Details

analyze125.0ms (2.2%)

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)

sample46.0ms (0.8%)

Algorithm

1×

intervals

Results

33.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 140 to 65 computations (53.6% saved)

simplify112.0ms (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 → 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
▶	0.1b	(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) (.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))))))
	0.5b	(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)))

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) (*.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))))))

0.5b

(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)))

Compiler

Compiled 205 to 119 computations (42% saved)

localize31.0ms (0.5%)

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)

rewrite286.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

34×	`add-exp-log_binary64`
30×	`add-sqr-sqrt_binary64`
27×	`associate-*l/_binary64`
19×	`pow1_binary64`
19×	`add-cube-cbrt_binary64`

Counts

4 → 171

Calls

4 calls:

44.0ms	(.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)))))
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)))
18.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
10.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 12800 to 4458 computations (65.2% saved)

series72.0ms (1.3%)

Error

0.0b

Counts

4 → 9

Calls

4 calls:

44.0ms	(.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)))))
11.0ms	(.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)

simplify226.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

493×	`unswap-sqr_binary64`
373×	`associate-r_binary64`
325×	`associate-l_binary64`
295×	`exp-prod_binary64`
262×	`fma-neg_binary64`

Counts

180 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	241	5516
1	668	4199
2	2855	3605
3	4569	3531
4	4995	3531
5	5000	3531
6	4866	3531

prune107.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	97	5	102

Error

Counts

102 → 5

Alt Table

Status	Error	Program
	1.1b	(fabs.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 PI.f64) (cbrt.f64 (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	(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)))))))
✓	0.1b	(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) (.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))))))
	31.2b	(fabs.f64 (.f64 (cbrt.f64 (.f64 (/.f64 1 PI.f64) (pow.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))))) 2))) (cbrt.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)))))
	0.5b	(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)))

Compiler

Compiled 5052 to 2428 computations (51.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite251.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

24×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`fma-udef_binary64`
18×	`pow1_binary64`
16×	`add-cbrt-cube_binary64`

Counts

4 → 149

Calls

4 calls:

16.0ms	(.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))))))
14.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
10.0ms	(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
9.0ms	(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)))))

Compiler

Compiled 4878 to 3406 computations (30.2% saved)

series102.0ms (1.8%)

Error

Counts

4 → 12

Calls

4 calls:

39.0ms	(.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))))))
29.0ms	(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)))))
18.0ms	(fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))
11.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))

Compiler

Compiled 858 to 656 computations (23.5% saved)

simplify140.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-neg_binary64`
583×	`fma-def_binary64`
247×	`cancel-sign-sub-inv_binary64`
184×	`associate-l_binary64`
163×	`associate-r_binary64`

Counts

161 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	4371
1	436	3885
2	1737	3870
3	4448	3870
4	4973	3870

prune92.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	84	5	89

Error

Counts

89 → 5

Alt Table

Status	Error	Program
	1.1b	(fabs.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 PI.f64) (cbrt.f64 (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	(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)))))))
✓	0.1b	(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) (.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))))))
	31.2b	(fabs.f64 (.f64 (cbrt.f64 (.f64 (/.f64 1 PI.f64) (pow.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))))) 2))) (cbrt.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)))))
▶	0.5b	(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)))

Compiler

Compiled 2845 to 1937 computations (31.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(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)))))
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)

rewrite189.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`add-cube-cbrt_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`
17×	`pow1_binary64`
14×	`add-exp-log_binary64`

Counts

4 → 149

Calls

4 calls:

15.0ms	(*.f64 2/3 (pow.f64 x 3))
12.0ms	(/.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))
10.0ms	(sqrt.f64 PI.f64)
9.0ms	(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)))))

Compiler

Compiled 3804 to 2821 computations (25.8% saved)

series64.0ms (1.1%)

Error

Counts

4 → 27

Calls

4 calls:

25.0ms	(/.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))
17.0ms	(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)))))
7.0ms	(*.f64 2/3 (pow.f64 x 3))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1009 to 835 computations (17.2% saved)

simplify121.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

581×	`times-frac_binary64`
435×	`fma-def_binary64`
384×	`distribute-rgt-in_binary64`
372×	`distribute-lft-in_binary64`
245×	`associate-/l*_binary64`

Counts

176 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	3297
1	381	3068
2	1231	2866
3	4956	2866
4	4927	2866

prune71.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	1	2
Picked	0	1	1
Done	1	1	2
Total	83	4	87

Error

Counts

87 → 4

Alt Table

Status	Error	Program
	1.1b	(fabs.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 PI.f64) (cbrt.f64 (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	(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))))))
▶	0.3b	(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))))) (.f64 (pow.f64 PI.f64 1/4) (pow.f64 PI.f64 1/4))))
✓	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)))

Compiler

Compiled 2085 to 1512 computations (27.5% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
0.0b	(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)))))
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))))) (.f64 (pow.f64 PI.f64 1/4) (pow.f64 PI.f64 1/4)))

rewrite208.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`add-cube-cbrt_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`
17×	`pow1_binary64`
12×	`add-exp-log_binary64`

Counts

4 → 147

Calls

4 calls:

15.0ms	(/.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))))) (.f64 (pow.f64 PI.f64 1/4) (pow.f64 PI.f64 1/4)))
14.0ms	(*.f64 2/3 (pow.f64 x 3))
9.0ms	(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
9.0ms	(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)))))

Compiler

Compiled 4515 to 3585 computations (20.6% saved)

series93.0ms (1.6%)

Error

Counts

4 → 36

Calls

4 calls:

23.0ms	(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
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))))) (.f64 (pow.f64 PI.f64 1/4) (pow.f64 PI.f64 1/4)))
17.0ms	(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)))))
10.0ms	(*.f64 2/3 (pow.f64 x 3))

Compiler

Compiled 1571 to 1303 computations (17.1% saved)

simplify131.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

929×	`times-frac_binary64`
558×	`fma-def_binary64`
493×	`distribute-rgt-in_binary64`
119×	`cancel-sign-sub-inv_binary64`
115×	`associate-l_binary64`

Counts

183 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	3877
1	461	3585
2	1569	3375
3	5049	3375

prune127.0ms (2.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	88	4	92

Error

Counts

92 → 4

Alt Table

Status	Error	Program
	1.1b	(fabs.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 PI.f64) (cbrt.f64 (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	(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))))))
	0.3b	(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))))) (.f64 (pow.f64 PI.f64 1/4) (pow.f64 PI.f64 1/4))))
	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)))

Compiler

Compiled 2314 to 1767 computations (23.6% saved)

regimes1.4s (25.1%)

Accuracy

Total 0.1b remaining (74.6%)

Threshold costs 0.1b (74.6%)

Compiler

Compiled 31125 to 20893 computations (32.9% 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 (28.6%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
112.0ms	8001×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 306 to 177 computations (42.2% saved)

Details

analyze125.0ms (2.2%)

sample46.0ms (0.8%)

simplify112.0ms (2%)

prune5.0ms (0.1%)

localize31.0ms (0.5%)

rewrite286.0ms (5%)

series72.0ms (1.3%)

simplify226.0ms (3.9%)

prune107.0ms (1.9%)

localize16.0ms (0.3%)

rewrite251.0ms (4.4%)

series102.0ms (1.8%)

simplify140.0ms (2.4%)

prune92.0ms (1.6%)

localize14.0ms (0.3%)

rewrite189.0ms (3.3%)

series64.0ms (1.1%)

simplify121.0ms (2.1%)

prune71.0ms (1.2%)

localize17.0ms (0.3%)

rewrite208.0ms (3.6%)

series93.0ms (1.6%)

simplify131.0ms (2.3%)

prune127.0ms (2.2%)

regimes1.4s (25.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.6s (28.6%)

Profiling