma.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (.f64 (log.f64 u1) -1/18)))) (cos.f64 (.f64 (*.f64 2 PI.f64) u2)) 1/2)

Compiler

Compiled 2111 to 1618 computations (23.4% saved)

regimes3.8s (28.8%)

Accuracy

Total 0.2b remaining (76.9%)

Threshold costs 0.2b (76.9%)

Compiler

Compiled 29329 to 25997 computations (11.4% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	16	21
2	16	21

end1.0ms (0%)

Compiler: Compiled 15 to 13 computations (13.3% saved)

sample3.2s (24%)

Algorithm

1×

intervals

Results

2.0s	8000×	body	128	valid
383.0ms	8000×	pre	128	true

Compiler

Compiled 131 to 115 computations (12.2% saved)

Details

analyze261.0ms (2%)

sample89.0ms (0.7%)

simplify138.0ms (1%)

prune4.0ms (0%)

localize12.0ms (0.1%)

rewrite19.0ms (0.1%)

series1.4s (10.6%)

simplify126.0ms (1%)

prune112.0ms (0.8%)

localize13.0ms (0.1%)

rewrite17.0ms (0.1%)

series441.0ms (3.3%)

simplify96.0ms (0.7%)

prune313.0ms (2.4%)

localize10.0ms (0.1%)

rewrite7.0ms (0.1%)

series891.0ms (6.7%)

simplify92.0ms (0.7%)

prune133.0ms (1%)

localize12.0ms (0.1%)

rewrite5.0ms (0%)

series1.8s (13.8%)

simplify98.0ms (0.7%)

prune114.0ms (0.9%)

regimes3.8s (28.8%)

simplify6.0ms (0%)

end1.0ms (0%)

sample3.2s (24%)

Profiling