Details

analyze35.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample1.1s (45%)

Results

1.1s	8256×	body	128	valid
46.0ms	372×	body	128	invalid

Compiler

Compiled 52 to 30 computations (42.3% saved)

preprocess27.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

303×	`associate-/l*_binary64`
282×	`associate-/r/_binary64`
258×	`times-frac_binary64`
232×	`fma-def_binary64`
190×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	47	34
2	137	30
3	394	30
4	1282	30
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 15 to 8 computations (46.7% saved)

simplify19.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
600×	`associate-/r*_binary64`
362×	`distribute-rgt-in_binary64`
331×	`distribute-lft-in_binary64`
206×	`div-sub_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	72	15
3	201	15
4	549	15
5	1979	15

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

13.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.3b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
▶	13.3b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 79 to 45 computations (43% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	0.0b	(-.f64 (.f64 a a) (.f64 b b))
✓	12.9b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

series47.0ms (1.9%)

Counts

3 → 72

Calls

18 calls:

6.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))	b	inf
5.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))	b	-inf
4.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))	b	0
4.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))	b	0
3.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))	a	-inf

rewrite72.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

881×	`prod-diff_binary64`
132×	`egg-rr`
113×	`add-sqr-sqrt_binary64`
110×	`*-un-lft-identity_binary64`
110×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	46
1	214	38
2	3326	38
0	9	46

Stop Event

1×	saturated
1×	node limit

Counts

3 → 211

simplify40.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

727×	`associate-/r*_binary64`
691×	`associate-/l/_binary64`
497×	`associate-/r/_binary64`
166×	`times-frac_binary64`
127×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	963
1	37	891
2	92	843
3	296	843
4	1352	843

Stop Event

1×	node limit

Counts

283 → 223

prune141.0ms (5.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	221	2	223
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	222	3	225

Error

0.0b

Counts

225 → 3

Alt Table

Status	Error	Program
	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
▶	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
✓	13.3b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 5420 to 2266 computations (58.2% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
✓	0.3b	(*.f64 (/.f64 b a) (/.f64 b a))

series42.0ms (1.7%)

Counts

2 → 48

Calls

12 calls:

7.0ms	(*.f64 (/.f64 b a) (/.f64 b a))	b	inf
6.0ms	(*.f64 (/.f64 b a) (/.f64 b a))	b	-inf
6.0ms	(*.f64 (/.f64 b a) (/.f64 b a))	b	0
3.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))	a	inf
3.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))	a	-inf

rewrite46.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

909×	`log1p-expm1-u_binary64`
909×	`expm1-log1p-u_binary64`
101×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64`
97×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	199	19
2	2772	19
0	9	27

Stop Event

1×	saturated
1×	node limit

Counts

2 → 61

simplify39.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

361×	`distribute-neg-frac_binary64`
351×	`associate-/l*_binary64`
286×	`unswap-sqr_binary64`
259×	`associate-/r*_binary64`
251×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	648
1	24	648
2	45	600
3	119	600
4	528	600
5	3048	600

Stop Event

1×	node limit

Counts

109 → 65

prune54.0ms (2.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	66	2	68

Error

Counts

68 → 2

Alt Table

Status	Error	Program
▶	0.0b	(exp.f64 (*.f64 (log1p.f64 (neg.f64 (pow.f64 (/.f64 b a) 2))) 1/2))
	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 b (*.f64 a (/.f64 a b))))))

Compiler

Compiled 862 to 560 computations (35% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (log1p.f64 (neg.f64 (pow.f64 (/.f64 b a) 2))) 1/2)
✓	0.0b	(log1p.f64 (neg.f64 (pow.f64 (/.f64 b a) 2)))
✓	0.3b	(pow.f64 (/.f64 b a) 2)

series98.0ms (3.9%)

Counts

3 → 72

Calls

18 calls:

31.0ms	(log1p.f64 (neg.f64 (pow.f64 (/.f64 b a) 2)))	a	-inf
7.0ms	(*.f64 (log1p.f64 (neg.f64 (pow.f64 (/.f64 b a) 2))) 1/2)	b	-inf
6.0ms	(*.f64 (log1p.f64 (neg.f64 (pow.f64 (/.f64 b a) 2))) 1/2)	b	inf
6.0ms	(*.f64 (log1p.f64 (neg.f64 (pow.f64 (/.f64 b a) 2))) 1/2)	a	-inf
6.0ms	(log1p.f64 (neg.f64 (pow.f64 (/.f64 b a) 2)))	b	inf

rewrite44.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

800×	`expm1-log1p-u_binary64`
799×	`log1p-expm1-u_binary64`
101×	`add-sqr-sqrt_binary64`
97×	`pow1_binary64`
96×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	210	28
2	2461	28
0	10	32

Stop Event

1×	saturated
1×	node limit

Counts

3 → 78

simplify44.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

466×	`fma-def_binary64`
305×	`associate--r+_binary64`
252×	`times-frac_binary64`
229×	`distribute-neg-in_binary64`
195×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	1952
1	422	1924
2	1363	1863

Stop Event

1×	node limit

Counts

150 → 142

prune102.0ms (4.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	142	2	144

Error

Counts

144 → 2

Alt Table

Status	Error	Program
✓	0.0b	(exp.f64 (*.f64 (log1p.f64 (neg.f64 (pow.f64 (/.f64 b a) 2))) 1/2))
▶	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 b (*.f64 a (/.f64 a b))))))

Compiler

Compiled 2834 to 1937 computations (31.7% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 b (*.f64 a (/.f64 a b))))))
✓	0.2b	(/.f64 b (*.f64 a (/.f64 a b)))
✓	0.3b	(*.f64 a (/.f64 a b))

series55.0ms (2.2%)

Counts

3 → 72

Calls

18 calls:

9.0ms	(/.f64 b (*.f64 a (/.f64 a b)))	b	inf
6.0ms	(/.f64 b (*.f64 a (/.f64 a b)))	b	-inf
6.0ms	(/.f64 b (*.f64 a (/.f64 a b)))	b	0
6.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 b (*.f64 a (/.f64 a b))))))	b	0
3.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 b (*.f64 a (/.f64 a b))))))	b	-inf

rewrite56.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

441×	`prod-diff_binary64`
176×	`fma-def_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`
145×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	218	26
2	3073	26
0	10	34

Stop Event

1×	saturated
1×	node limit

Counts

3 → 93

simplify43.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

366×	`distribute-neg-frac_binary64`
354×	`associate-/l*_binary64`
312×	`unswap-sqr_binary64`
272×	`associate-/r*_binary64`
265×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	816
1	25	816
2	46	768
3	122	768
4	550	768
5	3220	768

Stop Event

1×	node limit

Counts

165 → 99

prune66.0ms (2.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	99	2	101

Error

Counts

101 → 2

Alt Table

Status	Error	Program
✓	0.0b	(exp.f64 (*.f64 (log1p.f64 (neg.f64 (pow.f64 (/.f64 b a) 2))) 1/2))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 b (*.f64 a (/.f64 a b))))))

Compiler

Compiled 1394 to 862 computations (38.2% saved)

regimes221.0ms (8.8%)

Accuracy

Total 0.0b remaining (27.1%)

Threshold costs 0.0b (27.1%)

Counts

28 → 1

Compiler

Compiled 2757 to 2057 computations (25.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	16	16
2	18	16
3	19	16

Stop Event

1×

saturated

end50.0ms (2%)

Stop Event

1×

done

Compiler

Compiled 49 to 39 computations (20.4% saved)

Details

analyze35.0ms (1.4%)

sample1.1s (45%)

preprocess27.0ms (1.1%)

simplify19.0ms (0.8%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series47.0ms (1.9%)

rewrite72.0ms (2.9%)

simplify40.0ms (1.6%)

prune141.0ms (5.6%)

localize6.0ms (0.3%)

series42.0ms (1.7%)

rewrite46.0ms (1.8%)

simplify39.0ms (1.5%)

prune54.0ms (2.2%)

localize7.0ms (0.3%)

series98.0ms (3.9%)

rewrite44.0ms (1.8%)

simplify44.0ms (1.7%)

prune102.0ms (4.1%)

localize9.0ms (0.3%)

series55.0ms (2.2%)

rewrite56.0ms (2.2%)

simplify43.0ms (1.7%)

prune66.0ms (2.6%)

regimes221.0ms (8.8%)

simplify2.0ms (0.1%)

end50.0ms (2%)

Profiling