Details

analyze8.0ms (0.2%)

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)

sample153.0ms (3.2%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify104.0ms (2.2%)

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

0.0b

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))))
▶	0.2b	(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 272 to 147 computations (46% saved)

localize25.0ms (0.5%)

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

series129.0ms (2.7%)

Counts

4 → 36

Calls

4 calls:

78.0ms	(.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)))))
40.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
10.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 (PI.f64))

rewrite108.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

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:

33.0ms	(.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)))))
27.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
10.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0ms	(sqrt.f64 (PI.f64))

simplify171.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

562×	`associate-r_binary64`
468×	`associate-l_binary64`
379×	`unswap-sqr_binary64`
325×	`fma-neg_binary64`
225×	`*-commutative_binary64`

Counts

213 → 251

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	7992
1	926	6478
2	3695	5539
3	5013	5539

prune325.0ms (6.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	248	3	251
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	249	4	253

Error

Counts

253 → 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))))
	0.8b	(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)))))))))
▶	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.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)))))))
	0.4b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))) (.f64 (/.f64 1 (sqrt.f64 (cbrt.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 20708 to 8025 computations (61.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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)))))
✓	0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
✓	0.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.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))))))
✓	0.1b	(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))

series181.0ms (3.8%)

Counts

4 → 36

Calls

4 calls:

81.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.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))))))
53.0ms	(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)))))
29.0ms	(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
18.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
19×	`associate-l_binary64`
18×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
16×	`sqrt-prod_binary64`

Counts

4 → 92

Calls

4 calls:

7.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
6.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.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	(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
0.0ms	(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)))))

simplify123.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

618×	`distribute-rgt-in_binary64`
617×	`distribute-lft-in_binary64`
600×	`associate-+l+_binary64`
529×	`associate-l_binary64`
453×	`associate-r_binary64`

Counts

128 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	4283
1	265	4015
2	813	4003
3	3517	4003
4	5634	4003

prune187.0ms (3.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	114	4	118

Error

Counts

118 → 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))))
	0.8b	(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)))))))))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.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)))))))
▶	0.4b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))) (.f64 (/.f64 1 (sqrt.f64 (cbrt.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 4709 to 3236 computations (31.3% saved)

localize29.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(cbrt.f64 (PI.f64))
✓	1.0b	(sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))
✓	1.0b	(*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))
✓	1.0b	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))))

series0.0ms (0%)

Counts

4 → 0

Calls

4 calls:

0.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))))
0.0ms	(*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))
0.0ms	(sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))
0.0ms	(cbrt.f64 (PI.f64))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
28×	`pow1_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
19×	`cbrt-prod_binary64`

Counts

4 → 123

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))
5.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))))
3.0ms	(sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))
1.0ms	(cbrt.f64 (PI.f64))

simplify137.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

842×	`fma-neg_binary64`
489×	`unswap-sqr_binary64`
441×	`sqr-pow_binary64`
324×	`times-frac_binary64`
305×	`*-commutative_binary64`

Counts

123 → 158

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	94	1266
1	128	1018
2	229	988
3	558	972
4	1611	817
5	2431	817
6	3276	817
7	4645	809
8	4869	809
9	4785	809

prune299.0ms (6.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	182	4	186

Error

Counts

186 → 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))))
	0.8b	(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)))))))))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.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)))))))
✓	0.4b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))) (.f64 (/.f64 1 (sqrt.f64 (cbrt.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 15006 to 5138 computations (65.8% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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))

series43.0ms (0.9%)

Counts

3 → 24

Calls

3 calls:

31.0ms

(*.f64 2/3 (pow.f64 x 3))

8.0ms

(/.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)))

4.0ms

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

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
12×	`associate-r_binary64`

Counts

3 → 84

Calls

3 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)))

0.0ms

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

simplify136.0ms (2.8%)

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

108 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	3342
1	305	3139
2	796	3025
3	3438	3025
4	4851	3025
5	4876	3025

prune163.0ms (3.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	131	4	135

Error

Counts

135 → 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))))
	0.8b	(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)))))))))
✓	0.1b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.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)))))))
✓	0.4b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))))) (.f64 (/.f64 1 (sqrt.f64 (cbrt.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 4255 to 3107 computations (27% saved)

regimes721.0ms (15.1%)

Accuracy

Total 0.1b remaining (83.4%)

Threshold costs 0.1b (83.4%)

Counts

68 → 1

Compiler

Compiled 24065 to 13333 computations (44.6% saved)

simplify3.0ms (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 (34.4%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
148.0ms	8000×	pre	128	true

Compiler

Compiled 306 to 192 computations (37.3% saved)

Details

analyze8.0ms (0.2%)

sample153.0ms (3.2%)

simplify104.0ms (2.2%)

prune5.0ms (0.1%)

localize25.0ms (0.5%)

series129.0ms (2.7%)

rewrite108.0ms (2.3%)

simplify171.0ms (3.6%)

prune325.0ms (6.8%)

localize15.0ms (0.3%)

series181.0ms (3.8%)

rewrite20.0ms (0.4%)

simplify123.0ms (2.6%)

prune187.0ms (3.9%)

localize29.0ms (0.6%)

series0.0ms (0%)

rewrite21.0ms (0.4%)

simplify137.0ms (2.9%)

prune299.0ms (6.2%)

localize13.0ms (0.3%)

series43.0ms (0.9%)

rewrite13.0ms (0.3%)

simplify136.0ms (2.8%)

prune163.0ms (3.4%)

regimes721.0ms (15.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.6s (34.4%)

Profiling