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)

sample159.0ms (2.7%)

Algorithm

1×

intervals

Results

37.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify102.0ms (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

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)

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 (.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))

series121.0ms (2%)

Counts

4 → 36

Calls

4 calls:

89.0ms	(.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)))))
22.0ms	(.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)))
10.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 (PI.f64))

rewrite159.0ms (2.7%)

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:

77.0ms	(.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)))
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)))))
10.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0ms	(sqrt.f64 (PI.f64))

simplify227.0ms (3.8%)

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

prune397.0ms (6.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	260	3	263
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	261	4	265

Error

Counts

265 → 4

Alt Table

Status	Error	Program
	6.1b	(fabs.f64 (exp.f64 (log.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))))))
▶	0.1b	(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)))))
	0.4b	(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 (pow.f64 (fabs.f64 x) 7) 21))))
	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))))

Compiler

Compiled 21690 to 8287 computations (61.8% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/21 (pow.f64 (fabs.f64 x) 6))
✓	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))

series118.0ms (2%)

Counts

2 → 12

Calls

2 calls:

99.0ms

(*.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))))

19.0ms

(*.f64 1/21 (pow.f64 (fabs.f64 x) 6))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
25×	`associate-l_binary64`
22×	`times-frac_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`

Counts

2 → 87

Calls

2 calls:

22.0ms

(*.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))))

6.0ms

(*.f64 1/21 (pow.f64 (fabs.f64 x) 6))

simplify131.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

863×	`fma-def_binary64`
597×	`fma-neg_binary64`
258×	`associate-+l+_binary64`
210×	`associate-l_binary64`
203×	`associate-r_binary64`

Counts

99 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	4897
1	472	3911
2	1868	3324
3	4571	3324
4	4963	3324

prune362.0ms (6.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	204	4	208

Error

Counts

208 → 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 (fabs.f64 x) 6)) (fabs.f64 x)))))
▶	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 (pow.f64 (fabs.f64 x) 7) 21))))
	0.8b	(fabs.f64 (/.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))))
	6.1b	(fabs.f64 (exp.f64 (log.f64 (/.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))))))

Compiler

Compiled 12736 to 6056 computations (52.4% saved)

localize24.0ms (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 (pow.f64 (fabs.f64 x) 7) 21)))
	0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
✓	0.3b	(/.f64 (pow.f64 (fabs.f64 x) 7) 21)
	1.0b	(sqrt.f64 (PI.f64))

series160.0ms (2.7%)

Counts

2 → 24

Calls

2 calls:

116.0ms

(*.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 (pow.f64 (fabs.f64 x) 7) 21)))

44.0ms

(/.f64 (pow.f64 (fabs.f64 x) 7) 21)

rewrite60.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
55×	`times-frac_binary64`
44×	`*-un-lft-identity_binary64`
40×	`add-cube-cbrt_binary64`
28×	`unpow-prod-down_binary64`

Counts

2 → 126

Calls

2 calls:

26.0ms

(*.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 (pow.f64 (fabs.f64 x) 7) 21)))

6.0ms

(/.f64 (pow.f64 (fabs.f64 x) 7) 21)

simplify212.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

526×	`fma-neg_binary64`
288×	`associate-r_binary64`
265×	`cancel-sign-sub-inv_binary64`
257×	`associate-l_binary64`
190×	`distribute-rgt-in_binary64`

Counts

150 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	283	6505
1	806	5823
2	2996	5283
3	4536	5277
4	4986	5277
5	4923	5277

prune414.0ms (6.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	255	4	259

Error

Counts

259 → 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 (fabs.f64 x) 6)) (fabs.f64 x)))))
✓	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 (pow.f64 (fabs.f64 x) 7) 21))))
▶	0.8b	(fabs.f64 (/.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))))
	6.1b	(fabs.f64 (exp.f64 (log.f64 (/.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))))))

Compiler

Compiled 16659 to 8074 computations (51.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series128.0ms (2.1%)

Counts

3 → 24

Calls

3 calls:

73.0ms

(/.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)))

33.0ms

(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))))

22.0ms

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

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

7.0ms

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

3.0ms

(/.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

(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))))

simplify157.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

980×	`fma-def_binary64`
329×	`associate-l_binary64`
326×	`associate-*l/_binary64`
315×	`associate-*r/_binary64`
300×	`fma-neg_binary64`

Counts

108 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	4452
1	335	4024
2	761	3248
3	2249	3236
4	4668	3236
5	4951	3236
6	4951	3236

prune248.0ms (4.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	162	4	166

Error

Counts

166 → 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 (fabs.f64 x) 6)) (fabs.f64 x)))))
✓	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 (pow.f64 (fabs.f64 x) 7) 21))))
✓	0.8b	(fabs.f64 (/.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	(fabs.f64 (+.f64 (.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 7))) (+.f64 (.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (.f64 (fabs.f64 x) (pow.f64 x 2)))) (+.f64 (.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 5))) (.f64 2 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x)))))))

Compiler

Compiled 5926 to 3694 computations (37.7% saved)

regimes958.0ms (16%)

Accuracy

Total 0.1b remaining (95%)

Threshold costs 0.1b (95%)

Counts

118 → 1

Compiler

Compiled 23817 to 16076 computations (32.5% saved)

simplify3.0ms (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	31	71
1	49	71
2	53	71
3	49	71

end1.0ms (0%)

Compiler: Compiled 45 to 26 computations (42.2% saved)

sample1.7s (28.5%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
131.0ms	8000×	pre	128	true

Compiler

Compiled 295 to 176 computations (40.3% saved)

Details

analyze6.0ms (0.1%)

sample159.0ms (2.7%)

simplify102.0ms (1.7%)

prune5.0ms (0.1%)

localize25.0ms (0.4%)

series121.0ms (2%)

rewrite159.0ms (2.7%)

simplify227.0ms (3.8%)

prune397.0ms (6.6%)

localize23.0ms (0.4%)

series118.0ms (2%)

rewrite42.0ms (0.7%)

simplify131.0ms (2.2%)

prune362.0ms (6.1%)

localize24.0ms (0.4%)

series160.0ms (2.7%)

rewrite60.0ms (1%)

simplify212.0ms (3.5%)

prune414.0ms (6.9%)

localize14.0ms (0.2%)

series128.0ms (2.1%)

rewrite17.0ms (0.3%)

simplify157.0ms (2.6%)

prune248.0ms (4.1%)

regimes958.0ms (16%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.7s (28.5%)

Profiling