Details

analyze46.0ms (1.4%)

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)

sample23.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 22 to 20 computations (9.1% saved)

simplify14.0ms (0.4%)

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

prune5.0ms (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)

localize5.0ms (0.2%)

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)

simplify147.0ms (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

prune20.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Error

0.0b

Counts

16 → 4

Alt Table

Status	Error	Program
	15.0b	(*.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)
▶	1.8b	(.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)))
	19.9b	(cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))

Compiler

Compiled 186 to 154 computations (17.2% saved)

localize12.0ms (0.4%)

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)))
✓	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))

series28.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

15.0ms

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

10.0ms

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

3.0ms

(*.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 (0.6%)

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)))

6.0ms

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

2.0ms

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

simplify204.0ms (6.1%)

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

prune554.0ms (16.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	319	5	324
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	321	7	328

Error

0.0b

Counts

328 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)
	16.1b	(.f64 (cbrt.f64 (.f64 (fma.f64 841/108 x 4/29) (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	19.9b	(cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))
	1.8b	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)
▶	1.0b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	34.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (/.f64 -841/108 (/.f64 -1 x))))
	16.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))))

Compiler

Compiled 8169 to 6890 computations (15.7% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))
	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))
✓	0.8b	(cbrt.f64 (fma.f64 x 841/108 4/29))
✓	1.0b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5)

series53.0ms (1.6%)

Counts

3 → 36

Calls

3 calls:

32.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5)
11.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))
10.0ms	(cbrt.f64 (fma.f64 x 841/108 4/29))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 55

Calls

3 calls:

6.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5)
2.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))
1.0ms	(cbrt.f64 (fma.f64 x 841/108 4/29))

simplify168.0ms (5%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary64`
429×	`associate-r_binary64`
424×	`associate-l_binary64`
390×	`fma-neg_binary64`
216×	`times-frac_binary64`

Counts

91 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	225	2442
1	551	2323
2	1470	2033
3	4852	2033
4	5082	2033

prune418.0ms (12.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	238	7	245

Error

0.0b

Counts

245 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)
	16.1b	(.f64 (cbrt.f64 (.f64 (fma.f64 841/108 x 4/29) (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	19.9b	(cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))
▶	1.8b	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)
✓	1.0b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 841/108 4/29))) 5) (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	34.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (/.f64 -841/108 (/.f64 -1 x))))
	16.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))) (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)))))

Compiler

Compiled 8126 to 7016 computations (13.7% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 841/108 x 4/29)
	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))
✓	0.8b	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)

series258.0ms (7.7%)

Counts

1 → 12

Calls

1 calls:

258.0ms

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

rewrite6.0ms (0.2%)

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:

4.0ms

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

simplify99.0ms (3%)

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

prune126.0ms (3.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	3	1	4
Picked	0	1	1
Done	1	1	2
Total	116	5	121

Error

Counts

121 → 5

Alt Table

Status	Error	Program
	19.9b	(cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))
	0.1b	(+.f64 (.f64 24389/432 (.f64 (pow.f64 64/24389 1/3) x)) (pow.f64 64/24389 1/3))
✓	0.1b	(fma.f64 841/108 x 4/29)
	34.6b	(/.f64 -841/108 (/.f64 -1 x))
✓	1.8b	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)

Compiler

Compiled 1653 to 1440 computations (12.9% saved)

regimes288.0ms (8.6%)

Accuracy

Total 0.1b remaining (79.2%)

Threshold costs 0.1b (79.2%)

Counts

41 → 1

Compiler

Compiled 2185 to 1858 computations (15% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end1.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

sample798.0ms (23.9%)

Algorithm

1×

intervals

Results

455.0ms	7998×	body	128	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 56 to 49 computations (12.5% saved)

Details

analyze46.0ms (1.4%)

sample23.0ms (0.7%)

simplify14.0ms (0.4%)

prune5.0ms (0.1%)

localize5.0ms (0.2%)

series2.0ms (0.1%)

rewrite1.0ms (0%)

simplify147.0ms (4.4%)

prune20.0ms (0.6%)

localize12.0ms (0.4%)

series28.0ms (0.8%)

rewrite22.0ms (0.6%)

simplify204.0ms (6.1%)

prune554.0ms (16.6%)

localize16.0ms (0.5%)

series53.0ms (1.6%)

rewrite14.0ms (0.4%)

simplify168.0ms (5%)

prune418.0ms (12.5%)

localize10.0ms (0.3%)

series258.0ms (7.7%)

rewrite6.0ms (0.2%)

simplify99.0ms (3%)

prune126.0ms (3.8%)

regimes288.0ms (8.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample798.0ms (23.9%)

Profiling