Details

analyze4.0ms (0.2%)

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)

sample799.0ms (30%)

Results

748.0ms	8255×	body	128	valid
0.0ms	1×	body	1024	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)

localize2.0ms (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)

simplify115.0ms (4.3%)

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

0.1b

Counts

16 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)
	17.2b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
▶	1.7b	(.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)

localize8.0ms (0.3%)

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)))
✓	0.7b	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.7b	(cbrt.f64 (fma.f64 841/108 x 4/29))

series13.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

6.0ms

(*.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)))

rewrite22.0ms (0.8%)

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:

8.0ms

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

7.0ms

(*.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)))

1.0ms

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

simplify110.0ms (4.1%)

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

prune271.0ms (10.2%)

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 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))) (.f64 (cbrt.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)))
▶	1.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))))
	18.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5) (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
	17.2b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	1.7b	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)
	17.9b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 x 841/108 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 8201 to 6918 computations (15.6% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	0.7b	(cbrt.f64 (fma.f64 841/108 x 4/29))
✓	0.7b	(cbrt.f64 (fma.f64 x 841/108 4/29))
✓	0.8b	(cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6))

series13.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

8.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6))
5.0ms	(cbrt.f64 (fma.f64 x 841/108 4/29))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
9×	`unpow-prod-down_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`

Counts

2 → 36

Calls

2 calls:

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

simplify92.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

525×	`fma-neg_binary64`
396×	`associate-l_binary64`
394×	`fma-def_binary64`
376×	`associate-r_binary64`
164×	`sub-neg_binary64`

Counts

60 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	1761
1	404	1679
2	1055	1361
3	3764	1181
4	4873	1181
5	4919	1181

prune405.0ms (15.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	307	8	315

Error

0.0b

Counts

315 → 8

Alt Table

Status	Error	Program
	1.8b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29)))) (.f64 (cbrt.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)))
✓	1.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))))
	18.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5) (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
	17.2b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
▶	1.7b	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)
	17.4b	(.f64 (cbrt.f64 (.f64 (fma.f64 841/108 x 4/29) (fma.f64 841/108 x 4/29))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))))
	17.9b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) (sqrt.f64 (fma.f64 x 841/108 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 12336 to 10631 computations (13.8% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 841/108 x 4/29)
	0.7b	(cbrt.f64 (fma.f64 841/108 x 4/29))
✓	0.9b	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)

series126.0ms (4.7%)

Counts

1 → 12

Calls

1 calls:

125.0ms

(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

1 → 32

Calls

1 calls:

2.0ms

(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)

simplify67.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

420×	`distribute-rgt-in_binary64`
405×	`distribute-lft-in_binary64`
394×	`associate-l_binary64`
372×	`exp-prod_binary64`
335×	`log-prod_binary64`

Counts

44 → 52

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	686
1	169	621
2	437	607
3	1887	432
4	4631	432
5	4923	432

prune74.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	2	5
Picked	0	1	1
Done	2	0	2
Total	116	6	122

Error

0.0b

Counts

122 → 6

Alt Table

Status	Error	Program
	18.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5) (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))))
	29.9b	(/.f64 -841/108 (/.f64 -1 x))
✓	1.7b	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)
	17.4b	(.f64 (cbrt.f64 (.f64 (fma.f64 841/108 x 4/29) (fma.f64 841/108 x 4/29))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29)))))
	0.2b	(.f64 (+.f64 (/.f64 432/24389 x) 1) (.f64 x 841/108))
	0.1b	(+.f64 (.f64 24389/432 (.f64 (pow.f64 64/24389 1/3) x)) (pow.f64 64/24389 1/3))

Compiler

Compiled 1694 to 1475 computations (12.9% saved)

regimes395.0ms (14.8%)

Accuracy

Total 0.1b remaining (76.8%)

Threshold costs 0.1b (76.8%)

Counts

112 → 1

Compiler

Compiled 6118 to 5227 computations (14.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	5
1	9	5
2	8	5

end99.0ms (3.7%)

Compiler: Compiled 90 to 77 computations (14.4% saved)

Details

analyze4.0ms (0.2%)

sample799.0ms (30%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series2.0ms (0.1%)

rewrite1.0ms (0%)

simplify115.0ms (4.3%)

prune11.0ms (0.4%)

localize8.0ms (0.3%)

series13.0ms (0.5%)

rewrite22.0ms (0.8%)

simplify110.0ms (4.1%)

prune271.0ms (10.2%)

localize13.0ms (0.5%)

series13.0ms (0.5%)

rewrite4.0ms (0.2%)

simplify92.0ms (3.4%)

prune405.0ms (15.2%)

localize5.0ms (0.2%)

series126.0ms (4.7%)

rewrite3.0ms (0.1%)

simplify67.0ms (2.5%)

prune74.0ms (2.8%)

regimes395.0ms (14.8%)

simplify2.0ms (0.1%)

end99.0ms (3.7%)

Profiling