Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 71 to 33 computations (53.5% saved)

sample1.6s (27.2%)

Results

1.5s	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify101.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1509×	`associate-/l*_binary64`
766×	`distribute-rgt-out_binary64`
744×	`distribute-lft-out_binary64`
549×	`unswap-sqr_binary64`
497×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	32	75
1	74	59
2	239	41
3	928	37
4	1549	37
5	3195	37
6	3534	37
7	3698	33
8	2289	33
9	2775	33
10	2823	33
11	4807	33
12	5324	33

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
▶	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Status

Error

Program

0.5b

(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))

▶

0.1b

(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 272 to 147 computations (46% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
✓	0.1b	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
✓	0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
✓	1.0b	(sqrt.f64 (PI.f64))

series92.0ms (1.5%)

Counts

4 → 36

Calls

4 calls:

74.0ms	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
9.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
8.0ms	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 (PI.f64))

rewrite70.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`pow1_binary64`
43×	`add-exp-log_binary64`
42×	`add-sqr-sqrt_binary64`
39×	`add-cbrt-cube_binary64`
36×	`associate-l_binary64`

Counts

4 → 163

Calls

4 calls:

21.0ms	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
12.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
9.0ms	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 (PI.f64))

simplify211.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

559×	`associate-r_binary64`
501×	`associate-l_binary64`
392×	`fma-neg_binary64`
291×	`unswap-sqr_binary64`
219×	`*-commutative_binary64`

Counts

199 → 222

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	294	7365
1	889	5784
2	3698	4992
3	4903	4984
4	4999	4984
5	4866	4984

prune339.0ms (5.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	265	3	268
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	266	4	270

Error

Counts

270 → 4

Alt Table

Status	Error	Program
	0.2b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (PI.f64)))) (/.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) 2 (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (sqrt.f64 (PI.f64))))))
▶	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	28.3b	(fabs.f64 (/.f64 (.f64 1 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 (.f64 2 (fabs.f64 x)) (.f64 2 (fabs.f64 x))) (.f64 (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))))) 5) (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 1 (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) 21) (.f64 (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) 5) (.f64 1 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))) (.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) 5) 21))))
	0.5b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))

Compiler

Compiled 21717 to 8448 computations (61.1% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
	0.1b	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
	0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
	1.0b	(sqrt.f64 (PI.f64))

series56.0ms (0.9%)

Counts

1 → 12

Calls

1 calls:

56.0ms

(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`associate-l_binary64`
22×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

1 → 62

Calls

1 calls:

18.0ms

(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))

simplify148.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-neg_binary64`
399×	`associate-r_binary64`
362×	`associate-l_binary64`
356×	`cancel-sign-sub-inv_binary64`
245×	`distribute-rgt-neg-in_binary64`

Counts

74 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	6212
1	714	4837
2	2964	4177
3	4528	4149
4	4917	4149

prune365.0ms (6.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	224	3	227
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	227	4	231

Error

Counts

231 → 4

Alt Table

Status	Error	Program
	28.6b	(fabs.f64 (/.f64 (fma.f64 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 (pow.f64 (fabs.f64 x) 5) -1/5))) (.f64 21 (fma.f64 (.f64 x x) (.f64 (+.f64 2 (.f64 2/3 (.f64 x x))) (+.f64 2 (.f64 2/3 (.f64 x x)))) (.f64 (.f64 (pow.f64 x 4) (pow.f64 x 6)) -1/25)))) (.f64 (sqrt.f64 (PI.f64)) (.f64 21 (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 (pow.f64 (fabs.f64 x) 5) -1/5)))))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	0.5b	(fabs.f64 (+.f64 (/.f64 (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (sqrt.f64 (PI.f64))) (.f64 (pow.f64 (fabs.f64 x) 7) (/.f64 1/21 (sqrt.f64 (PI.f64))))))
▶	0.1b	(fabs.f64 (fma.f64 1/5 (.f64 (pow.f64 (fabs.f64 x) 5) (sqrt.f64 (/.f64 1 (PI.f64)))) (fma.f64 2 (.f64 (fabs.f64 x) (sqrt.f64 (/.f64 1 (PI.f64)))) (fma.f64 2/3 (.f64 (pow.f64 (fabs.f64 x) 3) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/21 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 7)))))))

Compiler

Compiled 16822 to 8339 computations (50.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 7)))
✓	0.1b	(*.f64 (pow.f64 (fabs.f64 x) 3) (sqrt.f64 (/.f64 1 (PI.f64))))
✓	0.1b	(*.f64 (fabs.f64 x) (sqrt.f64 (/.f64 1 (PI.f64))))
✓	0.2b	(fma.f64 2/3 (.f64 (pow.f64 (fabs.f64 x) 3) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/21 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 7))))

series109.0ms (1.8%)

Counts

4 → 36

Calls

4 calls:

52.0ms	(fma.f64 2/3 (.f64 (pow.f64 (fabs.f64 x) 3) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/21 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 7))))
30.0ms	(.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 7)))
16.0ms	(*.f64 (pow.f64 (fabs.f64 x) 3) (sqrt.f64 (/.f64 1 (PI.f64))))
10.0ms	(*.f64 (fabs.f64 x) (sqrt.f64 (/.f64 1 (PI.f64))))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`add-sqr-sqrt_binary64`
59×	`sqrt-prod_binary64`
44×	`unswap-sqr_binary64`
42×	`times-frac_binary64`
40×	`*-un-lft-identity_binary64`

Counts

4 → 167

Calls

4 calls:

15.0ms	(*.f64 (pow.f64 (fabs.f64 x) 3) (sqrt.f64 (/.f64 1 (PI.f64))))
8.0ms	(*.f64 (fabs.f64 x) (sqrt.f64 (/.f64 1 (PI.f64))))
7.0ms	(.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 7)))
0.0ms	(fma.f64 2/3 (.f64 (pow.f64 (fabs.f64 x) 3) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/21 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 7))))

simplify156.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary64`
466×	`unswap-sqr_binary64`
465×	`associate-/l*_binary64`
292×	`log-prod_binary64`
270×	`associate-l_binary64`

Counts

203 → 218

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	179	4628
1	359	4460
2	1285	3780
3	1998	3592
4	4558	3592
5	5049	3592

prune386.0ms (6.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	218	4	222

Error

Counts

222 → 4

Alt Table

Status	Error	Program
	28.6b	(fabs.f64 (/.f64 (fma.f64 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 (pow.f64 (fabs.f64 x) 5) -1/5))) (.f64 21 (fma.f64 (.f64 x x) (.f64 (+.f64 2 (.f64 2/3 (.f64 x x))) (+.f64 2 (.f64 2/3 (.f64 x x)))) (.f64 (.f64 (pow.f64 x 4) (pow.f64 x 6)) -1/25)))) (.f64 (sqrt.f64 (PI.f64)) (.f64 21 (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 (pow.f64 (fabs.f64 x) 5) -1/5)))))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
▶	0.5b	(fabs.f64 (+.f64 (/.f64 (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (sqrt.f64 (PI.f64))) (.f64 (pow.f64 (fabs.f64 x) 7) (/.f64 1/21 (sqrt.f64 (PI.f64))))))
✓	0.1b	(fabs.f64 (fma.f64 1/5 (.f64 (pow.f64 (fabs.f64 x) 5) (sqrt.f64 (/.f64 1 (PI.f64)))) (fma.f64 2 (.f64 (fabs.f64 x) (sqrt.f64 (/.f64 1 (PI.f64)))) (fma.f64 2/3 (.f64 (pow.f64 (fabs.f64 x) 3) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/21 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 7)))))))

Compiler

Compiled 11221 to 8094 computations (27.9% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
✓	0.3b	(/.f64 (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (sqrt.f64 (PI.f64)))
	1.0b	(sqrt.f64 (PI.f64))
✓	1.0b	(/.f64 1/21 (sqrt.f64 (PI.f64)))

series75.0ms (1.3%)

Counts

3 → 24

Calls

3 calls:

51.0ms

(/.f64 (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (sqrt.f64 (PI.f64)))

24.0ms

(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))

0.0ms

(/.f64 1/21 (sqrt.f64 (PI.f64)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
24×	`sqrt-prod_binary64`

Counts

3 → 92

Calls

3 calls:

3.0ms

(/.f64 1/21 (sqrt.f64 (PI.f64)))

3.0ms

(/.f64 (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (sqrt.f64 (PI.f64)))

0.0ms

(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))

simplify118.0ms (2%)

Algorithm

1×	egg-herbie

Rules

849×	`distribute-rgt-in_binary64`
838×	`distribute-lft-in_binary64`
717×	`fma-def_binary64`
233×	`times-frac_binary64`
146×	`fma-neg_binary64`

Counts

116 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	3512
1	222	3323
2	527	3323
3	1482	3181
4	4899	3181
5	4954	3181

prune211.0ms (3.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	154	4	158

Error

Counts

158 → 4

Alt Table

Status	Error	Program
	28.6b	(fabs.f64 (/.f64 (fma.f64 (pow.f64 (fabs.f64 x) 7) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 (pow.f64 (fabs.f64 x) 5) -1/5))) (.f64 21 (fma.f64 (.f64 x x) (.f64 (+.f64 2 (.f64 2/3 (.f64 x x))) (+.f64 2 (.f64 2/3 (.f64 x x)))) (.f64 (.f64 (pow.f64 x 4) (pow.f64 x 6)) -1/25)))) (.f64 (sqrt.f64 (PI.f64)) (.f64 21 (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 (pow.f64 (fabs.f64 x) 5) -1/5)))))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (pow.f64 x 4) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
✓	0.5b	(fabs.f64 (+.f64 (/.f64 (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (.f64 1/5 (pow.f64 (fabs.f64 x) 5)))) (sqrt.f64 (PI.f64))) (.f64 (pow.f64 (fabs.f64 x) 7) (/.f64 1/21 (sqrt.f64 (PI.f64))))))
✓	0.1b	(fabs.f64 (fma.f64 1/5 (.f64 (pow.f64 (fabs.f64 x) 5) (sqrt.f64 (/.f64 1 (PI.f64)))) (fma.f64 2 (.f64 (fabs.f64 x) (sqrt.f64 (/.f64 1 (PI.f64)))) (fma.f64 2/3 (.f64 (pow.f64 (fabs.f64 x) 3) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/21 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 7)))))))

Compiler

Compiled 6356 to 3792 computations (40.3% saved)

regimes1.5s (26%)

Accuracy

Total 0.1b remaining (92%)

Threshold costs 0.1b (92%)

Counts

178 → 1

Compiler

Compiled 47934 to 32533 computations (32.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`fabs-mul_binary64`
1×	`sqr-abs_binary64`
1×	`fabs-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	95
1	59	95
2	63	95
3	58	95

end164.0ms (2.7%)

Compiler: Compiled 328 to 204 computations (37.8% saved)

Details

analyze5.0ms (0.1%)

sample1.6s (27.2%)

simplify101.0ms (1.7%)

prune6.0ms (0.1%)

localize23.0ms (0.4%)

series92.0ms (1.5%)

rewrite70.0ms (1.2%)

simplify211.0ms (3.5%)

prune339.0ms (5.7%)

localize25.0ms (0.4%)

series56.0ms (0.9%)

rewrite36.0ms (0.6%)

simplify148.0ms (2.5%)

prune365.0ms (6.1%)

localize18.0ms (0.3%)

series109.0ms (1.8%)

rewrite44.0ms (0.7%)

simplify156.0ms (2.6%)

prune386.0ms (6.5%)

localize15.0ms (0.3%)

series75.0ms (1.3%)

rewrite13.0ms (0.2%)

simplify118.0ms (2%)

prune211.0ms (3.5%)

regimes1.5s (26%)

simplify3.0ms (0.1%)

end164.0ms (2.7%)

Profiling