Details

analyze7.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample1.2s (47.9%)

Results

1.0s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify116.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1332×	`fma-def_binary64`
889×	`associate-/r*_binary64`
605×	`neg-sub0_binary64`
599×	`neg-mul-1_binary64`
576×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	42	28
2	102	26
3	261	26
4	684	26
5	1088	24
6	1801	24
7	3541	24
8	3914	24
9	4002	24
10	4416	24
11	4409	24
12	4415	24
13	5159	24

prune5.0ms (0.2%)

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
▶	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Status

Error

Program

▶

0.0b

(/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

1.0b

(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))

Compiler

Compiled 113 to 85 computations (24.8% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (PI.f64) (fma.f64 v v -1))
✓	0.0b	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
✓	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
✓	1.0b	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))

series40.0ms (1.7%)

Counts

4 → 48

Calls

4 calls:

24.0ms	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
7.0ms	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
5.0ms	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
3.0ms	(*.f64 (PI.f64) (fma.f64 v v -1))

rewrite71.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

251×	`expm1-udef_binary64`
251×	`log1p-udef_binary64`
216×	`log-pow_binary64`
151×	`log-div_binary64`
142×	`add-sqr-sqrt_binary64`

Counts

4 → 103

Calls

4 calls:

68.0ms	(*.f64 (PI.f64) (fma.f64 v v -1))
68.0ms	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
68.0ms	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
68.0ms	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	293	55
2	3504	55
3	4889	55
0	0	0
1	0	0

simplify59.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

762×	`fma-def_binary64`
741×	`times-frac_binary64`
293×	`cancel-sign-sub-inv_binary64`
187×	`fma-neg_binary64`
172×	`sub-neg_binary64`

Counts

151 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	216	1794
1	691	1745
2	2407	1699
3	5038	1699

prune209.0ms (8.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	169	2	171

Error

Counts

171 → 2

Alt Table

Status	Error	Program
	0.0b	(.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (pow.f64 (fma.f64 v (*.f64 v -6) 2) -1/2))
▶	0.0b	(/.f64 (/.f64 -4/3 (-.f64 (.f64 (pow.f64 v 2) (PI.f64)) (PI.f64))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

Status

Error

Program

0.0b

(*.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (pow.f64 (fma.f64 v (*.f64 v -6) 2) -1/2))

▶

0.0b

(/.f64 (/.f64 -4/3 (-.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

Compiler

Compiled 4641 to 3519 computations (24.2% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
✓	0.0b	(/.f64 (/.f64 -4/3 (-.f64 (.f64 (pow.f64 v 2) (PI.f64)) (PI.f64))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
✓	0.1b	(*.f64 (pow.f64 v 2) (PI.f64))
✓	1.0b	(/.f64 -4/3 (-.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (PI.f64)))

series34.0ms (1.4%)

Counts

3 → 24

Calls

3 calls:

24.0ms	(/.f64 (/.f64 -4/3 (-.f64 (.f64 (pow.f64 v 2) (PI.f64)) (PI.f64))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
6.0ms	(/.f64 -4/3 (-.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (PI.f64)))
3.0ms	(*.f64 (pow.f64 v 2) (PI.f64))

rewrite82.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

649×	`prod-diff_binary64`
151×	`add-sqr-sqrt_binary64`
146×	`log1p-expm1-u_binary64`
146×	`expm1-log1p-u_binary64`
143×	`add-log-exp_binary64`

Counts

3 → 75

Calls

3 calls:

80.0ms	(/.f64 (/.f64 -4/3 (-.f64 (.f64 (pow.f64 v 2) (PI.f64)) (PI.f64))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
80.0ms	(*.f64 (pow.f64 v 2) (PI.f64))
80.0ms	(/.f64 -4/3 (-.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (PI.f64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	50
1	311	48
2	3822	48
3	4907	48
0	0	0
1	0	0

simplify72.0ms (3%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
660×	`times-frac_binary64`
600×	`fma-neg_binary64`
252×	`cancel-sign-sub-inv_binary64`
130×	`associate-/r*_binary64`

Counts

99 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	175	1347
1	559	1325
2	1994	1239
3	4765	1233
4	5151	1233

prune133.0ms (5.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	158	2	160

Error

Counts

160 → 2

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (pow.f64 (fma.f64 v (*.f64 v -6) 2) -1/2))
✓	0.0b	(/.f64 (/.f64 -4/3 (-.f64 (.f64 (pow.f64 v 2) (PI.f64)) (PI.f64))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

Status

Error

Program

▶

0.0b

(*.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (pow.f64 (fma.f64 v (*.f64 v -6) 2) -1/2))

✓

0.0b

(/.f64 (/.f64 -4/3 (-.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

Compiler

Compiled 4562 to 3398 computations (25.5% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (PI.f64) (fma.f64 v v -1))
	1.0b	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
✓	1.0b	(.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (pow.f64 (fma.f64 v (*.f64 v -6) 2) -1/2))

series25.0ms (1%)

Counts

1 → 12

Calls

1 calls:

24.0ms

(*.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (pow.f64 (fma.f64 v (*.f64 v -6) 2) -1/2))

rewrite60.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

658×	`log-prod_binary64`
264×	`expm1-udef_binary64`
264×	`log1p-udef_binary64`
224×	`log-pow_binary64`
151×	`add-sqr-sqrt_binary64`

Counts

1 → 32

Calls

1 calls:

59.0ms

(*.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (pow.f64 (fma.f64 v (*.f64 v -6) 2) -1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	314	25
2	3499	25
3	5766	25
0	0	0
1	0	0

simplify39.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

640×	`associate-/r*_binary64`
632×	`times-frac_binary64`
510×	`fma-def_binary64`
373×	`associate-/l*_binary64`
236×	`cancel-sign-sub-inv_binary64`

Counts

44 → 55

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	1005
1	430	995
2	1625	888
3	5063	888

prune112.0ms (4.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	118	2	120

Error

Counts

120 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (pow.f64 (fma.f64 v (*.f64 v -6) 2) -1/2))
✓	0.0b	(/.f64 (/.f64 -4/3 (-.f64 (.f64 (pow.f64 v 2) (PI.f64)) (PI.f64))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

Status

Error

Program

✓

0.0b

(*.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (pow.f64 (fma.f64 v (*.f64 v -6) 2) -1/2))

✓

0.0b

(/.f64 (/.f64 -4/3 (-.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

Compiler

Compiled 3341 to 2551 computations (23.6% saved)

regimes109.0ms (4.5%)

Accuracy

Total 0.0b remaining (41.2%)

Threshold costs 0.0b (41.2%)

Counts

19 → 1

Compiler

Compiled 1542 to 1224 computations (20.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	18	27
2	23	27
3	25	27
4	26	27
5	26	27

end58.0ms (2.4%)

Compiler: Compiled 72 to 56 computations (22.2% saved)

Details

analyze7.0ms (0.3%)

sample1.2s (47.9%)

simplify116.0ms (4.8%)

prune5.0ms (0.2%)

localize9.0ms (0.4%)

series40.0ms (1.7%)

rewrite71.0ms (2.9%)

simplify59.0ms (2.4%)

prune209.0ms (8.6%)

localize9.0ms (0.4%)

series34.0ms (1.4%)

rewrite82.0ms (3.4%)

simplify72.0ms (3%)

prune133.0ms (5.5%)

localize10.0ms (0.4%)

series25.0ms (1%)

rewrite60.0ms (2.5%)

simplify39.0ms (1.6%)

prune112.0ms (4.6%)

regimes109.0ms (4.5%)

simplify3.0ms (0.1%)

end58.0ms (2.4%)

Profiling