Details

analyze7.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.8%	0.1%	0.1%	12
99.8%	0%	0.1%	13
99.8%	0%	0.2%	14

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample782.0ms (30.4%)

Results

749.0ms	8249×	body	128	valid
1.0ms	4×	body	1024	valid
0.0ms	2×	body	512	valid
0.0ms	1×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 29 computations (9.4% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	16	5
3	14	5

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)

series2.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(fma.f64 841/108 x 4/29)

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 841/108 x 4/29)

simplify112.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

639×	`associate-*r/_binary64`
493×	`distribute-rgt-in_binary64`
446×	`distribute-lft-out_binary64`
406×	`distribute-rgt-out_binary64`
402×	`associate-l_binary64`

Counts

22 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	142
1	19	131
2	42	131
3	104	131
4	284	131
5	900	131
6	1555	131
7	2510	131
8	2614	131
9	3104	131
10	4503	131
11	4867	131
12	4989	131
13	4799	131

prune10.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	13	2	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	3	16

Error

0.1b

Counts

16 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)
▶	14.6b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	21.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 841/108 x 4/29) (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)))

Compiler

Compiled 166 to 136 computations (18.1% saved)

localize4.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 841/108 x 4/29))
	0.1b	(fma.f64 841/108 x 4/29)
✓	0.1b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))

series13.0ms (0.5%)

Counts

2 → 16

Calls

2 calls:

11.0ms	(sqrt.f64 (fma.f64 841/108 x 4/29))
2.0ms	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
1.0ms	(sqrt.f64 (fma.f64 841/108 x 4/29))

simplify94.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

454×	`fma-def_binary64`
417×	`times-frac_binary64`
363×	`associate-/l*_binary64`
271×	`distribute-lft-in_binary64`
271×	`distribute-rgt-in_binary64`

Counts

84 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	796
1	143	736
2	393	716
3	1299	662
4	4570	662
5	4715	662
6	4812	662
7	5097	662

prune96.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	137	6	143

Error

0.0b

Counts

143 → 6

Alt Table

Status	Error	Program
	15.2b	(.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))))
✓	0.1b	(fma.f64 841/108 x 4/29)
	15.2b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29))))
▶	15.0b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) 4))
✓	14.6b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	21.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 841/108 x 4/29) (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)))

Compiler

Compiled 2338 to 1985 computations (15.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) 4))
✓	0.1b	(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))))
✓	0.1b	(cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.2b	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) 4)

series27.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

15.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) 4)
5.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))))
5.0ms	(cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))
2.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) 4))

rewrite29.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`cbrt-prod_binary64`
52×	`add-sqr-sqrt_binary64`
30×	`sqrt-prod_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 141

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) 4))
6.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))))
2.0ms	(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) 4)
1.0ms	(cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))

simplify162.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

615×	`fma-def_binary64`
225×	`unswap-sqr_binary64`
216×	`times-frac_binary64`
202×	`fma-neg_binary64`
192×	`cancel-sign-sub-inv_binary64`

Counts

189 → 265

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	266	4229
1	629	3780
2	1917	3275
3	4664	3211
4	4990	3211
5	4915	3211

prune400.0ms (15.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	357	2	359
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	359	6	365

Error

0.0b

Counts

365 → 6

Alt Table

Status	Error	Program
✓	14.6b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	15.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))) 4)) (cbrt.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))) 4)))) (cbrt.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) 4)))
✓	0.1b	(fma.f64 841/108 x 4/29)
▶	15.2b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29))))
	15.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (pow.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)) (sqrt.f64 4)))
	21.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 841/108 x 4/29) (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)))

Compiler

Compiled 11453 to 9987 computations (12.8% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (fma.f64 841/108 x 4/29))
✓	0.1b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29))))
	0.1b	(fma.f64 841/108 x 4/29)
✓	0.6b	(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29)))

series7.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

6.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29)))

2.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29))))

rewrite27.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`sqrt-pow1_binary64`
48×	`pow1_binary64`
42×	`add-sqr-sqrt_binary64`
37×	`sqrt-prod_binary64`
36×	`pow-prod-up_binary64`

Counts

2 → 100

Calls

2 calls:

11.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29))))

8.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29)))

simplify126.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

506×	`times-frac_binary64`
423×	`distribute-rgt-in_binary64`
296×	`associate-l_binary64`
281×	`cancel-sign-sub-inv_binary64`
253×	`fma-neg_binary64`

Counts

124 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	2137
1	306	1826
2	776	1541
3	2270	1428
4	5145	1428

prune201.0ms (7.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	266	1	267
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	267	6	273

Error

0.0b

Counts

273 → 6

Alt Table

Status	Error	Program
✓	14.6b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	15.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))) 4)) (cbrt.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x 841/108 4/29))) 4)))) (cbrt.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) 4)))
	15.1b	(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (pow.f64 (fma.f64 841/108 x 4/29) 3/4))
✓	0.1b	(fma.f64 841/108 x 4/29)
✓	15.2b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 841/108 x 4/29))))
	21.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 841/108 x 4/29) (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)))

Compiler

Compiled 6357 to 5474 computations (13.9% saved)

regimes332.0ms (12.9%)

Accuracy

Total 0.0b remaining (31.1%)

Threshold costs 0.0b (31.1%)

Counts

79 → 1

Compiler

Compiled 4931 to 4295 computations (12.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end102.0ms (4%)

Compiler: Compiled 113 to 96 computations (15% saved)

Details

analyze7.0ms (0.3%)

sample782.0ms (30.4%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite1.0ms (0%)

simplify112.0ms (4.4%)

prune10.0ms (0.4%)

localize4.0ms (0.2%)

series13.0ms (0.5%)

rewrite9.0ms (0.3%)

simplify94.0ms (3.7%)

prune96.0ms (3.8%)

localize8.0ms (0.3%)

series27.0ms (1.1%)

rewrite29.0ms (1.1%)

simplify162.0ms (6.3%)

prune400.0ms (15.6%)

localize7.0ms (0.3%)

series7.0ms (0.3%)

rewrite27.0ms (1%)

simplify126.0ms (4.9%)

prune201.0ms (7.8%)

regimes332.0ms (12.9%)

simplify2.0ms (0.1%)

end102.0ms (4%)

Profiling