Details

analyze6.0ms (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)

sample1.8s (25.3%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify109.0ms (1.6%)

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

prune7.0ms (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)

localize24.0ms (0.3%)

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 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
✓	0.3b	(.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))

series116.0ms (1.7%)

Counts

4 → 36

Calls

4 calls:

85.0ms	(.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)))))
20.0ms	(.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)))
11.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 (PI.f64))

rewrite164.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

181×	`add-exp-log_binary64`
128×	`prod-exp_binary64`
107×	`add-cbrt-cube_binary64`
70×	`cbrt-unprod_binary64`
51×	`pow1_binary64`

Counts

4 → 191

Calls

4 calls:

75.0ms	(.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)))
29.0ms	(.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)))
1.0ms	(sqrt.f64 (PI.f64))

simplify241.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

589×	`associate-l_binary64`
539×	`unswap-sqr_binary64`
306×	`fma-neg_binary64`
270×	`cancel-sign-sub-inv_binary64`
254×	`*-commutative_binary64`

Counts

227 → 263

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	360	8608
1	985	6724
2	3042	5704
3	4987	5692
4	4951	5692

prune391.0ms (5.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	260	3	263
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	262	3	265

Error

Counts

265 → 3

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 (fabs.f64 x) 6)) (fabs.f64 x)))))
	0.8b	(fabs.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 (PI.f64))))
	1.0b	(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 21662 to 8275 computations (61.8% saved)

localize24.0ms (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 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 (fabs.f64 x) 6)) (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))

series109.0ms (1.6%)

Counts

2 → 24

Calls

2 calls:

92.0ms

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

17.0ms

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

rewrite74.0ms (1.1%)

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:

28.0ms

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

19.0ms

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

simplify171.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-neg_binary64`
377×	`unswap-sqr_binary64`
319×	`associate-l_binary64`
312×	`associate-r_binary64`
267×	`associate-/l*_binary64`

Counts

138 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	5801
1	512	4506
2	2185	3896
3	4570	3892
4	4936	3892

prune352.0ms (5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	235	3	238

Error

Counts

238 → 3

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 (fabs.f64 x) 6)) (fabs.f64 x)))))
▶	0.8b	(fabs.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 (PI.f64))))
	1.0b	(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 14545 to 7000 computations (51.9% saved)

localize16.0ms (0.2%)

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)))
✓	0.2b	(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)))))
✓	0.3b	(/.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 (PI.f64)))
	1.0b	(sqrt.f64 (PI.f64))

series170.0ms (2.4%)

Counts

3 → 36

Calls

3 calls:

84.0ms

(/.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 (PI.f64)))

57.0ms

(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)))))

28.0ms

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

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

4.0ms

(/.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 (PI.f64)))

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)))))

simplify147.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

950×	`fma-def_binary64`
677×	`fma-neg_binary64`
393×	`associate-+l+_binary64`
317×	`associate-*l/_binary64`
292×	`associate-*r/_binary64`

Counts

97 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	4412
1	176	4150
2	476	4150
3	1804	3964
4	4910	3964
5	5431	3964

prune144.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	112	3	115

Error

Counts

115 → 3

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 (fabs.f64 x) 6)) (fabs.f64 x)))))
✓	0.8b	(fabs.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 (PI.f64))))
▶	0.8b	(fabs.f64 (/.f64 1 (/.f64 (sqrt.f64 (PI.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)))))))

Compiler

Compiled 4692 to 2871 computations (38.8% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(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))))
✓	0.3b	(/.f64 (sqrt.f64 (PI.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)))))
✓	0.3b	(/.f64 1 (/.f64 (sqrt.f64 (PI.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))))))
	1.0b	(sqrt.f64 (PI.f64))

series193.0ms (2.8%)

Counts

3 → 36

Calls

3 calls:

110.0ms

(/.f64 (sqrt.f64 (PI.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)))))

54.0ms

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

29.0ms

(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))))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
93×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
93×	`add-cube-cbrt_binary64`
48×	`sqrt-prod_binary64`

Counts

3 → 165

Calls

3 calls:

5.0ms

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

3.0ms

(/.f64 (sqrt.f64 (PI.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)))))

0.0ms

(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))))

simplify233.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

398×	`distribute-rgt-in_binary64`
384×	`distribute-lft-in_binary64`
229×	`cancel-sign-sub-inv_binary64`
225×	`fma-def_binary64`
163×	`*-commutative_binary64`

Counts

201 → 253

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	13488
1	780	12396
2	2666	10336
3	5086	10336

prune379.0ms (5.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	269	3	272

Error

Counts

272 → 3

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 (fabs.f64 x) 6)) (fabs.f64 x)))))
✓	0.8b	(fabs.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 (PI.f64))))
✓	0.8b	(fabs.f64 (/.f64 1 (/.f64 (sqrt.f64 (PI.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)))))))

Compiler

Compiled 13073 to 8386 computations (35.9% saved)

regimes1.9s (27.3%)

Accuracy

Total 0.1b remaining (85.6%)

Threshold costs 0.1b (85.6%)

Counts

212 → 1

Compiler

Compiled 48265 to 32030 computations (33.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-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	32	68
1	50	68
2	54	68
3	51	68

end167.0ms (2.4%)

Compiler: Compiled 194 to 127 computations (34.5% saved)

Details

analyze6.0ms (0.1%)

sample1.8s (25.3%)

simplify109.0ms (1.6%)

prune7.0ms (0.1%)

localize24.0ms (0.3%)

series116.0ms (1.7%)

rewrite164.0ms (2.4%)

simplify241.0ms (3.5%)

prune391.0ms (5.6%)

localize24.0ms (0.3%)

series109.0ms (1.6%)

rewrite74.0ms (1.1%)

simplify171.0ms (2.5%)

prune352.0ms (5%)

localize16.0ms (0.2%)

series170.0ms (2.4%)

rewrite9.0ms (0.1%)

simplify147.0ms (2.1%)

prune144.0ms (2.1%)

localize18.0ms (0.3%)

series193.0ms (2.8%)

rewrite33.0ms (0.5%)

simplify233.0ms (3.3%)

prune379.0ms (5.4%)

regimes1.9s (27.3%)

simplify5.0ms (0.1%)

end167.0ms (2.4%)

Profiling