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)

sample1.1s (37.2%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 62 to 50 computations (19.4% saved)

simplify34.0ms (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 (0.3%)

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))

series12.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
3.0ms	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
2.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
1.0ms	(fma.f64 x 4481/100000 99229/100000)

rewrite73.0ms (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:

70.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
70.0ms	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
70.0ms	(fma.f64 x 4481/100000 99229/100000)
70.0ms	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

simplify40.0ms (1.4%)

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

prune240.0ms (8.1%)

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
	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)))))
	0.1b	(fma.f64 x -70711/100000 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000)) -1))

Compiler

Compiled 4508 to 3552 computations (21.2% saved)

localize15.0ms (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))

prune234.0ms (7.9%)

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

Compiler

Compiled 4884 to 3932 computations (19.5% saved)

localize10.0ms (0.3%)

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)
✓	0.6b	(pow.f64 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000)) -1)
✓	14.6b	(/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000))

series8.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

5.0ms

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

3.0ms

(pow.f64 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000)) -1)

rewrite52.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

484×	`log-prod_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
175×	`log-pow_binary64`
126×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	267	32
2	2978	32

Stop Event

1×	node limit

Counts

2 → 81

Calls

2 calls:

51.0ms

(pow.f64 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000)) -1)

51.0ms

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

simplify46.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-def_binary64`
470×	`times-frac_binary64`
274×	`sub-neg_binary64`
235×	`associate-l_binary64`
230×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	326
1	176	306
2	450	296
3	1296	284
4	4000	284

Stop Event

1×	node limit

Counts

105 → 110

prune210.0ms (7.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	185	3	188

Error

0.0b

Counts

188 → 3

Alt Table

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

Compiler

Compiled 4163 to 3307 computations (20.6% saved)

localize20.0ms (0.7%)

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 (0.4%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(/.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)

rewrite112.0ms (3.8%)

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:

107.0ms	(pow.f64 (*.f64 x 1913510371/10000000000) 2)
107.0ms	(*.f64 x 1913510371/10000000000)
107.0ms	(/.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))
107.0ms	(/.f64 (-.f64 (pow.f64 (*.f64 x 1913510371/10000000000) 2) 266237158899274796689/100000000000000000000) (fma.f64 x 1913510371/10000000000 -16316775383/10000000000))

simplify38.0ms (1.3%)

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

prune313.0ms (10.5%)

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
✓	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)))))
✓	0.1b	(fma.f64 x -70711/100000 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000)) -1))

Compiler

Compiled 7903 to 6267 computations (20.7% saved)

regimes290.0ms (9.8%)

Accuracy

Total 0.0b remaining (14%)

Threshold costs 0.0b (14%)

Counts

87 → 1

Compiler

Compiled 4145 to 3236 computations (21.9% 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

end85.0ms (2.9%)

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

Details

analyze5.0ms (0.2%)

sample1.1s (37.2%)

simplify34.0ms (1.2%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series12.0ms (0.4%)

rewrite73.0ms (2.5%)

simplify40.0ms (1.4%)

prune240.0ms (8.1%)

localize15.0ms (0.5%)

prune234.0ms (7.9%)

localize10.0ms (0.3%)

series8.0ms (0.3%)

rewrite52.0ms (1.8%)

simplify46.0ms (1.5%)

prune210.0ms (7.1%)

localize20.0ms (0.7%)

series11.0ms (0.4%)

rewrite112.0ms (3.8%)

simplify38.0ms (1.3%)

prune313.0ms (10.5%)

regimes290.0ms (9.8%)

simplify2.0ms (0.1%)

end85.0ms (2.9%)

Profiling