Details

analyze477.0ms (8.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample1.1s (18.5%)

Results

957.0ms	8256×	body	128	valid
29.0ms	265×	body	128	invalid

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
505×	`times-frac_binary64`
497×	`div-sub_binary64`
469×	`neg-mul-1_binary64`
463×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	83	18
3	193	18
4	334	18
5	435	18
6	600	18
7	871	18
8	1369	16
9	3594	16
10	4298	16
11	4856	16

prune4.0ms (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

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.3b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	17.8b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	2.2b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series88.0ms (1.5%)

Counts

2 → 60

Calls

2 calls:

70.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
18.0ms	(/.f64 v (+.f64 t1 u))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`times-frac_binary64`
181×	`add-sqr-sqrt_binary64`
174×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`

Counts

2 → 186

Calls

2 calls:

12.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
4.0ms	(/.f64 v (+.f64 t1 u))

simplify202.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary64`
383×	`fma-def_binary64`
336×	`fma-neg_binary64`
293×	`associate-/l/_binary64`
286×	`distribute-rgt-in_binary64`

Counts

246 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	7288
1	848	7129
2	2435	7053
3	4601	7053
4	5003	7053

prune173.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	213	6	219
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	213	8	221

Error

0.5b

Counts

221 → 8

Alt Table

Status	Error	Program
	2.5b	(/.f64 (/.f64 1 (/.f64 (+.f64 t1 u) v)) (-.f64 -1 (/.f64 u t1)))
	3.0b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 v (cbrt.f64 (+.f64 t1 u))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	2.3b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
	5.2b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
✓	2.3b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
▶	2.1b	(.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	17.8b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	9.0b	(.f64 -1 (/.f64 v (+.f64 t1 (+.f64 (/.f64 (pow.f64 u 2) t1) (.f64 2 u)))))

Compiler

Compiled 5663 to 2150 computations (62% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 v) (cbrt.f64 v))
✓	0.6b	(cbrt.f64 v)
✓	0.9b	(/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
✓	9.8b	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))

series1.0s (17%)

Counts

4 → 84

Calls

4 calls:

874.0ms	(/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
58.0ms	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))
37.0ms	(*.f64 (cbrt.f64 v) (cbrt.f64 v))
32.0ms	(cbrt.f64 v)

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
25×	`cbrt-prod_binary64`
18×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`
14×	`cbrt-div_binary64`

Counts

4 → 104

Calls

4 calls:

17.0ms	(/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
6.0ms	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))
4.0ms	(*.f64 (cbrt.f64 v) (cbrt.f64 v))
1.0ms	(cbrt.f64 v)

simplify178.0ms (3%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-def_binary64`
381×	`unswap-sqr_binary64`
308×	`times-frac_binary64`
268×	`associate-/l*_binary64`
247×	`associate-r_binary64`

Counts

188 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	5663
1	1000	4654
2	3428	4230
3	5017	4230

prune402.0ms (6.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	353	0	353
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	353	8	361

Error

0.5b

Counts

361 → 8

Alt Table

Status	Error	Program
	2.5b	(/.f64 (/.f64 1 (/.f64 (+.f64 t1 u) v)) (-.f64 -1 (/.f64 u t1)))
	3.0b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 v (cbrt.f64 (+.f64 t1 u))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
▶	2.3b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
	5.2b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
✓	2.3b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
✓	2.1b	(.f64 (/.f64 (.f64 (cbrt.f64 v) (cbrt.f64 v)) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 (cbrt.f64 v) (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	17.8b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	9.0b	(.f64 -1 (/.f64 v (+.f64 t1 (+.f64 (/.f64 (pow.f64 u 2) t1) (.f64 2 u)))))

Compiler

Compiled 17083 to 8624 computations (49.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.6b	(/.f64 1 (-.f64 -1 (/.f64 u t1)))
✓	1.8b	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))

series82.0ms (1.4%)

Counts

2 → 60

Calls

2 calls:

73.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
9.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`add-sqr-sqrt_binary64`
62×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
28×	`add-exp-log_binary64`

Counts

2 → 122

Calls

2 calls:

18.0ms	(*.f64 (/.f64 v (+.f64 t1 u)) (/.f64 1 (-.f64 -1 (/.f64 u t1))))
7.0ms	(/.f64 1 (-.f64 -1 (/.f64 u t1)))

simplify120.0ms (2%)

Algorithm

1×	egg-herbie

Rules

766×	`associate-/l*_binary64`
478×	`associate-*l/_binary64`
442×	`associate-/r*_binary64`
294×	`fma-neg_binary64`
258×	`fma-def_binary64`

Counts

182 → 202

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	3921
1	576	3621
2	1776	3532
3	4978	3523
4	5138	3523

prune265.0ms (4.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	249	2	251
Fresh	1	4	5
Picked	1	0	1
Done	1	1	2
Total	252	7	259

Error

0.3b

Counts

259 → 7

Alt Table

Status	Error	Program
▶	2.5b	(/.f64 (/.f64 1 (/.f64 (+.f64 t1 u) v)) (-.f64 -1 (/.f64 u t1)))
	26.5b	(*.f64 (/.f64 v (+.f64 t1 u)) (neg.f64 (/.f64 t1 u)))
	3.0b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 v (cbrt.f64 (+.f64 t1 u))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	5.2b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
✓	2.3b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	17.8b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	2.6b	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))

Compiler

Compiled 5806 to 2644 computations (54.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 t1 u) v)
✓	0.5b	(/.f64 1 (/.f64 (+.f64 t1 u) v))
✓	2.2b	(/.f64 (/.f64 1 (/.f64 (+.f64 t1 u) v)) (-.f64 -1 (/.f64 u t1)))

series102.0ms (1.7%)

Counts

3 → 96

Calls

3 calls:

73.0ms	(/.f64 (/.f64 1 (/.f64 (+.f64 t1 u) v)) (-.f64 -1 (/.f64 u t1)))
18.0ms	(/.f64 1 (/.f64 (+.f64 t1 u) v))
10.0ms	(/.f64 (+.f64 t1 u) v)

rewrite136.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

1068×	`times-frac_binary64`
672×	`add-sqr-sqrt_binary64`
668×	`*-un-lft-identity_binary64`
402×	`add-cube-cbrt_binary64`
108×	`difference-of-squares_binary64`

Counts

3 → 527

Calls

3 calls:

21.0ms	(/.f64 (/.f64 1 (/.f64 (+.f64 t1 u) v)) (-.f64 -1 (/.f64 u t1)))
7.0ms	(/.f64 1 (/.f64 (+.f64 t1 u) v))
5.0ms	(/.f64 (+.f64 t1 u) v)

simplify517.0ms (8.8%)

Algorithm

1×	egg-herbie

Rules

350×	`fma-def_binary64`
282×	`associate-/l/_binary64`
274×	`distribute-rgt-in_binary64`
261×	`distribute-lft-in_binary64`
228×	`associate-/r*_binary64`

Counts

623 → 584

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	381	19640
1	1002	18146
2	2986	17818
3	4657	17818
4	4948	17818

prune431.0ms (7.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	584	0	584
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	584	7	591

Error

0.3b

Counts

591 → 7

Alt Table

Status	Error	Program
✓	2.5b	(/.f64 (/.f64 1 (/.f64 (+.f64 t1 u) v)) (-.f64 -1 (/.f64 u t1)))
	26.5b	(*.f64 (/.f64 v (+.f64 t1 u)) (neg.f64 (/.f64 t1 u)))
	3.0b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 v (cbrt.f64 (+.f64 t1 u))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
	5.2b	(*.f64 v (/.f64 (/.f64 1 (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
✓	2.3b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	17.8b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	2.6b	(/.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (+.f64 t1 u))

Compiler

Compiled 16536 to 6992 computations (57.7% saved)

regimes296.0ms (5%)

Accuracy

Total 1.6b remaining (92.9%)

Threshold costs 0b (0%)

Counts

75 → 1

Compiler

Compiled 6902 to 4058 computations (41.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	50
1	21	50
2	27	50
3	31	50
4	34	50
5	35	50
6	35	50

end97.0ms (1.6%)

Compiler: Compiled 200 to 123 computations (38.5% saved)

Details

analyze477.0ms (8.1%)

sample1.1s (18.5%)

simplify71.0ms (1.2%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series88.0ms (1.5%)

rewrite40.0ms (0.7%)

simplify202.0ms (3.4%)

prune173.0ms (2.9%)

localize15.0ms (0.2%)

series1.0s (17%)

rewrite35.0ms (0.6%)

simplify178.0ms (3%)

prune402.0ms (6.8%)

localize8.0ms (0.1%)

series82.0ms (1.4%)

rewrite37.0ms (0.6%)

simplify120.0ms (2%)

prune265.0ms (4.5%)

localize9.0ms (0.2%)

series102.0ms (1.7%)

rewrite136.0ms (2.3%)

simplify517.0ms (8.8%)

prune431.0ms (7.3%)

regimes296.0ms (5%)

simplify4.0ms (0.1%)

end97.0ms (1.6%)

Profiling