Details

analyze68.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample1.1s (34.5%)

Results

1.1s	8256×	body	128	valid
6.0ms	58×	body	128	invalid

Compiler

Compiled 67 to 49 computations (26.9% saved)

simplify21.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

560×	`fma-neg_binary64`
442×	`distribute-rgt-in_binary64`
376×	`unsub-neg_binary64`
325×	`fma-def_binary64`
302×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	20	19
2	46	17
3	131	17
4	464	17
5	2012	17

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
	0.1b	(*.f64 (-.f64 1 m) (fma.f64 (-.f64 1 m) (/.f64 m v) -1))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

series25.0ms (0.8%)

Counts

3 → 56

Calls

3 calls:

12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
11.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite56.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

501×	`prod-diff_binary64`
188×	`fma-def_binary64`
179×	`expm1-udef_binary64`
178×	`log1p-udef_binary64`
174×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	202	36
2	2933	34

Stop Event

1×	node limit

Counts

3 → 133

Calls

3 calls:

53.0ms	(*.f64 m (-.f64 1 m))
53.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
53.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

simplify39.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

307×	`fma-def_binary64`
261×	`sub-neg_binary64`
206×	`unsub-neg_binary64`
166×	`associate-l_binary64`
163×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	809
1	97	783
2	252	771
3	723	707
4	2860	707

Stop Event

1×	node limit

Counts

189 → 160

prune171.0ms (5.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	154	6	160
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	156	6	162

Error

Counts

162 → 6

Alt Table

Status	Error	Program
	19.9b	(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 3) -1) (-.f64 1 m)) (+.f64 (pow.f64 (*.f64 (/.f64 m v) (-.f64 1 m)) 2) (fma.f64 (/.f64 m v) (-.f64 1 m) 1)))
▶	0.1b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
	29.8b	(pow.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) 2)
	0.8b	(pow.f64 (cbrt.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) 3)
	0.2b	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) (-.f64 1 m))
	0.2b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))

Compiler

Compiled 3326 to 2116 computations (36.4% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (/.f64 (pow.f64 m 2) v))
✓	0.0b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
✓	7.5b	(/.f64 (pow.f64 m 3) v)
✓	11.4b	(/.f64 (pow.f64 m 2) v)

series55.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
15.0ms	(*.f64 2 (/.f64 (pow.f64 m 2) v))
13.0ms	(/.f64 (pow.f64 m 3) v)
11.0ms	(/.f64 (pow.f64 m 2) v)

rewrite45.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

181×	`add-sqr-sqrt_binary64`
181×	`log1p-expm1-u_binary64`
181×	`expm1-log1p-u_binary64`
177×	`add-cbrt-cube_binary64`
170×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	55
1	385	53

Stop Event

1×	node limit

Counts

4 → 131

Calls

4 calls:

42.0ms	(*.f64 2 (/.f64 (pow.f64 m 2) v))
42.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
42.0ms	(/.f64 (pow.f64 m 3) v)
42.0ms	(/.f64 (pow.f64 m 2) v)

simplify21.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

442×	`associate-l_binary64`
407×	`associate-r_binary64`
401×	`fma-neg_binary64`
381×	`cancel-sign-sub-inv_binary64`
237×	`associate-/l*_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	168
1	75	166
2	188	155
3	498	137
4	1467	127

Stop Event

1×	node limit

Counts

143 → 145

prune168.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	145	6	151

Error

Counts

151 → 6

Alt Table

Status	Error	Program
	19.9b	(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 3) -1) (-.f64 1 m)) (+.f64 (pow.f64 (*.f64 (/.f64 m v) (-.f64 1 m)) 2) (fma.f64 (/.f64 m v) (-.f64 1 m) 1)))
✓	0.1b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
	29.8b	(pow.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) 2)
	0.2b	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) (-.f64 1 m))
▶	0.1b	(-.f64 (+.f64 (.f64 (/.f64 (pow.f64 m 3/2) 1) (/.f64 (pow.f64 m 3/2) v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))
	0.2b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))

Compiler

Compiled 4832 to 2461 computations (49.1% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 2 (/.f64 (pow.f64 m 2) v))
✓	0.2b	(*.f64 (/.f64 (pow.f64 m 3/2) 1) (/.f64 (pow.f64 m 3/2) v))
	11.4b	(/.f64 (pow.f64 m 2) v)
✓	13.1b	(/.f64 (pow.f64 m 3/2) v)

series33.0ms (1%)

Counts

2 → 32

Calls

2 calls:

17.0ms	(/.f64 (pow.f64 m 3/2) v)
16.0ms	(*.f64 (/.f64 (pow.f64 m 3/2) 1) (/.f64 (pow.f64 m 3/2) v))

rewrite41.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

748×	`log1p-expm1-u_binary64`
748×	`expm1-log1p-u_binary64`
138×	`log1p-udef_binary64`
81×	`add-sqr-sqrt_binary64`
77×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	197	14
2	2166	14

Stop Event

1×	node limit

Counts

2 → 77

Calls

2 calls:

38.0ms	(*.f64 (/.f64 (pow.f64 m 3/2) 1) (/.f64 (pow.f64 m 3/2) v))
38.0ms	(/.f64 (pow.f64 m 3/2) v)

simplify51.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

565×	`associate-/r*_binary64`
472×	`associate-/r/_binary64`
362×	`unswap-sqr_binary64`
329×	`associate-/l/_binary64`
317×	`fabs-mul_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	284
1	23	248
2	40	224
3	78	224
4	153	224
5	444	224
6	1490	224
7	2800	224
8	3285	224
9	3490	224
10	3709	224
11	4029	224

Stop Event

1×	node limit

Counts

109 → 79

prune161.0ms (4.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	123	6	129

Error

Counts

129 → 6

Alt Table

Status	Error	Program
	19.9b	(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 3) -1) (-.f64 1 m)) (+.f64 (pow.f64 (*.f64 (/.f64 m v) (-.f64 1 m)) 2) (fma.f64 (/.f64 m v) (-.f64 1 m) 1)))
✓	0.1b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
	29.8b	(pow.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) 2)
▶	0.2b	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) (-.f64 1 m))
✓	0.1b	(-.f64 (+.f64 (.f64 (/.f64 (pow.f64 m 3/2) 1) (/.f64 (pow.f64 m 3/2) v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))
	0.2b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))

Compiler

Compiled 3818 to 2342 computations (38.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (-.f64 1 m))
✓	0.0b	(/.f64 (/.f64 v (-.f64 1 m)) m)
✓	0.1b	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) (-.f64 1 m))
✓	0.3b	(pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1)

series114.0ms (3.4%)

Counts

4 → 84

Calls

4 calls:

49.0ms	(pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1)
30.0ms	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) (-.f64 1 m))
24.0ms	(/.f64 (/.f64 v (-.f64 1 m)) m)
10.0ms	(/.f64 v (-.f64 1 m))

rewrite63.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

394×	`prod-diff_binary64`
211×	`expm1-udef_binary64`
210×	`log1p-udef_binary64`
163×	`egg-rr`
124×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	52
1	248	46
2	3546	46

Stop Event

1×	node limit

Counts

4 → 163

Calls

4 calls:

60.0ms	(/.f64 v (-.f64 1 m))
60.0ms	(/.f64 (/.f64 v (-.f64 1 m)) m)
60.0ms	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) (-.f64 1 m))
60.0ms	(pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1)

simplify40.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

359×	`fma-neg_binary64`
285×	`associate-r_binary64`
277×	`associate-l_binary64`
253×	`times-frac_binary64`
198×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	1312
1	215	1278
2	611	1244
3	1794	1164

Stop Event

1×	node limit

Counts

247 → 218

prune228.0ms (6.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	218	6	224

Error

Counts

224 → 6

Alt Table

Status	Error	Program
	29.8b	(pow.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) 2)
	10.7b	(*.f64 (-.f64 (/.f64 (/.f64 m (sqrt.f64 (/.f64 v (-.f64 1 m)))) (sqrt.f64 (/.f64 v (-.f64 1 m)))) 1) (-.f64 1 m))
	0.2b	(.f64 (-.f64 (.f64 (/.f64 1 v) (/.f64 m (/.f64 1 (-.f64 1 m)))) 1) (-.f64 1 m))
✓	0.1b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
✓	0.2b	(*.f64 (-.f64 (pow.f64 (/.f64 (/.f64 v (-.f64 1 m)) m) -1) 1) (-.f64 1 m))
✓	0.1b	(-.f64 (+.f64 (.f64 (/.f64 (pow.f64 m 3/2) 1) (/.f64 (pow.f64 m 3/2) v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))

Compiler

Compiled 4395 to 3038 computations (30.9% saved)

regimes627.0ms (18.8%)

Accuracy

Total 0.1b remaining (82.2%)

Threshold costs 0.1b (82.2%)

Counts

195 → 1

Compiler

Compiled 11490 to 8265 computations (28.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	30
1	20	30
2	24	30
3	26	30
4	27	30

Stop Event

1×

saturated

end112.0ms (3.4%)

Compiler: Compiled 174 to 125 computations (28.2% saved)

Details

analyze68.0ms (2%)

sample1.1s (34.5%)

simplify21.0ms (0.6%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series25.0ms (0.8%)

rewrite56.0ms (1.7%)

simplify39.0ms (1.2%)

prune171.0ms (5.1%)

localize12.0ms (0.4%)

series55.0ms (1.7%)

rewrite45.0ms (1.3%)

simplify21.0ms (0.6%)

prune168.0ms (5%)

localize17.0ms (0.5%)

series33.0ms (1%)

rewrite41.0ms (1.2%)

simplify51.0ms (1.5%)

prune161.0ms (4.8%)

localize8.0ms (0.2%)

series114.0ms (3.4%)

rewrite63.0ms (1.9%)

simplify40.0ms (1.2%)

prune228.0ms (6.8%)

regimes627.0ms (18.8%)

simplify2.0ms (0.1%)

end112.0ms (3.4%)

Profiling