Details

analyze4.0ms (0.1%)

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)

sample777.0ms (26.1%)

Results

749.0ms	8254×	body	128	valid
0.0ms	1×	body	1024	valid
0.0ms	3×	body	128	invalid
0.0ms	1×	body	256	valid

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

prune2.0ms (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)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(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)

simplify108.0ms (3.6%)

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

prune11.0ms (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

0.0b

Counts

16 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)
	15.4b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
▶	1.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))

Compiler

Compiled 170 to 140 computations (17.6% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 841/108 x 4/29)
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.8b	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))

series13.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

5.0ms

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

5.0ms

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

2.0ms

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

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

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

4.0ms

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

1.0ms

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

simplify112.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

492×	`times-frac_binary64`
423×	`fma-def_binary64`
413×	`fma-neg_binary64`
239×	`unswap-sqr_binary64`
210×	`*-commutative_binary64`

Counts

129 → 185

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	2495
1	418	2285
2	1171	1923
3	3158	1699
4	4947	1699
5	4970	1699

prune262.0ms (8.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	319	5	324
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	320	7	327

Error

0.0b

Counts

327 → 7

Alt Table

Status	Error	Program
	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	17.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (exp.f64 (log.f64 (fma.f64 841/108 x 4/29)))))
✓	0.1b	(fma.f64 841/108 x 4/29)
▶	1.5b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6) (cbrt.f64 (fma.f64 x 841/108 4/29)))
	1.9b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	2.0b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
	15.4b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))

Compiler

Compiled 8209 to 6926 computations (15.6% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6) (cbrt.f64 (fma.f64 x 841/108 4/29)))
✓	0.2b	(cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))
✓	0.6b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6)
✓	0.8b	(cbrt.f64 (fma.f64 x 841/108 4/29))

series35.0ms (1.2%)

Counts

4 → 48

Calls

4 calls:

19.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6)
8.0ms	(cbrt.f64 (fma.f64 x 841/108 4/29))
6.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))
2.0ms	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6) (cbrt.f64 (fma.f64 x 841/108 4/29)))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`cbrt-prod_binary64`
35×	`add-sqr-sqrt_binary64`
24×	`unpow-prod-down_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

4 → 98

Calls

4 calls:

6.0ms	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6) (cbrt.f64 (fma.f64 x 841/108 4/29)))
2.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6)
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))
1.0ms	(cbrt.f64 (fma.f64 x 841/108 4/29))

simplify156.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-def_binary64`
341×	`unswap-sqr_binary64`
248×	`times-frac_binary64`
206×	`associate-/l*_binary64`
204×	`log-prod_binary64`

Counts

146 → 210

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	3316
1	590	3147
2	1798	2668
3	4663	2668
4	4972	2668

prune227.0ms (7.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	247	3	250
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	249	8	257

Error

0.0b

Counts

257 → 8

Alt Table

Status	Error	Program
	17.5b	(*.f64 (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))))) 6) (cbrt.f64 (fma.f64 x 841/108 4/29)))
▶	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
✓	0.1b	(fma.f64 841/108 x 4/29)
✓	1.5b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6) (cbrt.f64 (fma.f64 x 841/108 4/29)))
	1.9b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	2.9b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)) (cbrt.f64 (fma.f64 x 841/108 4/29))))) 6) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 6)) (cbrt.f64 (fma.f64 x 841/108 4/29)))
	15.4b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	50.6b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (+.f64 (log.f64 841/108) (log.f64 x))))) 6) (cbrt.f64 (fma.f64 x 841/108 4/29)))

Compiler

Compiled 6698 to 5808 computations (13.3% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.3b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
	0.8b	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))

series11.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
5.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`

Counts

2 → 72

Calls

2 calls:

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

simplify110.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

531×	`fma-neg_binary64`
406×	`fma-def_binary64`
363×	`associate-l_binary64`
314×	`associate-r_binary64`
295×	`unswap-sqr_binary64`

Counts

96 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	2844
1	406	2644
2	1083	2258
3	3497	2075
4	4959	2075
5	4903	2075

prune649.0ms (21.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	574	2	576
Fresh	0	5	5
Picked	0	1	1
Done	1	1	2
Total	575	9	584

Error

0.0b

Counts

584 → 9

Alt Table

Status	Error	Program
	17.5b	(*.f64 (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))))) 6) (cbrt.f64 (fma.f64 x 841/108 4/29)))
✓	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
✓	0.1b	(fma.f64 841/108 x 4/29)
	1.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 5) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	1.9b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	2.9b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)) (cbrt.f64 (fma.f64 x 841/108 4/29))))) 6) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))) 6)) (cbrt.f64 (fma.f64 x 841/108 4/29)))
	2.3b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))))
	15.4b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	50.6b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (+.f64 (log.f64 841/108) (log.f64 x))))) 6) (cbrt.f64 (fma.f64 x 841/108 4/29)))

Compiler

Compiled 24815 to 21150 computations (14.8% saved)

regimes230.0ms (7.7%)

Accuracy

Total 0.0b remaining (44.6%)

Threshold costs 0.0b (44.6%)

Counts

62 → 1

Compiler

Compiled 4409 to 3785 computations (14.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end188.0ms (6.3%)

Compiler: Compiled 237 to 203 computations (14.3% saved)

Details

analyze4.0ms (0.1%)

sample777.0ms (26.1%)

simplify6.0ms (0.2%)

prune2.0ms (0.1%)

localize2.0ms (0.1%)

series3.0ms (0.1%)

rewrite1.0ms (0%)

simplify108.0ms (3.6%)

prune11.0ms (0.4%)

localize6.0ms (0.2%)

series13.0ms (0.4%)

rewrite16.0ms (0.5%)

simplify112.0ms (3.8%)

prune262.0ms (8.8%)

localize7.0ms (0.2%)

series35.0ms (1.2%)

rewrite14.0ms (0.5%)

simplify156.0ms (5.2%)

prune227.0ms (7.6%)

localize10.0ms (0.4%)

series11.0ms (0.4%)

rewrite13.0ms (0.5%)

simplify110.0ms (3.7%)

prune649.0ms (21.8%)

regimes230.0ms (7.7%)

simplify2.0ms (0.1%)

end188.0ms (6.3%)

Profiling