Details

analyze460.0ms (16.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.6s (55.5%)

Results

826.0ms	2730×	body	1024	valid
282.0ms	1348×	body	512	valid
245.0ms	3199×	body	128	valid
110.0ms	312×	body	2048	valid
97.0ms	667×	body	256	valid
0.0ms	1×	body	2048	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 18 to 12 computations (33.3% saved)

preprocess14.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

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

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 25 to 15 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

series11.0ms (0.4%)

Counts

1 → 12

Calls

3 calls:

6.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))	x	inf
4.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))	x	-inf
1.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))	x	0

rewrite33.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

477×	`log1p-expm1-u_binary64`
477×	`expm1-log1p-u_binary64`
332×	`unpow-prod-down_binary64`
258×	`log-prod_binary64`
131×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	99	8
2	1299	8

Stop Event

1×	node limit

Counts

1 → 66

simplify33.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1089×	`fma-neg_binary64`
754×	`fma-def_binary64`
260×	`cancel-sign-sub-inv_binary64`
211×	`associate-l_binary64`
208×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	110
1	46	106
2	101	104
3	306	104
4	830	104
5	1782	104
6	3144	104
7	4892	104

Stop Event

1×	node limit

Counts

78 → 75

prune30.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	2	76

Error

0.4b

Counts

76 → 2

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	23.1b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 982 to 430 computations (56.2% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (/.f64 1 x))

series1.0ms (0%)

Counts

1 → 3

Calls

3 calls:

1.0ms	(+.f64 1/2 (/.f64 1 x))	x	0
0.0ms	(+.f64 1/2 (/.f64 1 x))	x	-inf
0.0ms	(+.f64 1/2 (/.f64 1 x))	x	inf

rewrite32.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

588×	`log1p-expm1-u_binary64`
588×	`expm1-log1p-u_binary64`
241×	`log-prod_binary64`
109×	`expm1-udef_binary64`
109×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	130	7
2	1582	7

Stop Event

1×	node limit

Counts

1 → 38

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	7	6

Stop Event

1×

saturated

Counts

41 → 40

prune22.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	40	2	42

Error

0.4b

Counts

42 → 2

Alt Table

Status	Error	Program
▶	45.5b	(-.f64 (exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 1 x)))) 1)
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 439 to 366 computations (16.6% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1/2 (/.f64 1 x))
✓	0.0b	(log1p.f64 (+.f64 1/2 (/.f64 1 x)))
✓	0.0b	(-.f64 (exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 1 x)))) 1)
✓	1.8b	(exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 1 x))))

series25.0ms (0.9%)

Counts

3 → 36

Calls

9 calls:

5.0ms	(exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 1 x))))	x	0
4.0ms	(-.f64 (exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 1 x)))) 1)	x	0
4.0ms	(-.f64 (exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 1 x)))) 1)	x	-inf
4.0ms	(-.f64 (exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 1 x)))) 1)	x	inf
4.0ms	(exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 1 x))))	x	inf

rewrite99.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

834×	`expm1-log1p-u_binary64`
833×	`log1p-expm1-u_binary64`
201×	`prod-diff_binary64`
95×	`egg-rr`
85×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	180	23
2	2256	23

Stop Event

1×	node limit

Counts

3 → 95

simplify31.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

899×	`fma-neg_binary64`
543×	`cancel-sign-sub-inv_binary64`
277×	`associate-/l/_binary64`
276×	`fma-def_binary64`
170×	`sub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	45	567
1	117	407
2	290	306
3	772	303
4	2456	293

Stop Event

1×	node limit

Counts

131 → 119

prune91.0ms (3.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	159	2	161

Error

0.4b

Counts

161 → 2

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	62.2b	(-.f64 (exp.f64 (+.f64 (log.f64 3/2) (/.f64 2/3 x))) 1)

Compiler

Compiled 2091 to 1798 computations (14% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (+.f64 (log.f64 3/2) (/.f64 2/3 x)))
✓	0.0b	(+.f64 (log.f64 3/2) (/.f64 2/3 x))
✓	0.0b	(-.f64 (exp.f64 (+.f64 (log.f64 3/2) (/.f64 2/3 x))) 1)
✓	0.4b	(/.f64 2/3 x)

series14.0ms (0.5%)

Counts

4 → 36

Calls

12 calls:

3.0ms	(-.f64 (exp.f64 (+.f64 (log.f64 3/2) (/.f64 2/3 x))) 1)	x	inf
2.0ms	(+.f64 (log.f64 3/2) (/.f64 2/3 x))	x	-inf
2.0ms	(+.f64 (log.f64 3/2) (/.f64 2/3 x))	x	inf
1.0ms	(+.f64 (log.f64 3/2) (/.f64 2/3 x))	x	0
1.0ms	(-.f64 (exp.f64 (+.f64 (log.f64 3/2) (/.f64 2/3 x))) 1)	x	-inf

rewrite54.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

749×	`prod-diff_binary64`
265×	`fma-def_binary64`
179×	`expm1-udef_binary64`
179×	`log1p-udef_binary64`
176×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	219	32
2	2735	32

Stop Event

1×	node limit

Counts

4 → 131

simplify34.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

736×	`associate-/l*_binary64`
540×	`unswap-sqr_binary64`
465×	`fma-def_binary64`
358×	`associate-/r/_binary64`
258×	`associate-/r*_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	32	375
1	76	363
2	160	363
3	299	363
4	597	363
5	2082	355

Stop Event

1×	node limit

Counts

167 → 150

prune96.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	149	3	152

Error

0.4b

Counts

152 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
	62.2b	(-.f64 (fma.f64 (*.f64 (cbrt.f64 (fma.f64 3/2 (exp.f64 (/.f64 2/3 x)) 1)) (cbrt.f64 (fma.f64 3/2 (exp.f64 (/.f64 2/3 x)) 1))) (cbrt.f64 (fma.f64 3/2 (exp.f64 (/.f64 2/3 x)) 1)) -1) 1)
	62.2b	(-.f64 (cbrt.f64 (pow.f64 (*.f64 3/2 (exp.f64 (/.f64 2/3 x))) 3)) 1)

Compiler

Compiled 2153 to 1921 computations (10.8% saved)

regimes83.0ms (2.9%)

Accuracy

Total 0.1b remaining (18.1%)

Threshold costs 0.1b (18.1%)

Counts

37 → 1

Compiler

Compiled 1334 to 1153 computations (13.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8

Stop Event

1×

saturated

end61.0ms (2.1%)

Stop Event

1×

fuel

Compiler

Compiled 60 to 50 computations (16.7% saved)

Details

analyze460.0ms (16.2%)

sample1.6s (55.5%)

preprocess14.0ms (0.5%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series11.0ms (0.4%)

rewrite33.0ms (1.2%)

simplify33.0ms (1.2%)

prune30.0ms (1.1%)

localize3.0ms (0.1%)

series1.0ms (0%)

rewrite32.0ms (1.1%)

simplify6.0ms (0.2%)

prune22.0ms (0.8%)

localize7.0ms (0.3%)

series25.0ms (0.9%)

rewrite99.0ms (3.5%)

simplify31.0ms (1.1%)

prune91.0ms (3.2%)

localize6.0ms (0.2%)

series14.0ms (0.5%)

rewrite54.0ms (1.9%)

simplify34.0ms (1.2%)

prune96.0ms (3.4%)

regimes83.0ms (2.9%)

simplify2.0ms (0.1%)

end61.0ms (2.1%)

Profiling