Details

analyze1.8s (23.6%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
2.3%	91.3%	6.4%	9
3.5%	87%	9.5%	10
4.1%	86.4%	9.5%	11
18.4%	66.6%	15%	12
20.5%	61.8%	17.7%	13
21.9%	60.4%	17.7%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample3.4s (44.6%)

Results

1.3s	6327×	body	128	valid
699.0ms	961×	body	1024	valid
469.0ms	639×	body	512	valid
248.0ms	144×	body	256	invalid
246.0ms	1514×	body	128	invalid
147.0ms	327×	body	256	valid
136.0ms	198×	body	1024	invalid
114.0ms	251×	body	512	invalid
2.0ms	2×	body	2048	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess45.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

1096×	`sqr-pow_binary64`
1004×	`pow-sqr_binary64`
4×	`exp-prod_binary64`
4×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	80
1	50	80
2	63	80
3	83	80
4	115	80
5	175	80
6	279	80
7	479	80
8	839	80
9	1539	80
10	2827	80
11	2827	80
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1715×	`pow-sqr_binary64`
988×	`sqr-pow_binary64`
1×	`exp-prod_binary64`
1×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	16	20
2	20	20
3	25	20
4	33	20
5	48	20
6	74	20
7	124	20
8	214	20
9	389	20
10	711	20
11	1341	20
12	2517	20
13	4827	20
14	4827	20

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

1.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.2b	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y)))) y))
	4.8b	(+.f64 x (/.f64 (exp.f64 (*.f64 y (log.f64 (/.f64 y (+.f64 z y))))) y))

Compiler

Compiled 93 to 54 computations (41.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y)))) y))
✓	0.0b	(/.f64 y (+.f64 z y))
✓	0.1b	(pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y))))
✓	5.4b	(log.f64 (/.f64 y (+.f64 z y)))

series179.0ms (2.4%)

Counts

4 → 108

Calls

27 calls:

38.0ms	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y)))) y))	x	0
28.0ms	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y)))) y))	x	-inf
28.0ms	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y)))) y))	x	inf
9.0ms	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y)))) y))	y	0
8.0ms	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y)))) y))	z	inf

rewrite82.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

456×	`unpow-prod-down_binary64`
304×	`pow2_binary64`
299×	`log-prod_binary64`
226×	`log-pow_binary64`
214×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	50
1	218	50
2	2457	50

Stop Event

1×	node limit

Counts

4 → 121

simplify189.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

732×	`sqr-pow_binary64`
480×	`pow-sqr_binary64`
360×	`fma-def_binary64`
192×	`prod-exp_binary64`
132×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	289	3823
1	403	3823
2	448	3823
3	540	3823
4	675	3823
5	899	3823
6	1247	3823
7	1858	3823
8	2923	3823

Stop Event

1×	node limit

Counts

229 → 216

prune264.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	210	6	216
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	212	6	218

Error

0.0b

Counts

218 → 6

Alt Table

Status	Error	Program
	10.3b	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (*.f64 -1 (/.f64 z y))) y))
	14.4b	(-.f64 (+.f64 (/.f64 1 y) x) (/.f64 z y))
	27.8b	(+.f64 x (/.f64 (-.f64 (+.f64 1 (fma.f64 1/2 (.f64 z z) (.f64 1/2 (/.f64 (.f64 z z) y)))) (fma.f64 1/2 (/.f64 (pow.f64 z 3) y) (+.f64 z (fma.f64 1/6 (pow.f64 z 3) (.f64 1/3 (/.f64 (pow.f64 z 3) (*.f64 y y))))))) y))
	40.3b	(cbrt.f64 (pow.f64 (+.f64 x (/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y)))) y)) 3))
	31.2b	(pow.f64 (sqrt.f64 (+.f64 x (/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y)))) y))) 2)
▶	4.8b	(+.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x)

Compiler

Compiled 7083 to 3358 computations (52.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
✓	0.0b	(+.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x)
✓	0.0b	(/.f64 y (+.f64 y z))
✓	4.0b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series189.0ms (2.5%)

Counts

4 → 108

Calls

27 calls:

19.0ms	(+.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x)	x	0
15.0ms	(+.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x)	x	-inf
14.0ms	(+.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x)	x	inf
11.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)	y	-inf
11.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)	y	inf

rewrite51.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

845×	`log1p-expm1-u_binary64`
845×	`expm1-log1p-u_binary64`
102×	`add-sqr-sqrt_binary64`
97×	`add-cbrt-cube_binary64`
94×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	46
1	184	46
2	2135	46

Stop Event

1×	node limit

Counts

4 → 62

simplify234.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

792×	`sqr-pow_binary64`
519×	`pow-sqr_binary64`
420×	`fma-def_binary64`
192×	`prod-exp_binary64`
138×	`exp-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	362	5228
1	498	5228
2	543	5228
3	643	5228
4	788	5228
5	1029	5228
6	1401	5228
7	2056	5228
8	3193	5228

Stop Event

1×	node limit

Counts

170 → 182

prune245.0ms (3.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	182	6	188

Error

0.0b

Counts

188 → 6

Alt Table

Status	Error	Program
▶	10.3b	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (*.f64 -1 (/.f64 z y))) y))
	14.4b	(-.f64 (+.f64 (/.f64 1 y) x) (/.f64 z y))
	11.7b	(+.f64 (/.f64 (exp.f64 (neg.f64 z)) y) x)
✓	4.8b	(+.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x)
	40.2b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x) 3))
	31.2b	(pow.f64 (sqrt.f64 (+.f64 x (/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y)))) y))) 2)

Compiler

Compiled 6979 to 3641 computations (47.8% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (*.f64 -1 (/.f64 z y))) y))
✓	11.9b	(pow.f64 (exp.f64 y) (*.f64 -1 (/.f64 z y)))

series93.0ms (1.2%)

Counts

2 → 60

Calls

15 calls:

21.0ms	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (*.f64 -1 (/.f64 z y))) y))	x	0
16.0ms	(pow.f64 (exp.f64 y) (*.f64 -1 (/.f64 z y)))	y	0
15.0ms	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (*.f64 -1 (/.f64 z y))) y))	x	inf
15.0ms	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (*.f64 -1 (/.f64 z y))) y))	x	-inf
5.0ms	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (*.f64 -1 (/.f64 z y))) y))	y	inf

rewrite40.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

895×	`log1p-expm1-u_binary64`
895×	`expm1-log1p-u_binary64`
113×	`add-sqr-sqrt_binary64`
105×	`add-cbrt-cube_binary64`
104×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	211	30
2	2299	30

Stop Event

1×	node limit

Counts

2 → 32

simplify97.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1469×	`pow-sqr_binary64`
914×	`sqr-pow_binary64`
12×	`cube-mult_binary64`
12×	`exp-prod_binary64`
12×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	610
1	58	610
2	71	610
3	93	610
4	126	610
5	172	610
6	240	610
7	348	610
8	526	610
9	840	610
10	1395	610
11	2434	610
12	4345	610
13	4351	610
14	4353	610
15	4353	610

Stop Event

1×	node limit

Counts

92 → 54

prune42.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	54	6	60

Error

0.0b

Counts

60 → 6

Alt Table

Status	Error	Program
✓	10.3b	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (*.f64 -1 (/.f64 z y))) y))
	14.4b	(-.f64 (+.f64 (/.f64 1 y) x) (/.f64 z y))
▶	11.7b	(+.f64 (/.f64 (exp.f64 (neg.f64 z)) y) x)
✓	4.8b	(+.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x)
	40.2b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x) 3))
	31.2b	(pow.f64 (sqrt.f64 (+.f64 x (/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y)))) y))) 2)

Compiler

Compiled 951 to 527 computations (44.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (exp.f64 (neg.f64 z)) y) x)
✓	0.0b	(/.f64 (exp.f64 (neg.f64 z)) y)

series31.0ms (0.4%)

Counts

2 → 22

Calls

15 calls:

6.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)	y	-inf
2.0ms	(+.f64 (/.f64 (exp.f64 (neg.f64 z)) y) x)	z	-inf
2.0ms	(+.f64 (/.f64 (exp.f64 (neg.f64 z)) y) x)	z	inf
2.0ms	(+.f64 (/.f64 (exp.f64 (neg.f64 z)) y) x)	z	0
2.0ms	(+.f64 (/.f64 (exp.f64 (neg.f64 z)) y) x)	x	inf

rewrite53.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

649×	`log1p-expm1-u_binary64`
649×	`expm1-log1p-u_binary64`
205×	`log-prod_binary64`
155×	`log-pow_binary64`
150×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	151	19
2	1660	19

Stop Event

1×	node limit

Counts

2 → 42

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1469×	`pow-sqr_binary64`
914×	`sqr-pow_binary64`
12×	`cube-mult_binary64`
12×	`exp-prod_binary64`
12×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	252
1	54	252
2	67	252
3	88	252
4	121	252
5	167	252
6	235	252
7	343	252
8	521	252
9	835	252
10	1390	252
11	2429	252
12	4340	252
13	4346	252
14	4348	252
15	4348	252

Stop Event

1×	node limit

Counts

64 → 60

prune42.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	60	6	66

Error

Counts

66 → 6

Alt Table

Status	Error	Program
✓	10.3b	(+.f64 x (/.f64 (pow.f64 (exp.f64 y) (*.f64 -1 (/.f64 z y))) y))
	14.4b	(-.f64 (+.f64 (/.f64 1 y) x) (/.f64 z y))
✓	4.8b	(+.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x)
	34.8b	(+.f64 (exp.f64 (-.f64 (neg.f64 z) (log.f64 y))) x)
	40.2b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y) x) 3))
	31.2b	(pow.f64 (sqrt.f64 (+.f64 x (/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 z y)))) y))) 2)

Compiler

Compiled 846 to 340 computations (59.8% saved)

regimes283.0ms (3.7%)

Accuracy

Total 1.1b remaining (92.5%)

Threshold costs 0b (0%)

Counts

40 → 1

Compiler

Compiled 3232 to 2177 computations (32.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20

Stop Event

1×

saturated

end109.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 120 to 78 computations (35% saved)

Details

analyze1.8s (23.6%)

sample3.4s (44.6%)

preprocess45.0ms (0.6%)

simplify41.0ms (0.5%)

prune5.0ms (0.1%)

localize14.0ms (0.2%)

series179.0ms (2.4%)

rewrite82.0ms (1.1%)

simplify189.0ms (2.5%)

prune264.0ms (3.5%)

localize7.0ms (0.1%)

series189.0ms (2.5%)

rewrite51.0ms (0.7%)

simplify234.0ms (3.1%)

prune245.0ms (3.2%)

localize8.0ms (0.1%)

series93.0ms (1.2%)

rewrite40.0ms (0.5%)

simplify97.0ms (1.3%)

prune42.0ms (0.6%)

localize6.0ms (0.1%)

series31.0ms (0.4%)

rewrite53.0ms (0.7%)

simplify63.0ms (0.8%)

prune42.0ms (0.6%)

regimes283.0ms (3.7%)

simplify2.0ms (0%)

end109.0ms (1.4%)

Profiling