Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 21 to 17 computations (19% saved)

sample943.0ms (38.8%)

Results

888.0ms

8256×

body

128

valid

Compiler

Compiled 62 to 50 computations (19.4% saved)

simplify30.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-def_binary64`
646×	`fma-neg_binary64`
298×	`distribute-rgt-in_binary64`
239×	`div-sub_binary64`
214×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	34	22
2	67	22
3	107	22
4	153	22
5	195	20
6	292	20
7	529	20
8	1152	20
9	2277	20
10	4735	20

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 67 to 51 computations (23.9% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
✓	0.1b	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
✓	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	14.1b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series9.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
3.0ms	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
1.0ms	(fma.f64 x 4481/100000 99229/100000)
1.0ms	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)

rewrite62.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

509×	`unpow-prod-down_binary64`
418×	`log-prod_binary64`
268×	`pow2_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	225	35
2	2518	35

Stop Event

1×	node limit

Counts

4 → 165

Calls

4 calls:

59.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
59.0ms	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
59.0ms	(fma.f64 x 4481/100000 99229/100000)
59.0ms	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

simplify35.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-neg_binary64`
739×	`cancel-sign-sub-inv_binary64`
417×	`times-frac_binary64`
305×	`fma-def_binary64`
185×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	459
1	131	417
2	314	389
3	855	369
4	2771	369

Stop Event

1×	node limit

Counts

213 → 197

prune193.0ms (8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	194	3	197
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	195	3	198

Error

0.0b

Counts

198 → 3

Alt Table

Status	Error	Program
	0.1b	(fma.f64 x -70711/100000 (*.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
	15.5b	(fma.f64 x -70711/100000 (/.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x 1913510371/10000000000) 2) 266237158899274796689/100000000000000000000) (fma.f64 x 1913510371/10000000000 -16316775383/10000000000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
▶	0.1b	(fma.f64 x -70711/100000 (log1p.f64 (expm1.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 4508 to 3552 computations (21.2% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
	0.1b	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
	0.2b	(fma.f64 x 4481/100000 99229/100000)
	14.1b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

prune195.0ms (8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	197	3	200

Error

0.0b

Counts

200 → 3

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x -70711/100000 (*.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
	15.5b	(fma.f64 x -70711/100000 (/.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x 1913510371/10000000000) 2) 266237158899274796689/100000000000000000000) (fma.f64 x 1913510371/10000000000 -16316775383/10000000000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	0.1b	(fma.f64 x -70711/100000 (log1p.f64 (expm1.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 4884 to 3932 computations (19.5% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	0.3b	(/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
✓	13.8b	(*.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
3.0ms	(*.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

rewrite46.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

459×	`log-prod_binary64`
284×	`pow2_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`
200×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	248	28
2	2753	28

Stop Event

1×	node limit

Counts

2 → 63

Calls

2 calls:

45.0ms	(/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
45.0ms	(*.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

simplify27.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

535×	`fma-def_binary64`
344×	`cancel-sign-sub-inv_binary64`
290×	`associate-/r*_binary64`
270×	`fma-neg_binary64`
255×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	398
1	191	390
2	509	382
3	1511	366

Stop Event

1×	node limit

Counts

87 → 92

prune153.0ms (6.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	167	3	170

Error

0.0b

Counts

170 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x -70711/100000 (*.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
▶	15.5b	(fma.f64 x -70711/100000 (/.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x 1913510371/10000000000) 2) 266237158899274796689/100000000000000000000) (fma.f64 x 1913510371/10000000000 -16316775383/10000000000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	0.1b	(fma.f64 x -70711/100000 (log1p.f64 (expm1.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 3631 to 2881 computations (20.7% saved)

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (*.f64 x 1913510371/10000000000) 2)
✓	0.3b	(*.f64 x 1913510371/10000000000)
✓	14.1b	(/.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x 1913510371/10000000000) 2) 266237158899274796689/100000000000000000000) (fma.f64 x 1913510371/10000000000 -16316775383/10000000000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
✓	14.6b	(/.f64 (-.f64 (pow.f64 (*.f64 x 1913510371/10000000000) 2) 266237158899274796689/100000000000000000000) (fma.f64 x 1913510371/10000000000 -16316775383/10000000000))

series11.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(/.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x 1913510371/10000000000) 2) 266237158899274796689/100000000000000000000) (fma.f64 x 1913510371/10000000000 -16316775383/10000000000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
3.0ms	(/.f64 (-.f64 (pow.f64 (*.f64 x 1913510371/10000000000) 2) 266237158899274796689/100000000000000000000) (fma.f64 x 1913510371/10000000000 -16316775383/10000000000))
2.0ms	(pow.f64 (*.f64 x 1913510371/10000000000) 2)
1.0ms	(*.f64 x 1913510371/10000000000)

rewrite101.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

304×	`log1p-udef_binary64`
176×	`egg-rr`
173×	`add-sqr-sqrt_binary64`
170×	`log1p-expm1-u_binary64`
170×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	56
1	375	52
2	4585	52

Stop Event

1×	node limit

Counts

4 → 176

Calls

4 calls:

95.0ms	(pow.f64 (*.f64 x 1913510371/10000000000) 2)
95.0ms	(*.f64 x 1913510371/10000000000)
95.0ms	(/.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x 1913510371/10000000000) 2) 266237158899274796689/100000000000000000000) (fma.f64 x 1913510371/10000000000 -16316775383/10000000000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
95.0ms	(/.f64 (-.f64 (pow.f64 (*.f64 x 1913510371/10000000000) 2) 266237158899274796689/100000000000000000000) (fma.f64 x 1913510371/10000000000 -16316775383/10000000000))

simplify36.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-neg_binary64`
740×	`cancel-sign-sub-inv_binary64`
417×	`times-frac_binary64`
265×	`fma-def_binary64`
185×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	391
1	115	369
2	288	365
3	812	357
4	2679	357

Stop Event

1×	node limit

Counts

224 → 195

prune207.0ms (8.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	195	3	198

Error

0.0b

Counts

198 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x -70711/100000 (*.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
✓	15.5b	(fma.f64 x -70711/100000 (/.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x 1913510371/10000000000) 2) 266237158899274796689/100000000000000000000) (fma.f64 x 1913510371/10000000000 -16316775383/10000000000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	0.1b	(fma.f64 x -70711/100000 (log1p.f64 (expm1.f64 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Compiler

Compiled 7903 to 6267 computations (20.7% saved)

regimes241.0ms (9.9%)

Accuracy

Total 0.0b remaining (14.4%)

Threshold costs 0.0b (14.4%)

Counts

83 → 1

Compiler

Compiled 4028 to 3125 computations (22.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	17	24

Stop Event

1×

saturated

end77.0ms (3.2%)

Compiler: Compiled 96 to 75 computations (21.9% saved)

Details

analyze5.0ms (0.2%)

sample943.0ms (38.8%)

simplify30.0ms (1.2%)

prune3.0ms (0.1%)

localize9.0ms (0.4%)

series9.0ms (0.4%)

rewrite62.0ms (2.5%)

simplify35.0ms (1.5%)

prune193.0ms (8%)

localize13.0ms (0.5%)

prune195.0ms (8%)

localize10.0ms (0.4%)

series6.0ms (0.3%)

rewrite46.0ms (1.9%)

simplify27.0ms (1.1%)

prune153.0ms (6.3%)

localize14.0ms (0.6%)

series11.0ms (0.5%)

rewrite101.0ms (4.1%)

simplify36.0ms (1.5%)

prune207.0ms (8.5%)

regimes241.0ms (9.9%)

simplify2.0ms (0.1%)

end77.0ms (3.2%)

Profiling