Details

analyze180.0ms (5.3%)

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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample1.3s (37.3%)

Results

1.3s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 64 to 40 computations (37.5% saved)

preprocess35.0ms (1%)

Algorithm

2×	egg-herbie

Rules

421×	`fma-neg_binary64`
351×	`associate--l+_binary64`
326×	`associate-+l+_binary64`
312×	`unsub-neg_binary64`
293×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	78
1	101	74
2	350	74
3	1237	74
4	3107	66
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 31 to 19 computations (38.7% saved)

simplify29.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-def_binary64`
320×	`+-commutative_binary64`
277×	`sub-neg_binary64`
265×	`associate-l_binary64`
250×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	198	37
3	696	37
4	2292	33
5	4251	33

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
▶	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))

Status

Error

Program

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a))))) 1)

▶

0.0b

(fma.f64 4 (-.f64 (fma.f64 b (*.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))

Compiler

Compiled 166 to 105 computations (36.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))
✓	0.0b	(-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3))
✓	0.0b	(*.f64 b (+.f64 a 3))
✓	0.1b	(fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a))

series51.0ms (1.5%)

Counts

4 → 96

Calls

24 calls:

8.0ms	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))	b	0
6.0ms	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))	b	-inf
6.0ms	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))	b	inf
3.0ms	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))	a	inf
3.0ms	(fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a))	b	inf

rewrite68.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

302×	`log1p-udef_binary64`
180×	`add-sqr-sqrt_binary64`
177×	`pow1_binary64`
174×	`*-un-lft-identity_binary64`
171×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	74
1	365	74
2	4726	74
0	16	74

Stop Event

1×	saturated
1×	node limit

Counts

4 → 114

simplify52.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

689×	`fma-def_binary64`
615×	`fma-neg_binary64`
505×	`associate-+l+_binary64`
340×	`distribute-lft-out_binary64`
327×	`associate--l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	1690
1	221	1566
2	769	1422
3	3764	1398

Stop Event

1×	node limit

Counts

210 → 164

prune221.0ms (6.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	163	3	166

Error

Counts

166 → 3

Alt Table

Status	Error	Program
	19.8b	(cbrt.f64 (pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1)) 3))
▶	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 (*.f64 4 (pow.f64 a 3)) 1))
	12.2b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)

Compiler

Compiled 4873 to 3010 computations (38.2% saved)

localize25.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 4 (.f64 a (pow.f64 b 2)))
✓	0.2b	(*.f64 12 (pow.f64 b 2))
✓	0.8b	(*.f64 a (pow.f64 b 2))
✓	3.0b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series30.0ms (0.9%)

Counts

4 → 0

Calls

21 calls:

3.0ms	(*.f64 a (pow.f64 b 2))	a	0
2.0ms	(.f64 4 (.f64 a (pow.f64 b 2)))	a	0
2.0ms	(.f64 4 (.f64 a (pow.f64 b 2)))	a	inf
2.0ms	(.f64 4 (.f64 a (pow.f64 b 2)))	a	-inf
2.0ms	(*.f64 a (pow.f64 b 2))	a	-inf

rewrite45.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

538×	`log-prod_binary64`
277×	`pow2_binary64`
195×	`pow1/3_binary64`
193×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	248	31
2	2687	31
0	12	34

Stop Event

1×	saturated
1×	node limit

Counts

4 → 73

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

73 → 73

prune114.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	73	3	76

Error

Counts

76 → 3

Alt Table

Status	Error	Program
	19.8b	(cbrt.f64 (pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1)) 3))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 (*.f64 4 (pow.f64 a 3)) 1))
▶	12.2b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)

Compiler

Compiled 3679 to 2803 computations (23.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)
✓	0.1b	(*.f64 b (fma.f64 b b 12))

series7.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

2.0ms	(*.f64 b (fma.f64 b b 12))	b	inf
1.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)	b	-inf
1.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)	b	inf
1.0ms	(*.f64 b (fma.f64 b b 12))	b	-inf
1.0ms	(*.f64 b (fma.f64 b b 12))	b	0

rewrite36.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

615×	`pow1_binary64`
568×	`add-log-exp_binary64`
568×	`log1p-expm1-u_binary64`
568×	`expm1-log1p-u_binary64`
66×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	136	20
2	1506	20
0	7	20

Stop Event

1×	saturated
1×	node limit

Counts

2 → 38

simplify28.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

484×	`distribute-rgt-neg-in_binary64`
452×	`associate-l_binary64`
446×	`distribute-lft-neg-in_binary64`
337×	`associate-r_binary64`
272×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	207
1	44	207
2	84	195
3	172	195
4	505	195
5	2366	195

Stop Event

1×	node limit

Counts

62 → 50

prune52.0ms (1.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	50	3	53

Error

Counts

53 → 3

Alt Table

Status	Error	Program
▶	19.8b	(cbrt.f64 (pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1)) 3))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 (*.f64 4 (pow.f64 a 3)) 1))
✓	12.2b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)

Compiler

Compiled 727 to 478 computations (34.3% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 b (+.f64 a 3))
✓	0.1b	(pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1)) 3)
	0.1b	(fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a))
✓	18.5b	(cbrt.f64 (pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1)) 3))

series87.0ms (2.6%)

Counts

2 → 48

Calls

12 calls:

22.0ms	(pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1)) 3)	b	0
11.0ms	(pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1)) 3)	b	-inf
10.0ms	(pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1)) 3)	a	0
9.0ms	(pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1)) 3)	b	inf
8.0ms	(cbrt.f64 (pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1)) 3))	b	-inf

rewrite38.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

190×	`add-sqr-sqrt_binary64`
187×	`pow1_binary64`
183×	`*-un-lft-identity_binary64`
181×	`add-log-exp_binary64`
181×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	69
1	409	69
0	18	74

Stop Event

1×	saturated
1×	node limit

Counts

2 → 53

simplify49.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

818×	`associate-+r+_binary64`
742×	`fma-def_binary64`
476×	`associate-+l+_binary64`
228×	`associate-r_binary64`
170×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	334	3094
1	1222	2998

Stop Event

1×	node limit

Counts

101 → 108

prune227.0ms (6.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	174	3	177

Error

Counts

177 → 3

Alt Table

Status	Error	Program
✓	19.8b	(cbrt.f64 (pow.f64 (fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1)) 3))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 (*.f64 4 (pow.f64 a 3)) 1))
✓	12.2b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)

Compiler

Compiled 7541 to 5134 computations (31.9% saved)

regimes591.0ms (17.3%)

Accuracy

Total 0.0b remaining (40.1%)

Threshold costs 0.0b (40.1%)

Counts

117 → 1

Compiler

Compiled 13141 to 9615 computations (26.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`*-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	17	35
1	24	35
2	28	35
3	30	35
4	31	35

Stop Event

1×

saturated

end116.0ms (3.4%)

Stop Event

1×

done

Compiler

Compiled 138 to 101 computations (26.8% saved)

Details

analyze180.0ms (5.3%)

sample1.3s (37.3%)

preprocess35.0ms (1%)

simplify29.0ms (0.8%)

prune5.0ms (0.1%)

localize14.0ms (0.4%)

series51.0ms (1.5%)

rewrite68.0ms (2%)

simplify52.0ms (1.5%)

prune221.0ms (6.5%)

localize25.0ms (0.7%)

series30.0ms (0.9%)

rewrite45.0ms (1.3%)

simplify12.0ms (0.4%)

prune114.0ms (3.3%)

localize5.0ms (0.2%)

series7.0ms (0.2%)

rewrite36.0ms (1%)

simplify28.0ms (0.8%)

prune52.0ms (1.5%)

localize18.0ms (0.5%)

series87.0ms (2.6%)

rewrite38.0ms (1.1%)

simplify49.0ms (1.4%)

prune227.0ms (6.7%)

regimes591.0ms (17.3%)

simplify3.0ms (0.1%)

end116.0ms (3.4%)

Profiling