Details

analyze795.0ms (15.4%)

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
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample2.8s (54.8%)

Results

1.1s	1750×	body	1024	valid
657.0ms	4756×	body	128	valid
411.0ms	1019×	body	512	valid
187.0ms	183×	body	2048	valid
163.0ms	548×	body	256	valid
121.0ms	191×	body	1024	invalid
101.0ms	237×	body	512	invalid
46.0ms	391×	body	128	invalid
33.0ms	133×	body	256	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess40.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

1472×	`sqr-pow_binary64`
1342×	`pow-sqr_binary64`
2×	`exp-prod_binary64`
2×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	25	34
2	32	34
3	42	34
4	58	34
5	88	34
6	140	34
7	240	34
8	420	34
9	770	34
10	1414	34
11	2674	34
12	3514	34
13	3514	34
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify35.0ms (0.7%)

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	9	17
1	14	17
2	18	17
3	23	17
4	31	17
5	46	17
6	72	17
7	122	17
8	212	17
9	387	17
10	709	17
11	1339	17
12	2515	17
13	4825	17
14	4825	17

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

5.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.5b	(/.f64 (pow.f64 (exp.f64 x) (log.f64 (/.f64 x (+.f64 x y)))) x)
	12.4b	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)

Compiler

Compiled 76 to 43 computations (43.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (exp.f64 x) (log.f64 (/.f64 x (+.f64 x y)))) x)
✓	0.0b	(/.f64 x (+.f64 x y))
✓	0.2b	(pow.f64 (exp.f64 x) (log.f64 (/.f64 x (+.f64 x y))))
✓	10.0b	(log.f64 (/.f64 x (+.f64 x y)))

series84.0ms (1.6%)

Counts

4 → 96

Calls

24 calls:

11.0ms	(/.f64 (pow.f64 (exp.f64 x) (log.f64 (/.f64 x (+.f64 x y)))) x)	x	-inf
8.0ms	(/.f64 (pow.f64 (exp.f64 x) (log.f64 (/.f64 x (+.f64 x y)))) x)	y	-inf
8.0ms	(pow.f64 (exp.f64 x) (log.f64 (/.f64 x (+.f64 x y))))	y	-inf
6.0ms	(/.f64 (pow.f64 (exp.f64 x) (log.f64 (/.f64 x (+.f64 x y)))) x)	x	inf
6.0ms	(/.f64 (pow.f64 (exp.f64 x) (log.f64 (/.f64 x (+.f64 x y)))) x)	y	inf

rewrite47.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

750×	`log1p-expm1-u_binary64`
750×	`expm1-log1p-u_binary64`
167×	`expm1-udef_binary64`
167×	`log1p-udef_binary64`
94×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	47
1	175	47
2	1940	47

Stop Event

1×	node limit

Counts

4 → 75

simplify149.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

488×	`pow-sqr_binary64`
448×	`fma-def_binary64`
407×	`sqr-pow_binary64`
269×	`div-exp_binary64`
266×	`prod-exp_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	296	3765
1	408	3765
2	452	3457
3	533	3457
4	667	3457
5	894	3365
6	1306	3365
7	2050	3365
8	3565	3365

Stop Event

1×	node limit

Counts

171 → 164

prune140.0ms (2.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	162	4	166

Error

0.0b

Counts

166 → 4

Alt Table

Status	Error	Program
▶	11.3b	(/.f64 (pow.f64 (exp.f64 x) (*.f64 -1 (/.f64 y x))) x)
	12.4b	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
	35.9b	(-.f64 (fma.f64 1/2 (/.f64 (.f64 y y) (.f64 x x)) (+.f64 (/.f64 1 x) (.f64 1/2 (/.f64 (.f64 y y) x)))) (+.f64 (/.f64 y x) (fma.f64 1/6 (/.f64 (pow.f64 y 3) x) (fma.f64 1/3 (/.f64 (pow.f64 y 3) (pow.f64 x 3)) (.f64 1/2 (/.f64 (pow.f64 y 3) (.f64 x x)))))))
	33.6b	(/.f64 (-.f64 (+.f64 1 (fma.f64 1/2 (.f64 y y) (.f64 1/2 (/.f64 (.f64 y y) x)))) (+.f64 y (fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/2 (/.f64 (pow.f64 y 3) x) (.f64 1/3 (/.f64 (pow.f64 y 3) (*.f64 x x))))))) x)

Compiler

Compiled 5341 to 2690 computations (49.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (exp.f64 x) (*.f64 -1 (/.f64 y x))) x)
✓	12.8b	(pow.f64 (exp.f64 x) (*.f64 -1 (/.f64 y x)))

series46.0ms (0.9%)

Counts

2 → 48

Calls

12 calls:

21.0ms	(pow.f64 (exp.f64 x) (*.f64 -1 (/.f64 y x)))	x	0
9.0ms	(/.f64 (pow.f64 (exp.f64 x) (*.f64 -1 (/.f64 y x))) x)	x	0
3.0ms	(/.f64 (pow.f64 (exp.f64 x) (*.f64 -1 (/.f64 y x))) x)	y	0
3.0ms	(/.f64 (pow.f64 (exp.f64 x) (*.f64 -1 (/.f64 y x))) x)	x	-inf
2.0ms	(/.f64 (pow.f64 (exp.f64 x) (*.f64 -1 (/.f64 y x))) x)	x	inf

rewrite36.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

672×	`log1p-expm1-u_binary64`
672×	`expm1-log1p-u_binary64`
214×	`log-prod_binary64`
180×	`log-pow_binary64`
155×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	167	27
2	1760	25

Stop Event

1×	node limit

Counts

2 → 38

simplify74.0ms (1.4%)

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	35	502
1	52	502
2	65	502
3	87	502
4	120	502
5	166	502
6	234	502
7	342	502
8	520	502
9	834	502
10	1389	502
11	2428	502
12	4339	502
13	4345	502
14	4347	502
15	4347	502

Stop Event

1×	node limit

Counts

86 → 56

prune33.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	56	4	60

Error

Counts

60 → 4

Alt Table

Status	Error	Program
	13.8b	(/.f64 (exp.f64 (neg.f64 y)) x)
✓	11.3b	(/.f64 (pow.f64 (exp.f64 x) (*.f64 -1 (/.f64 y x))) x)
▶	12.4b	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
	23.6b	(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 (pow.f64 y 2) x))) (/.f64 y x))

Compiler

Compiled 863 to 316 computations (63.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
	0.0b	(/.f64 x (+.f64 x y))
✓	0.1b	(*.f64 x (log.f64 (/.f64 x (+.f64 x y))))
	10.0b	(log.f64 (/.f64 x (+.f64 x y)))

series52.0ms (1%)

Counts

2 → 48

Calls

12 calls:

8.0ms	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)	y	-inf
8.0ms	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)	x	-inf
6.0ms	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)	x	inf
5.0ms	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)	x	0
5.0ms	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)	y	inf

rewrite32.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

719×	`log1p-expm1-u_binary64`
719×	`expm1-log1p-u_binary64`
164×	`expm1-udef_binary64`
164×	`log1p-udef_binary64`
91×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	168	29
2	1842	29

Stop Event

1×	node limit

Counts

2 → 32

simplify267.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

554×	`pow-sqr_binary64`
458×	`sqr-pow_binary64`
405×	`fma-def_binary64`
238×	`div-exp_binary64`
236×	`prod-exp_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	228	2292
1	328	2292
2	377	2138
3	460	2138
4	602	2138
5	843	2092
6	1261	2092
7	2030	2092
8	3540	2092

Stop Event

1×	node limit

Counts

80 → 90

prune116.0ms (2.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	168	4	172

Error

Counts

172 → 4

Alt Table

Status	Error	Program
▶	13.8b	(/.f64 (exp.f64 (neg.f64 y)) x)
✓	11.3b	(/.f64 (pow.f64 (exp.f64 x) (*.f64 -1 (/.f64 y x))) x)
✓	12.4b	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
	23.6b	(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 (pow.f64 y 2) x))) (/.f64 y x))

Compiler

Compiled 4616 to 2356 computations (49% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.1%)

Counts

1 → 8

Calls

6 calls:

1.0ms	(/.f64 (exp.f64 (neg.f64 y)) x)	y	inf
1.0ms	(/.f64 (exp.f64 (neg.f64 y)) x)	y	-inf
1.0ms	(/.f64 (exp.f64 (neg.f64 y)) x)	x	-inf
1.0ms	(/.f64 (exp.f64 (neg.f64 y)) x)	y	0
1.0ms	(/.f64 (exp.f64 (neg.f64 y)) x)	x	inf

rewrite29.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

426×	`log1p-expm1-u_binary64`
426×	`expm1-log1p-u_binary64`
408×	`pow1_binary64`
163×	`unpow-prod-down_binary64`
144×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	107	8
2	1121	8

Stop Event

1×	node limit

Counts

1 → 32

simplify41.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1070×	`sqr-pow_binary64`
954×	`pow-sqr_binary64`
12×	`cube-mult_binary64`
12×	`unpow3_binary64`
11×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	106
1	40	106
2	53	106
3	72	106
4	100	106
5	136	106
6	186	106
7	261	106
8	380	106
9	585	106
10	941	106
11	1606	106
12	2821	106
13	2825	106
14	2827	106
15	2827	106

Stop Event

1×	node limit

Counts

40 → 40

prune20.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	40	4	44

Error

Counts

44 → 4

Alt Table

Status	Error	Program
✓	13.8b	(/.f64 (exp.f64 (neg.f64 y)) x)
✓	11.3b	(/.f64 (pow.f64 (exp.f64 x) (*.f64 -1 (/.f64 y x))) x)
✓	12.4b	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
	23.6b	(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 (pow.f64 y 2) x))) (/.f64 y x))

Compiler

Compiled 500 to 222 computations (55.6% saved)

regimes185.0ms (3.6%)

Accuracy

Total 1.0b remaining (98.3%)

Threshold costs 0b (0%)

Counts

28 → 5

Compiler

Compiled 1718 to 1110 computations (35.4% saved)

bsearch1.0ms (0%)

Algorithm

4×	left-value

Calls

4 calls:

0.0ms	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
0.0ms	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
0.0ms	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
0.0ms	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)

Steps

Iters	Point		Range
3.046188998270413e-149	∈ [	3.046188998270413e-149	,	5.901007701065366e-138	]
0.0	∈ [	0.0	,	3.905334600301685e-304	]
-4.399415670006494e-261	∈ [	-4.399415670006494e-261	,	-3.1732365587264064e-273	]
-234.66687405323307	∈ [	-234.66687405323307	,	-2.0576704916754465	]

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	178

Stop Event

1×

saturated

end76.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 279 to 109 computations (60.9% saved)

Details

analyze795.0ms (15.4%)

sample2.8s (54.8%)

preprocess40.0ms (0.8%)

simplify35.0ms (0.7%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series84.0ms (1.6%)

rewrite47.0ms (0.9%)

simplify149.0ms (2.9%)

prune140.0ms (2.7%)

localize6.0ms (0.1%)

series46.0ms (0.9%)

rewrite36.0ms (0.7%)

simplify74.0ms (1.4%)

prune33.0ms (0.6%)

localize7.0ms (0.1%)

series52.0ms (1%)

rewrite32.0ms (0.6%)

simplify267.0ms (5.2%)

prune116.0ms (2.2%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite29.0ms (0.6%)

simplify41.0ms (0.8%)

prune20.0ms (0.4%)

regimes185.0ms (3.6%)

bsearch1.0ms (0%)

simplify3.0ms (0%)

end76.0ms (1.5%)

Profiling