Details

analyze5.0ms (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)

sample1.7s (32.1%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify103.0ms (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 → 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

prune6.0ms (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
▶	0.1b	(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 272 to 147 computations (46% saved)

localize22.0ms (0.4%)

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 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
✓	0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
✓	1.0b	(sqrt.f64 (PI.f64))

series30.0ms (0.6%)

Counts

4 → 36

Calls

4 calls:

13.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (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)))
6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 (PI.f64))

rewrite57.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

633×	`log-prod_binary64`
240×	`expm1-udef_binary64`
240×	`log1p-udef_binary64`
207×	`log-pow_binary64`
148×	`add-sqr-sqrt_binary64`

Counts

4 → 81

Calls

4 calls:

55.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
55.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
55.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
55.0ms	(sqrt.f64 (PI.f64))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	34
1	340	22
2	3113	22
3	4930	22

simplify147.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1252×	`sqr-pow_binary64`
710×	`cube-prod_binary64`
698×	`pow-sqr_binary64`
694×	`fabs-mul_binary64`
416×	`unswap-sqr_binary64`

Counts

117 → 84

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	288
1	25	288
2	52	288
3	100	288
4	190	288
5	435	288
6	574	288
7	928	288
8	944	288
9	1100	288
10	1287	288
11	1549	288
12	1829	288
13	2244	288
14	2713	288
15	3373	288
16	3661	288
17	3957	288
18	4167	288
19	4255	288
20	4355	288
21	5376	288

prune181.0ms (3.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	123	5	128

Error

0.0b

Counts

128 → 5

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))))
	1.1b	(fabs.f64 (.f64 (/.f64 1 (expm1.f64 (log1p.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))))))
	1.2b	(fabs.f64 (.f64 (/.f64 1 (cbrt.f64 (pow.f64 (PI.f64) 3/2))) (+.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))))))
	1.8b	(fabs.f64 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) 3)) (+.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 8762 to 3551 computations (59.5% 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))))
✓	0.2b	(*.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))

series17.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

7.0ms

(/.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)))

6.0ms

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

4.0ms

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

rewrite68.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

326×	`log1p-udef_binary64`
239×	`prod-diff_binary64`
190×	`add-sqr-sqrt_binary64`
184×	`log1p-expm1-u_binary64`
184×	`expm1-log1p-u_binary64`

Counts

3 → 73

Calls

3 calls:

66.0ms

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

66.0ms

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

66.0ms

(/.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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	56
1	406	56
2	4252	56
3	5015	56

simplify138.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1073×	`fma-def_binary64`
750×	`cube-prod_binary64`
711×	`sqr-pow_binary64`
690×	`unswap-sqr_binary64`
582×	`fabs-mul_binary64`

Counts

97 → 92

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	627
1	102	627
2	243	535
3	580	475
4	1167	465
5	1645	465
6	1841	465
7	2088	465
8	2526	465
9	2549	465
10	2716	465
11	2979	465
12	3197	465
13	3572	465
14	4095	465
15	4379	465
16	4925	465

prune152.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	119	5	124

Error

Counts

124 → 5

Alt Table

Status	Error	Program
	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))))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))))
▶	0.1b	(fabs.f64 (+.f64 (.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5))) (+.f64 (.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))) (+.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)) (.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 7)))))))
	0.5b	(fabs.f64 (pow.f64 (/.f64 (sqrt.f64 (PI.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)))))) -1))
✓	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 (/.f64 1 (pow.f64 (PI.f64) 1/4)) (/.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))))) (pow.f64 (PI.f64) 1/4))))

Compiler

Compiled 3520 to 2670 computations (24.1% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
✓	0.1b	(.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5)))
✓	0.1b	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))
✓	0.2b	(.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3)))

series46.0ms (0.9%)

Counts

4 → 0

Calls

4 calls:

12.0ms	(.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5)))
12.0ms	(.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3)))
12.0ms	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))
9.0ms	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)

rewrite87.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

281×	`expm1-udef_binary64`
281×	`log1p-udef_binary64`
252×	`log-pow_binary64`
188×	`fma-neg_binary64`
165×	`add-sqr-sqrt_binary64`

Counts

4 → 60

Calls

4 calls:

86.0ms	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)
86.0ms	(.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5)))
86.0ms	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))
86.0ms	(.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	55
1	354	43
2	3746	43
3	4982	43
4	4872	43

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune112.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	60	5	65

Error

Counts

65 → 5

Alt Table

Status	Error	Program
▶	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))))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))))
✓	0.1b	(fabs.f64 (+.f64 (.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5))) (+.f64 (.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))) (+.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)) (.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 7)))))))
	0.5b	(fabs.f64 (pow.f64 (/.f64 (sqrt.f64 (PI.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)))))) -1))
✓	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 (/.f64 1 (pow.f64 (PI.f64) 1/4)) (/.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))))) (pow.f64 (PI.f64) 1/4))))

Compiler

Compiled 2844 to 2228 computations (21.7% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))))
	0.0b	(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
	0.2b	(*.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))))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2)))

series14.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

10.0ms

(/.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))))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))

3.0ms

(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)))))

rewrite67.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

240×	`prod-diff_binary64`
214×	`add-sqr-sqrt_binary64`
208×	`log1p-expm1-u_binary64`
208×	`expm1-log1p-u_binary64`
205×	`add-log-exp_binary64`

Counts

2 → 55

Calls

2 calls:

65.0ms

(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)))))

65.0ms

(/.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))))) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	57
1	461	56
2	4775	56
3	5010	56

simplify137.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1073×	`fma-def_binary64`
750×	`cube-prod_binary64`
711×	`sqr-pow_binary64`
690×	`unswap-sqr_binary64`
582×	`fabs-mul_binary64`

Counts

79 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	654
1	123	654
2	291	552
3	687	492
4	1265	492
5	1715	492
6	1875	492
7	2122	492
8	2560	492
9	2583	492
10	2750	492
11	3013	492
12	3231	492
13	3606	492
14	4129	492
15	4413	492
16	4959	492

prune155.0ms (3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	126	5	131

Error

Counts

131 → 5

Alt Table

Status	Error	Program
✓	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))))) (exp.f64 (.f64 (log.f64 (PI.f64)) 1/2))))
✓	0.1b	(fabs.f64 (+.f64 (.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5))) (+.f64 (.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))) (+.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)) (.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 7)))))))
	0.5b	(fabs.f64 (pow.f64 (/.f64 (sqrt.f64 (PI.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)))))) -1))
✓	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 (/.f64 1 (pow.f64 (PI.f64) 1/4)) (/.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))))) (pow.f64 (PI.f64) 1/4))))

Compiler

Compiled 3819 to 2964 computations (22.4% saved)

regimes1.7s (33.5%)

Accuracy

Total 0.1b remaining (80.1%)

Threshold costs 0.1b (80.1%)

Counts

218 → 1

Compiler

Compiled 48141 to 31132 computations (35.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	66
1	41	66
2	40	66

end162.0ms (3.2%)

Compiler: Compiled 274 to 203 computations (25.9% saved)

Details

analyze5.0ms (0.1%)

sample1.7s (32.1%)

simplify103.0ms (2%)

prune6.0ms (0.1%)

localize22.0ms (0.4%)

series30.0ms (0.6%)

rewrite57.0ms (1.1%)

simplify147.0ms (2.9%)

prune181.0ms (3.5%)

localize13.0ms (0.3%)

series17.0ms (0.3%)

rewrite68.0ms (1.3%)

simplify138.0ms (2.7%)

prune152.0ms (3%)

localize19.0ms (0.4%)

series46.0ms (0.9%)

rewrite87.0ms (1.7%)

simplify6.0ms (0.1%)

prune112.0ms (2.2%)

localize16.0ms (0.3%)

series14.0ms (0.3%)

rewrite67.0ms (1.3%)

simplify137.0ms (2.7%)

prune155.0ms (3%)

regimes1.7s (33.5%)

simplify3.0ms (0.1%)

end162.0ms (3.2%)

Profiling