Details

analyze122.0ms (1.6%)

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)

sample48.0ms (0.6%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify111.0ms (1.5%)

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 → 1

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

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 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)))
▶	0.2b	(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)))

▶

0.2b

(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 205 to 119 computations (42% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

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 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 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite297.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

119×	`add-exp-log_binary64`
76×	`prod-exp_binary64`
75×	`add-cbrt-cube_binary64`
48×	`associate-l_binary64`
46×	`add-sqr-sqrt_binary64`

Counts

4 → 177

Calls

4 calls:

25.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
24.0ms	(.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)))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 14265 to 4867 computations (65.9% saved)

series67.0ms (0.9%)

Error

0.0b

Counts

4 → 9

Calls

4 calls:

37.0ms	(.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 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
11.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1079 to 618 computations (42.7% saved)

simplify174.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

565×	`associate-r_binary64`
472×	`associate-l_binary64`
379×	`unswap-sqr_binary64`
325×	`fma-neg_binary64`
225×	`*-commutative_binary64`

Counts

186 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	327	7452
1	926	5938
2	3695	4999
3	5013	4999

prune144.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	158	4	162

Error

Counts

162 → 4

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)))
✓	0.2b	(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))))))
	1.6b	(fabs.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (cbrt.f64 (/.f64 1 (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))))) (cbrt.f64 (/.f64 1 (sqrt.f64 PI.f64))))))
	0.6b	(fabs.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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))))))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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)))))))))

Compiler

Compiled 6372 to 3133 computations (50.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
0.1b	(*.f64 2/3 (pow.f64 x 3))
0.3b	(/.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))
1.0b	(sqrt.f64 PI.f64)

rewrite118.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
15×	`sqrt-prod_binary64`

Counts

4 → 99

Calls

4 calls:

5.0ms	(*.f64 2/3 (pow.f64 x 3))
3.0ms	(/.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))
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))

Compiler

Compiled 2885 to 2116 computations (26.7% saved)

series65.0ms (0.9%)

Error

Counts

4 → 24

Calls

4 calls:

22.0ms	(/.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))
21.0ms	(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
8.0ms	(*.f64 2/3 (pow.f64 x 3))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1001 to 830 computations (17.1% saved)

simplify151.0ms (2%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-l_binary64`
610×	`associate-r_binary64`
285×	`log-prod_binary64`
262×	`fma-def_binary64`
184×	`swap-sqr_binary64`

Counts

123 → 58

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	3403
1	310	3199
2	801	3085
3	3443	3085
4	4859	3085
5	4883	3085

prune45.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	58	4	62

Error

Counts

62 → 4

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)))
✓	0.2b	(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))))))
	1.6b	(fabs.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (cbrt.f64 (/.f64 1 (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))))) (cbrt.f64 (/.f64 1 (sqrt.f64 PI.f64))))))
▶	0.6b	(fabs.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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))))))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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)))))))))

Compiler

Compiled 1296 to 936 computations (27.8% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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)))))))
0.5b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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))))))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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))))))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite274.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

228×	`add-sqr-sqrt_binary64`
148×	`rem-sqrt-square_binary64`
98×	`mul-fabs_binary64`
90×	`sqrt-prod_binary64`
86×	`times-frac_binary64`

Counts

4 → 178

Calls

4 calls:

18.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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))))))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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))))))))
13.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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)))))))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 8658 to 5776 computations (33.3% saved)

series99.0ms (1.3%)

Error

Counts

4 → 6

Calls

4 calls:

56.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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)))))))
37.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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))))))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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))))))))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 765 to 574 computations (25% saved)

simplify289.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

639×	`sqr-pow_binary64`
401×	`*-commutative_binary64`
372×	`fma-def_binary64`
331×	`associate-/l/_binary64`
311×	`associate-/r*_binary64`

Counts

184 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	6978
1	262	6417
2	886	6315
3	1736	5925
4	2805	5925
5	3382	5925
6	4108	5925
7	4994	5925

prune118.0ms (1.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	145	4	149

Error

Counts

149 → 4

Alt Table

Status	Error	Program
▶	0.7b	(fabs.f64 (.f64 (/.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 PI.f64)) (sqrt.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))))))))
✓	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)))
✓	0.2b	(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))))))
✓	0.6b	(fabs.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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))))))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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)))))))))

Compiler

Compiled 4059 to 2596 computations (36% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.4b	(/.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 PI.f64))
0.4b	(.f64 (/.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 PI.f64)) (sqrt.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)))))))
1.0b	(sqrt.f64 PI.f64)

rewrite351.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

108×	`add-sqr-sqrt_binary64`
97×	`sqrt-prod_binary64`
80×	`times-frac_binary64`
64×	`*-un-lft-identity_binary64`
64×	`add-cube-cbrt_binary64`

Counts

4 → 186

Calls

4 calls:

13.0ms	(.f64 (/.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 PI.f64)) (sqrt.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)))))))
6.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
4.0ms	(/.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 PI.f64))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 10325 to 6401 computations (38% saved)

series385.0ms (5.1%)

Error

Counts

4 → 15

Calls

4 calls:

270.0ms	(.f64 (/.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 PI.f64)) (sqrt.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)))))))
41.0ms	(/.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 PI.f64))
14.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 7267 to 5196 computations (28.5% saved)

simplify341.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

524×	`times-frac_binary64`
430×	`unswap-sqr_binary64`
377×	`associate-r_binary64`
364×	`associate-l_binary64`
315×	`*-commutative_binary64`

Counts

201 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	427	15899
1	1040	13192
2	3408	10323
3	4402	9959
4	4957	9959

prune264.0ms (3.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	181	4	185

Error

Counts

185 → 4

Alt Table

Status	Error	Program
	0.7b	(fabs.f64 (.f64 (/.f64 (sqrt.f64 (fma.f64 1/21 (pow.f64 (fabs.f64 x) 7) (fma.f64 (fabs.f64 x) (fma.f64 2/3 (.f64 x x) 2) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 PI.f64)) (sqrt.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))))))))
	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)))
	0.2b	(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))))))
	0.6b	(fabs.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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))))))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (sqrt.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)))))))))

Compiler

Compiled 8347 to 5900 computations (29.3% saved)

regimes2.4s (31.9%)

Accuracy

Total 0.1b remaining (86.9%)

Threshold costs 0.1b (86.9%)

Compiler

Compiled 58952 to 39642 computations (32.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	69
1	41	69
2	40	69

end1.0ms (0%)

Compiler: Compiled 43 to 36 computations (16.3% saved)

sample1.6s (20.9%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
111.0ms	8001×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 318 to 200 computations (37.1% saved)

Details

analyze122.0ms (1.6%)

sample48.0ms (0.6%)

simplify111.0ms (1.5%)

prune5.0ms (0.1%)

localize26.0ms (0.3%)

rewrite297.0ms (3.9%)

series67.0ms (0.9%)

simplify174.0ms (2.3%)

prune144.0ms (1.9%)

localize15.0ms (0.2%)

rewrite118.0ms (1.6%)

series65.0ms (0.9%)

simplify151.0ms (2%)

prune45.0ms (0.6%)

localize23.0ms (0.3%)

rewrite274.0ms (3.6%)

series99.0ms (1.3%)

simplify289.0ms (3.8%)

prune118.0ms (1.6%)

localize25.0ms (0.3%)

rewrite351.0ms (4.7%)

series385.0ms (5.1%)

simplify341.0ms (4.5%)

prune264.0ms (3.5%)

regimes2.4s (31.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.6s (20.9%)

Profiling