Details

analyze1.4s (16.4%)

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
15.6%	84.3%	0.1%	7
18.7%	81.1%	0.1%	8
25.7%	73.3%	0.9%	9
28.5%	60.8%	10.7%	10
30.2%	58.7%	11.1%	11
32.7%	52.2%	15.2%	12
33.5%	39.2%	27.4%	13
34.3%	37.8%	27.9%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.9s (22.7%)

Results

1.2s	8256×	body	128	valid
552.0ms	3769×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify137.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

614×	`*-commutative_binary64`
613×	`associate-l_binary64`
526×	`sqr-pow_binary64`
394×	`associate-*r/_binary64`
380×	`cube-prod_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	27	18
2	55	17
3	104	17
4	225	17
5	591	17
6	1774	17
7	2466	17
8	2534	17
9	2692	17
10	2908	17
11	3166	17
12	3656	17
13	4497	17
14	5019	17

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

1.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.9b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

Compiler

Compiled 66 to 41 computations (37.9% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	1.9b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

series558.0ms (6.7%)

Counts

2 → 72

Calls

2 calls:

345.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
213.0ms	(*.f64 a (pow.f64 k m))

rewrite71.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

529×	`fma-def_binary64`
248×	`expm1-udef_binary64`
247×	`log1p-udef_binary64`
218×	`fma-neg_binary64`
141×	`add-sqr-sqrt_binary64`

Counts

2 → 62

Calls

2 calls:

69.0ms	(*.f64 a (pow.f64 k m))
69.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	285	25
2	3705	24
3	5114	24
0	0	0
1	0	0

simplify135.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-neg_binary64`
526×	`associate-r_binary64`
492×	`associate-l_binary64`
479×	`fma-def_binary64`
279×	`associate-/l*_binary64`

Counts

134 → 101

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1549
1	342	1460
2	1102	1240
3	3974	1236
4	5176	1236

prune91.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	3	102

Error

0.0b

Counts

102 → 3

Alt Table

Status	Error	Program
✓	1.9b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
▶	5.8b	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
	18.6b	(/.f64 (cbrt.f64 (pow.f64 (.f64 a (pow.f64 k m)) 3)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

Compiler

Compiled 2464 to 1381 computations (44% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))
✓	0.0b	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
✓	0.0b	(fma.f64 k 10 1)
✓	0.3b	(sqrt.f64 (fma.f64 k 10 1))

series385.0ms (4.6%)

Counts

4 → 64

Calls

4 calls:

308.0ms	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
70.0ms	(/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))
6.0ms	(sqrt.f64 (fma.f64 k 10 1))
2.0ms	(fma.f64 k 10 1)

rewrite75.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`
221×	`log-pow_binary64`
151×	`log-div_binary64`
143×	`prod-diff_binary64`

Counts

4 → 136

Calls

4 calls:

72.0ms	(/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))
72.0ms	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
72.0ms	(fma.f64 k 10 1)
72.0ms	(sqrt.f64 (fma.f64 k 10 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	56
1	273	43
2	3339	43
3	4951	43
0	0	0
1	0	0

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

930×	`fma-neg_binary64`
491×	`associate-r_binary64`
423×	`associate-l_binary64`
385×	`fma-def_binary64`
257×	`cancel-sign-sub-inv_binary64`

Counts

200 → 179

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	1202
1	305	1091
2	901	1028
3	3394	1021
4	4970	1021
5	4957	1021

prune233.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	241	2	243
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	242	4	246

Error

0.0b

Counts

246 → 4

Alt Table

Status	Error	Program
	5.9b	(/.f64 (pow.f64 k m) (*.f64 (/.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) a) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
✓	1.9b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
✓	5.8b	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
▶	5.8b	(/.f64 (/.f64 (*.f64 a (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))

Compiler

Compiled 6114 to 3898 computations (36.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k 10 1)
✓	0.0b	(/.f64 (*.f64 a (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
✓	0.0b	(/.f64 (/.f64 (*.f64 a (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
	0.3b	(sqrt.f64 (fma.f64 k 10 1))

series849.0ms (10.2%)

Counts

2 → 58

Calls

2 calls:

555.0ms

(/.f64 (*.f64 a (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))

294.0ms

(/.f64 (/.f64 (*.f64 a (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))

rewrite114.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

273×	`log1p-udef_binary64`
271×	`expm1-udef_binary64`
194×	`prod-diff_binary64`
154×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`

Counts

2 → 96

Calls

2 calls:

110.0ms

(/.f64 (*.f64 a (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))

110.0ms

(/.f64 (/.f64 (*.f64 a (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	64
1	316	40
2	4063	40
3	4994	40
4	5262	40
0	0	0
1	0	0

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

753×	`associate-l_binary64`
741×	`associate-r_binary64`
670×	`fma-neg_binary64`
594×	`fma-def_binary64`
290×	`cancel-sign-sub-inv_binary64`

Counts

154 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1768
1	321	1578
2	1088	1464
3	4812	1464
4	5346	1464

prune439.0ms (5.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	326	1	327
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	327	4	331

Error

0.0b

Counts

331 → 4

Alt Table

Status	Error	Program
▶	6.3b	(.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) 3/2)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) -1/2))
✓	1.9b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
✓	5.8b	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
✓	5.8b	(/.f64 (/.f64 (*.f64 a (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))

Compiler

Compiled 11243 to 7593 computations (32.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k 10 1)
✓	0.1b	(.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) 3/2)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) -1/2))
	0.3b	(sqrt.f64 (fma.f64 k 10 1))
✓	1.7b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) 3/2))

series666.0ms (8%)

Counts

2 → 58

Calls

2 calls:

370.0ms

(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) 3/2))

296.0ms

(*.f64 (/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) 3/2)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) -1/2))

rewrite69.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

295×	`expm1-udef_binary64`
295×	`log1p-udef_binary64`
171×	`add-sqr-sqrt_binary64`
165×	`log1p-expm1-u_binary64`
165×	`expm1-log1p-u_binary64`

Counts

2 → 72

Calls

2 calls:

67.0ms

(*.f64 (/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) 3/2)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) -1/2))

66.0ms

(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) 3/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	59
1	359	56
2	4060	56
3	5079	56
0	0	0
1	0	0

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

753×	`associate-l_binary64`
741×	`associate-r_binary64`
670×	`fma-neg_binary64`
594×	`fma-def_binary64`
290×	`cancel-sign-sub-inv_binary64`

Counts

130 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1768
1	321	1578
2	1088	1464
3	4812	1464
4	5346	1464

prune317.0ms (3.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	239	4	243

Error

0.0b

Counts

243 → 4

Alt Table

Status	Error	Program
✓	6.3b	(.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) 3/2)) (pow.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) -1/2))
✓	1.9b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
✓	5.8b	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
✓	5.8b	(/.f64 (/.f64 (*.f64 a (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))

Compiler

Compiled 7323 to 4714 computations (35.6% saved)

regimes519.0ms (6.3%)

Accuracy

Total 0.0b remaining (17.8%)

Threshold costs 0.0b (17.8%)

Counts

101 → 2

Compiler

Compiled 9380 to 6674 computations (28.8% saved)

bsearch15.0ms (0.2%)

Steps

Iters	Range		Point
3	5.917567332906647e+78	6.954909080275509e+78	6.890075221064955e+78

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	65
1	27	65
2	26	65

end109.0ms (1.3%)

Compiler: Compiled 198 to 137 computations (30.8% saved)

Details

analyze1.4s (16.4%)

sample1.9s (22.7%)

simplify137.0ms (1.7%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series558.0ms (6.7%)

rewrite71.0ms (0.9%)

simplify135.0ms (1.6%)

prune91.0ms (1.1%)

localize11.0ms (0.1%)

series385.0ms (4.6%)

rewrite75.0ms (0.9%)

simplify75.0ms (0.9%)

prune233.0ms (2.8%)

localize12.0ms (0.1%)

series849.0ms (10.2%)

rewrite114.0ms (1.4%)

simplify76.0ms (0.9%)

prune439.0ms (5.3%)

localize14.0ms (0.2%)

series666.0ms (8%)

rewrite69.0ms (0.8%)

simplify74.0ms (0.9%)

prune317.0ms (3.8%)

regimes519.0ms (6.3%)

bsearch15.0ms (0.2%)

simplify3.0ms (0%)

end109.0ms (1.3%)

Profiling