Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50%	0.4%	49.6%	10
50.2%	0.2%	49.6%	11
50.2%	0.1%	49.7%	12
50.2%	0%	49.8%	13
50.2%	0%	49.8%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.9s (64%)

Results

2.8s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess43.0ms (1%)

Algorithm

2×	egg-herbie

Rules

1715×	`pow-sqr_binary64`
988×	`sqr-pow_binary64`
1×	`exp-1-e_binary64`
1×	`1-exp_binary64`
1×	`exp-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	11	11
2	14	11
3	17	11
4	21	11
5	26	11
6	34	11
7	49	11
8	75	11
9	125	11
10	215	11
11	390	11
12	712	11
13	1342	11
14	2518	11
15	4828	11
16	4828	11
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 8 to 6 computations (25% saved)

simplify33.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1715×	`pow-sqr_binary64`
988×	`sqr-pow_binary64`
1×	`exp-1-e_binary64`
1×	`1-exp_binary64`
1×	`exp-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	11	11
2	14	11
3	17	11
4	21	11
5	26	11
6	34	11
7	49	11
8	75	11
9	125	11
10	215	11
11	390	11
12	712	11
13	1342	11
14	2518	11
15	4828	11
16	4828	11

Stop Event

1×	node limit

Counts

1 → 1

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

1.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))	x	0
1.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))	x	inf
1.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))	x	-inf

rewrite26.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`log1p-expm1-u_binary64`
503×	`expm1-log1p-u_binary64`
200×	`unpow-prod-down_binary64`
162×	`pow2_binary64`
152×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	129	11
2	1324	11

Stop Event

1×	node limit

Counts

1 → 39

simplify42.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1203×	`sqr-pow_binary64`
1012×	`pow-sqr_binary64`
12×	`cube-mult_binary64`
12×	`exp-prod_binary64`
12×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	153
1	42	137
2	60	137
3	81	137
4	110	137
5	151	137
6	207	137
7	293	137
8	430	137
9	661	137
10	1068	137
11	1801	137
12	3165	137
13	3171	137
14	3173	137
15	3173	137

Stop Event

1×	node limit

Counts

51 → 48

prune38.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Error

0.0b

Counts

49 → 4

Alt Table

Status	Error	Program
	0.3b	(log1p.f64 (expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))))
	0.3b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (exp.f64 (neg.f64 (-.f64 1 (.f64 x x))))))) (log.f64 (sqrt.f64 (exp.f64 (exp.f64 (neg.f64 (-.f64 1 (.f64 x x))))))))
▶	0.0b	(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) -2))
	63.8b	(pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (-.f64 1 (.f64 x x))))) (sqrt.f64 (sqrt.f64 (neg.f64 (-.f64 1 (.f64 x x)))))) (sqrt.f64 (sqrt.f64 (neg.f64 (-.f64 1 (*.f64 x x))))))

Compiler

Compiled 916 to 652 computations (28.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (-.f64 1 (*.f64 x x)))
✓	0.0b	(pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) -2)

series26.0ms (0.6%)

Counts

2 → 24

Calls

6 calls:

11.0ms	(pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) -2)	x	-inf
10.0ms	(pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) -2)	x	inf
3.0ms	(pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) -2)	x	0
1.0ms	(exp.f64 (-.f64 1 (*.f64 x x)))	x	0
1.0ms	(exp.f64 (-.f64 1 (*.f64 x x)))	x	inf

rewrite33.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

584×	`log1p-expm1-u_binary64`
584×	`expm1-log1p-u_binary64`
258×	`unpow-prod-down_binary64`
186×	`pow2_binary64`
173×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	157	21
2	1569	21

Stop Event

1×	node limit

Counts

2 → 48

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1378×	`sqr-pow_binary64`
1137×	`pow-sqr_binary64`
13×	`exp-prod_binary64`
12×	`cube-mult_binary64`
12×	`unpow3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	468
1	85	436
2	107	416
3	141	416
4	177	416
5	225	416
6	290	416
7	388	416
8	544	416
9	805	416
10	1266	416
11	2093	416
12	3636	416
13	3642	416
14	3644	416
15	3644	416

Stop Event

1×	node limit

Counts

72 → 68

prune69.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	70	2	72

Error

Counts

72 → 2

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (.f64 x x))) 2)) 2) -1) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)) -1)))
	0.3b	(log1p.f64 (expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))))

Status

Error

Program

▶

0.0b

(sqrt.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)) 2) -1) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)) -1)))

0.3b

(log1p.f64 (expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))))

Compiler

Compiled 1310 to 1005 computations (23.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(exp.f64 (-.f64 1 (*.f64 x x)))
✓	1.0b	(pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)) 2)
✓	1.0b	(cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2))
✓	1.0b	(pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)

series214.0ms (4.8%)

Counts

3 → 36

Calls

9 calls:

46.0ms	(pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)) 2)	x	-inf
44.0ms	(cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2))	x	inf
43.0ms	(pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)) 2)	x	inf
41.0ms	(cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2))	x	-inf
19.0ms	(pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)) 2)	x	0

rewrite38.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

637×	`log1p-expm1-u_binary64`
637×	`expm1-log1p-u_binary64`
190×	`log-prod_binary64`
150×	`log-pow_binary64`
141×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	190	40
2	1821	38

Stop Event

1×	node limit

Counts

3 → 54

simplify92.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1312×	`sqr-pow_binary64`
921×	`pow-sqr_binary64`
20×	`fma-def_binary64`
13×	`exp-prod_binary64`
12×	`unpow1/3_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	129	1084
1	229	1034
2	299	991
3	372	949
4	451	910
5	542	910
6	645	910
7	785	910
8	987	910
9	1307	910
10	1843	910
11	2790	910
12	3420	910
13	3422	910
14	3422	910

Stop Event

1×	node limit

Counts

90 → 83

prune262.0ms (5.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	210	2	212

Error

Counts

212 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (.f64 x x))) 2)) 2) -1) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)) -1)))
▶	0.3b	(log1p.f64 (expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))))

Status

Error

Program

✓

0.0b

(sqrt.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)) 2) -1) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)) -1)))

▶

0.3b

(log1p.f64 (expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))))

Compiler

Compiled 7433 to 5929 computations (20.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))))
	0.0b	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
✓	1.0b	(expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x)))))

series8.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

3.0ms	(expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x)))))	x	0
2.0ms	(expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x)))))	x	inf
1.0ms	(expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x)))))	x	-inf
1.0ms	(log1p.f64 (expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))))	x	0
1.0ms	(log1p.f64 (expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))))	x	-inf

rewrite36.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

568×	`expm1-log1p-u_binary64`
567×	`log1p-expm1-u_binary64`
225×	`unpow-prod-down_binary64`
181×	`pow2_binary64`
172×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	150	24
2	1495	24

Stop Event

1×	node limit

Counts

2 → 51

simplify76.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1412×	`sqr-pow_binary64`
1004×	`pow-sqr_binary64`
170×	`exp-prod_binary64`
23×	`fma-def_binary64`
22×	`cube-mult_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	59	465
1	96	424
2	123	421
3	159	421
4	205	421
5	273	421
6	371	421
7	528	421
8	785	421
9	1237	421
10	2049	421
11	3571	421
12	3723	421
13	3729	421
14	3731	421
15	3731	421

Stop Event

1×	node limit

Counts

75 → 70

prune89.0ms (2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	118	2	120

Error

Counts

120 → 2

Alt Table

Status

Error

Program

✓

0.0b

(sqrt.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)) 2) -1) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (-.f64 1 (*.f64 x x))) 2)) -1)))

✓

0.3b

(log1p.f64 (expm1.f64 (exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))))

Compiler

Compiled 2168 to 1653 computations (23.8% saved)

regimes297.0ms (6.6%)

Accuracy

Total 0.0b remaining (19.8%)

Threshold costs 0.0b (19.8%)

Counts

77 → 1

Compiler

Compiled 6542 to 5247 computations (19.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	17	41

Stop Event

1×

saturated

end74.0ms (1.7%)

Stop Event

1×

done

Compiler

Compiled 91 to 74 computations (18.7% saved)

Details

analyze4.0ms (0.1%)

sample2.9s (64%)

preprocess43.0ms (1%)

simplify33.0ms (0.7%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite26.0ms (0.6%)

simplify42.0ms (0.9%)

prune38.0ms (0.9%)

localize7.0ms (0.1%)

series26.0ms (0.6%)

rewrite33.0ms (0.7%)

simplify66.0ms (1.5%)

prune69.0ms (1.6%)

localize13.0ms (0.3%)

series214.0ms (4.8%)

rewrite38.0ms (0.9%)

simplify92.0ms (2.1%)

prune262.0ms (5.9%)

localize9.0ms (0.2%)

series8.0ms (0.2%)

rewrite36.0ms (0.8%)

simplify76.0ms (1.7%)

prune89.0ms (2%)

regimes297.0ms (6.6%)

simplify2.0ms (0.1%)

end74.0ms (1.7%)

Profiling