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 (19%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify101.0ms (1.2%)

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

prune5.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.8b	(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))))
▶	0.4b	(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

0.8b

(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))))

▶

0.4b

(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)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
✓	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)))))
✓	0.2b	(.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)))
✓	1.0b	(sqrt.f64 (PI.f64))

series104.0ms (1.3%)

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)))))
23.0ms	(.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)))
6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 (PI.f64))

rewrite131.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`add-exp-log_binary64`
119×	`prod-exp_binary64`
94×	`add-cbrt-cube_binary64`
61×	`cbrt-unprod_binary64`
61×	`pow1_binary64`

Counts

4 → 189

Calls

4 calls:

58.0ms	(.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)))
23.0ms	(.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)))))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 (PI.f64))

simplify205.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

569×	`associate-l_binary64`
506×	`unswap-sqr_binary64`
301×	`fma-neg_binary64`
258×	`cancel-sign-sub-inv_binary64`
229×	`*-commutative_binary64`

Counts

225 → 248

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	327	8444
1	925	6457
2	2894	5410
3	4967	5400
4	4943	5400

prune468.0ms (5.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	333	3	336
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	334	4	338

Error

Counts

338 → 4

Alt Table

Status	Error	Program
▶	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 (pow.f64 x 6)) (fabs.f64 x)))))
	0.8b	(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))))
	0.5b	(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))))))
	40.4b	(fabs.f64 (cbrt.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 1 (sqrt.f64 (PI.f64)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (.f64 (.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)))) (+.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))))) (+.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 26943 to 10015 computations (62.8% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
	0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
✓	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 (pow.f64 x 6)) (fabs.f64 x))))
	1.0b	(sqrt.f64 (PI.f64))

series67.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

48.0ms

(*.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 (pow.f64 x 6)) (fabs.f64 x))))

19.0ms

(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))

rewrite60.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-exp-log_binary64`
64×	`prod-exp_binary64`
52×	`add-cbrt-cube_binary64`
35×	`associate-l_binary64`
35×	`add-sqr-sqrt_binary64`

Counts

2 → 114

Calls

2 calls:

23.0ms

(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))

15.0ms

(*.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 (pow.f64 x 6)) (fabs.f64 x))))

simplify146.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-neg_binary64`
326×	`associate-l_binary64`
325×	`associate-r_binary64`
314×	`associate-+l+_binary64`
314×	`unswap-sqr_binary64`

Counts

138 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	5968
1	544	4855
2	2254	3940
3	4936	3940
4	5341	3940

prune441.0ms (5.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	266	3	269
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	269	4	273

Error

Counts

273 → 4

Alt Table

Status	Error	Program
▶	0.4b	(fabs.f64 (+.f64 (.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 5))) (+.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))) (+.f64 (.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 3))) (.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 (fabs.f64 x) (pow.f64 x 6))))))))
	0.5b	(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x))))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x))))))
	0.8b	(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 (/.f64 1/21 (sqrt.f64 (PI.f64))) (pow.f64 (fabs.f64 x) 7))))
✓	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 (pow.f64 x 6)) (fabs.f64 x)))))

Compiler

Compiled 16059 to 7761 computations (51.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 3))
✓	0.1b	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
✓	0.1b	(.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 3)))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (.f64 (fabs.f64 x) (pow.f64 x 6)))

series60.0ms (0.7%)

Counts

4 → 0

Calls

4 calls:

22.0ms	(.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 3)))
17.0ms	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 3))
13.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (.f64 (fabs.f64 x) (pow.f64 x 6)))
8.0ms	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))

rewrite53.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`add-sqr-sqrt_binary64`
72×	`sqrt-prod_binary64`
51×	`times-frac_binary64`
51×	`associate-l_binary64`
48×	`*-un-lft-identity_binary64`

Counts

4 → 192

Calls

4 calls:

12.0ms	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 3))
8.0ms	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))
8.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (.f64 (fabs.f64 x) (pow.f64 x 6)))
8.0ms	(.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 3)))

simplify164.0ms (2%)

Algorithm

1×	egg-herbie

Rules

741×	`associate-/l*_binary64`
404×	`fma-def_binary64`
359×	`associate-r_binary64`
337×	`associate-l_binary64`
317×	`associate-/r*_binary64`

Counts

192 → 254

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	4193
1	387	3984
2	1404	3402
3	1887	3402
4	4679	3402
5	4974	3402
6	4959	3402

prune497.0ms (6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	254	0	254
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	254	4	258

Error

Counts

258 → 4

Alt Table

Status	Error	Program
✓	0.4b	(fabs.f64 (+.f64 (.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 5))) (+.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))) (+.f64 (.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 3))) (.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 (fabs.f64 x) (pow.f64 x 6))))))))
▶	0.5b	(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x))))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x))))))
	0.8b	(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 (/.f64 1/21 (sqrt.f64 (PI.f64))) (pow.f64 (fabs.f64 x) 7))))
✓	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 (pow.f64 x 6)) (fabs.f64 x)))))

Compiler

Compiled 14367 to 10433 computations (27.4% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x)))))
✓	0.3b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x))))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x)))))
	1.0b	(sqrt.f64 (PI.f64))

series176.0ms (2.1%)

Counts

2 → 24

Calls

2 calls:

125.0ms

(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x)))))

51.0ms

(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x))))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x)))))

rewrite87.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
28×	`sqrt-div_binary64`
26×	`times-frac_binary64`
26×	`add-exp-log_binary64`
24×	`sqrt-prod_binary64`

Counts

2 → 104

Calls

2 calls:

30.0ms

(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x))))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x)))))

19.0ms

(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x)))))

simplify228.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

921×	`times-frac_binary64`
298×	`associate-r_binary64`
298×	`associate-l_binary64`
272×	`fma-def_binary64`
217×	`*-commutative_binary64`

Counts

128 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	13024
1	915	10674
2	3390	9848
3	4968	9848

prune748.0ms (9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	371	0	371
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	371	4	375

Error

Counts

375 → 4

Alt Table

Status	Error	Program
✓	0.4b	(fabs.f64 (+.f64 (.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 5))) (+.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x))) (+.f64 (.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 3))) (.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 (fabs.f64 x) (pow.f64 x 6))))))))
✓	0.5b	(fabs.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x))))) (sqrt.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 (pow.f64 x 6)) (fabs.f64 x))))))
	0.8b	(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 (/.f64 1/21 (sqrt.f64 (PI.f64))) (pow.f64 (fabs.f64 x) 7))))
✓	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 (pow.f64 x 6)) (fabs.f64 x)))))

Compiler

Compiled 44018 to 20893 computations (52.5% saved)

regimes2.7s (33%)

Accuracy

Total 0.1b remaining (90.4%)

Threshold costs 0.1b (90.4%)

Counts

266 → 1

Compiler

Compiled 101557 to 56680 computations (44.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`fabs-mul_binary64`
1×	`fabs-div_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	47
1	32	47
2	36	47
3	34	47

end154.0ms (1.9%)

Compiler: Compiled 294 to 187 computations (36.4% saved)

Details

analyze5.0ms (0.1%)

sample1.6s (19%)

simplify101.0ms (1.2%)

prune5.0ms (0.1%)

localize22.0ms (0.3%)

series104.0ms (1.3%)

rewrite131.0ms (1.6%)

simplify205.0ms (2.5%)

prune468.0ms (5.6%)

localize21.0ms (0.3%)

series67.0ms (0.8%)

rewrite60.0ms (0.7%)

simplify146.0ms (1.8%)

prune441.0ms (5.3%)

localize20.0ms (0.2%)

series60.0ms (0.7%)

rewrite53.0ms (0.6%)

simplify164.0ms (2%)

prune497.0ms (6%)

localize25.0ms (0.3%)

series176.0ms (2.1%)

rewrite87.0ms (1%)

simplify228.0ms (2.7%)

prune748.0ms (9%)

regimes2.7s (33%)

simplify2.0ms (0%)

end154.0ms (1.9%)

Profiling