Details

analyze2.3s (21.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample3.1s (28.9%)

Results

1.9s	8256×	body	128	valid
1.1s	4884×	body	128	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

simplify48.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-neg_binary64`
433×	`exp-sum_binary64`
321×	`distribute-rgt-in_binary64`
303×	`distribute-lft-in_binary64`
279×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	47
1	55	42
2	136	40
3	512	40
4	2106	40
5	4520	40
6	4992	40

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

2.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))) x))

Compiler

Compiled 135 to 87 computations (35.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
✓	0.4b	(/.f64 2/3 t)
✓	1.6b	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
✓	5.4b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

series132.0ms (1.2%)

Counts

4 → 88

Calls

4 calls:

67.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
37.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
26.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
1.0ms	(/.f64 2/3 t)

rewrite77.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

520×	`prod-diff_binary64`
202×	`add-sqr-sqrt_binary64`
195×	`log1p-expm1-u_binary64`
195×	`expm1-log1p-u_binary64`
189×	`add-log-exp_binary64`

Counts

4 → 91

Calls

4 calls:

75.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
75.0ms	(/.f64 2/3 t)
75.0ms	(fma.f64 (-.f64 (+.f64 a 5/6) (/.f64 2/3 t)) (-.f64 c b) (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t))
75.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	53
1	394	53
2	4874	53
3	5989	53
0	0	0
1	0	0

simplify112.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

590×	`associate--r+_binary64`
467×	`associate-r_binary64`
435×	`associate-l_binary64`
416×	`cancel-sign-sub-inv_binary64`
254×	`fma-def_binary64`

Counts

179 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	2727
1	604	2679
2	2021	2658
3	4821	2656
4	4984	2656
5	4964	2656

prune232.0ms (2.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	3	164

Error

Counts

164 → 3

Alt Table

Status	Error	Program
	25.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (-.f64 (fma.f64 5/6 c (fma.f64 z (sqrt.f64 (/.f64 1 t)) (.f64 2/3 (/.f64 b t)))) (fma.f64 5/6 b (.f64 2/3 (/.f64 c t))))) x))
	26.5b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))
▶	20.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))

Compiler

Compiled 5968 to 3151 computations (47.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
✓	0.0b	(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x)
✓	0.0b	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
✓	0.1b	(*.f64 (+.f64 a 5/6) (-.f64 c b))

series371.0ms (3.5%)

Counts

4 → 192

Calls

4 calls:

224.0ms	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
121.0ms	(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x)
15.0ms	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
10.0ms	(*.f64 (+.f64 a 5/6) (-.f64 c b))

rewrite77.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

513×	`prod-diff_binary64`
168×	`add-sqr-sqrt_binary64`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`
157×	`add-log-exp_binary64`

Counts

4 → 117

Calls

4 calls:

74.0ms	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))
74.0ms	(fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x)
74.0ms	(pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b)))
74.0ms	(*.f64 (+.f64 a 5/6) (-.f64 c b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	66
1	328	66
2	4180	66
3	5140	66
0	0	0
1	0	0

simplify165.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
488×	`associate-/l*_binary64`
432×	`*-commutative_binary64`
314×	`associate-r_binary64`
182×	`+-commutative_binary64`

Counts

309 → 227

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	786	11389
1	2774	11163
2	4990	11163

prune341.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	227	3	230

Error

Counts

230 → 3

Alt Table

Status	Error	Program
▶	25.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (-.f64 (fma.f64 5/6 c (fma.f64 z (sqrt.f64 (/.f64 1 t)) (.f64 2/3 (/.f64 b t)))) (fma.f64 5/6 b (.f64 2/3 (/.f64 c t))))) x))
	26.5b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))
✓	20.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))

Compiler

Compiled 14491 to 9363 computations (35.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 2/3 (/.f64 b t))
✓	0.3b	(*.f64 2/3 (/.f64 c t))
✓	0.4b	(fma.f64 z (sqrt.f64 (/.f64 1 t)) (*.f64 2/3 (/.f64 b t)))
✓	0.9b	(-.f64 (fma.f64 5/6 c (fma.f64 z (sqrt.f64 (/.f64 1 t)) (.f64 2/3 (/.f64 b t)))) (fma.f64 5/6 b (.f64 2/3 (/.f64 c t))))

series79.0ms (0.7%)

Counts

4 → 64

Calls

4 calls:

45.0ms	(-.f64 (fma.f64 5/6 c (fma.f64 z (sqrt.f64 (/.f64 1 t)) (.f64 2/3 (/.f64 b t)))) (fma.f64 5/6 b (.f64 2/3 (/.f64 c t))))
20.0ms	(fma.f64 z (sqrt.f64 (/.f64 1 t)) (*.f64 2/3 (/.f64 b t)))
7.0ms	(*.f64 2/3 (/.f64 c t))
7.0ms	(*.f64 2/3 (/.f64 b t))

rewrite102.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

811×	`prod-diff_binary64`
190×	`add-sqr-sqrt_binary64`
178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`
176×	`add-cbrt-cube_binary64`

Counts

4 → 122

Calls

4 calls:

99.0ms	(*.f64 2/3 (/.f64 b t))
99.0ms	(*.f64 2/3 (/.f64 c t))
99.0ms	(fma.f64 z (sqrt.f64 (/.f64 1 t)) (*.f64 2/3 (/.f64 b t)))
99.0ms	(-.f64 (fma.f64 5/6 c (fma.f64 z (sqrt.f64 (/.f64 1 t)) (.f64 2/3 (/.f64 b t)))) (fma.f64 5/6 b (.f64 2/3 (/.f64 c t))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	63
1	384	59
2	4730	59
3	6306	59
0	0	0
1	0	0

simplify203.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

3115×	`fma-neg_binary64`
615×	`fma-def_binary64`
529×	`sub-neg_binary64`
408×	`associate-+l-_binary64`
332×	`unsub-neg_binary64`

Counts

186 → 143

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	1384
1	124	1322
2	304	1266
3	621	1182
4	1762	1070
5	2273	1070
6	2444	1070
7	2517	1070
8	2533	1070
9	2533	1070
10	2828	1070
11	2623	1070
12	2591	1070
13	2591	1070
14	5431	1070

prune174.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	143	3	146

Error

Counts

146 → 3

Alt Table

Status	Error	Program
✓	25.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (-.f64 (fma.f64 5/6 c (fma.f64 z (sqrt.f64 (/.f64 1 t)) (.f64 2/3 (/.f64 b t)))) (fma.f64 5/6 b (.f64 2/3 (/.f64 c t))))) x))
▶	26.5b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))
✓	20.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))

Compiler

Compiled 5613 to 3392 computations (39.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))
✓	0.1b	(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))
✓	0.3b	(*.f64 c -2/3)
✓	2.0b	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)

series78.0ms (0.7%)

Counts

4 → 123

Calls

4 calls:

45.0ms	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)
20.0ms	(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))
11.0ms	(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))
1.0ms	(*.f64 c -2/3)

rewrite67.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

595×	`log-prod_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
211×	`log-pow_binary64`
203×	`prod-diff_binary64`

Counts

4 → 115

Calls

4 calls:

65.0ms	(fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3)))
65.0ms	(fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))
65.0ms	(*.f64 c -2/3)
65.0ms	(/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	263	45
2	3001	45
3	5436	45
0	0	0
1	0	0

simplify172.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1339×	`fma-neg_binary64`
622×	`fma-def_binary64`
370×	`cancel-sign-sub-inv_binary64`
197×	`distribute-rgt-in_binary64`
192×	`unsub-neg_binary64`

Counts

238 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	1707
1	80	1535
2	177	1508
3	351	1391
4	677	1391
5	1259	1391
6	1818	1391
7	1906	1391
8	2164	1391
9	2164	1391
10	2177	1391
11	2181	1391
12	2181	1391
13	2080	1391

prune139.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	140	3	143

Error

Counts

143 → 3

Alt Table

Status	Error	Program
✓	25.2b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (-.f64 (fma.f64 5/6 c (fma.f64 z (sqrt.f64 (/.f64 1 t)) (.f64 2/3 (/.f64 b t)))) (fma.f64 5/6 b (.f64 2/3 (/.f64 c t))))) x))
✓	26.5b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (/.f64 (fma.f64 2/3 b (fma.f64 z (sqrt.f64 a) (*.f64 c -2/3))) t)) x))
✓	20.1b	(/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (*.f64 (+.f64 a 5/6) (-.f64 c b))) x))

Compiler

Compiled 3596 to 2132 computations (40.7% saved)

regimes2.5s (23.8%)

Accuracy

Total 1.8b remaining (90.6%)

Threshold costs 0b (0%)

Counts

162 → 1

Compiler

Compiled 63243 to 45726 computations (27.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	40
1	35	40
2	45	40
3	49	40
4	51	40
5	49	40

end90.0ms (0.8%)

Compiler: Compiled 155 to 108 computations (30.3% saved)

Details

analyze2.3s (21.5%)

sample3.1s (28.9%)

simplify48.0ms (0.4%)

prune5.0ms (0%)

localize21.0ms (0.2%)

series132.0ms (1.2%)

rewrite77.0ms (0.7%)

simplify112.0ms (1.1%)

prune232.0ms (2.2%)

localize11.0ms (0.1%)

series371.0ms (3.5%)

rewrite77.0ms (0.7%)

simplify165.0ms (1.6%)

prune341.0ms (3.2%)

localize21.0ms (0.2%)

series79.0ms (0.7%)

rewrite102.0ms (1%)

simplify203.0ms (1.9%)

prune174.0ms (1.6%)

localize15.0ms (0.1%)

series78.0ms (0.7%)

rewrite67.0ms (0.6%)

simplify172.0ms (1.6%)

prune139.0ms (1.3%)

regimes2.5s (23.8%)

simplify6.0ms (0.1%)

end90.0ms (0.8%)

Profiling