Details

analyze111.0ms (4.5%)

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
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	18.7%	12.6%	7
68.7%	12.5%	18.8%	8
68.7%	12.5%	18.8%	9
68.7%	9.4%	22%	10
68.7%	9.4%	22%	11
68.7%	7.8%	23.5%	12
68.7%	7.8%	23.5%	13
68.7%	7%	24.3%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample19.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	20×	body	128	overflowed

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	8	13
2	8	13

prune2.0ms (0.1%)

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

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series36.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
5×	`distribute-lft-out_binary64`

Counts

2 → 52

Calls

2 calls:

5.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify86.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-neg_binary64`
536×	`times-frac_binary64`
493×	`fma-def_binary64`
389×	`associate-/l*_binary64`
245×	`associate-/r*_binary64`

Counts

100 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	1981
1	449	1869
2	1403	1853
3	4915	1853
4	5640	1853

prune100.0ms (4.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	103	5	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	5	109

Error

0.2b

Counts

109 → 5

Alt Table

Status	Error	Program
	8.6b	(/.f64 1 (+.f64 1 (exp.f64 b)))
	20.9b	(.f64 (/.f64 (exp.f64 a) (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3))) (+.f64 (.f64 (exp.f64 a) (exp.f64 a)) (-.f64 (.f64 (exp.f64 b) (exp.f64 b)) (.f64 (exp.f64 a) (exp.f64 b)))))
	0.8b	(*.f64 (exp.f64 a) (/.f64 1 (+.f64 (exp.f64 a) (exp.f64 b))))
▶	0.8b	(/.f64 1 (/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (exp.f64 a)))
	22.7b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))

Compiler

Compiled 2367 to 903 computations (61.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.0b	(/.f64 1 (/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (exp.f64 a)))
✓	0.7b	(/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (exp.f64 a))

series48.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(/.f64 1 (/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (exp.f64 a)))
16.0ms	(/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (exp.f64 a))

rewrite27.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
92×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

2 → 125

Calls

2 calls:

11.0ms	(/.f64 1 (/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (exp.f64 a)))
6.0ms	(/.f64 (+.f64 (exp.f64 a) (exp.f64 b)) (exp.f64 a))

simplify142.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

794×	`times-frac_binary64`
487×	`fma-def_binary64`
362×	`fma-neg_binary64`
211×	`associate-/r/_binary64`
194×	`distribute-rgt-in_binary64`

Counts

173 → 194

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	212	4260
1	539	3945
2	1748	3867
3	4460	3864
4	5013	3864

prune193.0ms (7.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	233	5	238

Error

Counts

238 → 5

Alt Table

Status	Error	Program
	22.5b	(/.f64 1 (+.f64 1 (*.f64 (exp.f64 (neg.f64 a)) (+.f64 b 1))))
	20.9b	(.f64 (/.f64 (exp.f64 a) (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3))) (+.f64 (.f64 (exp.f64 a) (exp.f64 a)) (-.f64 (.f64 (exp.f64 b) (exp.f64 b)) (.f64 (exp.f64 a) (exp.f64 b)))))
	8.6b	(/.f64 1 (+.f64 1 (exp.f64 b)))
▶	0.8b	(*.f64 (exp.f64 a) (/.f64 1 (+.f64 (exp.f64 a) (exp.f64 b))))
	22.7b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))

Compiler

Compiled 5173 to 1825 computations (64.7% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.0b	(/.f64 1 (+.f64 (exp.f64 a) (exp.f64 b)))
✓	0.7b	(*.f64 (exp.f64 a) (/.f64 1 (+.f64 (exp.f64 a) (exp.f64 b))))

series61.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

33.0ms	(*.f64 (exp.f64 a) (/.f64 1 (+.f64 (exp.f64 a) (exp.f64 b))))
28.0ms	(/.f64 1 (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite20.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

2 → 82

Calls

2 calls:

10.0ms	(*.f64 (exp.f64 a) (/.f64 1 (+.f64 (exp.f64 a) (exp.f64 b))))
5.0ms	(/.f64 1 (+.f64 (exp.f64 a) (exp.f64 b)))

simplify107.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

818×	`times-frac_binary64`
528×	`fma-def_binary64`
510×	`associate-/l*_binary64`
486×	`fma-neg_binary64`
198×	`distribute-rgt-in_binary64`

Counts

130 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	2760
1	504	2537
2	1731	2510
3	4999	2510
4	5324	2510

prune168.0ms (6.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	180	4	184

Error

Counts

184 → 4

Alt Table

Status	Error	Program
	22.5b	(/.f64 1 (+.f64 1 (*.f64 (exp.f64 (neg.f64 a)) (+.f64 b 1))))
	20.9b	(.f64 (/.f64 (exp.f64 a) (+.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (exp.f64 b) 3))) (+.f64 (.f64 (exp.f64 a) (exp.f64 a)) (-.f64 (.f64 (exp.f64 b) (exp.f64 b)) (.f64 (exp.f64 a) (exp.f64 b)))))
▶	8.6b	(/.f64 1 (+.f64 1 (exp.f64 b)))
	22.7b	(*.f64 (exp.f64 a) (-.f64 (/.f64 1 (+.f64 1 (exp.f64 a))) (/.f64 b (pow.f64 (+.f64 1 (exp.f64 a)) 2))))

Compiler

Compiled 4123 to 1874 computations (54.5% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series9.0ms (0.4%)

Counts

2 → 8

Calls

2 calls:

8.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
2.0ms	(+.f64 1 (exp.f64 b))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
6×	`add-exp-log_binary64`

Counts

2 → 56

Calls

2 calls:

4.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
3.0ms	(+.f64 1 (exp.f64 b))

simplify74.0ms (3%)

Algorithm

1×	egg-herbie

Rules

561×	`fma-neg_binary64`
525×	`fma-def_binary64`
498×	`unswap-sqr_binary64`
428×	`associate-+l+_binary64`
349×	`cancel-sign-sub-inv_binary64`

Counts

64 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	733
1	185	669
2	382	663
3	887	653
4	2169	653
5	3922	653
6	5318	653

prune51.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	76	3	79

Error

Counts

79 → 3

Alt Table

Status	Error	Program
	8.6b	(exp.f64 (neg.f64 (log1p.f64 (exp.f64 b))))
	22.7b	(*.f64 (exp.f64 a) (-.f64 (/.f64 1 (+.f64 1 (exp.f64 a))) (/.f64 b (pow.f64 (+.f64 1 (exp.f64 a)) 2))))
	22.5b	(/.f64 1 (+.f64 1 (*.f64 (exp.f64 (neg.f64 a)) (+.f64 b 1))))

Compiler

Compiled 910 to 666 computations (26.8% saved)

regimes546.0ms (22.2%)

Accuracy

Total 0.5b remaining (96.1%)

Threshold costs 0.5b (96.1%)

Counts

136 → 1

Compiler

Compiled 11955 to 8121 computations (32.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`cancel-sign-sub-inv_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-neg-in_binary64`
4×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	17	17
2	25	17
3	37	15
4	48	15
5	51	15
6	47	15

end0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample603.0ms (24.6%)

Algorithm

1×

intervals

Results

295.0ms	8000×	body	128	valid
22.0ms	670×	body	128	overflowed

Compiler

Compiled 64 to 48 computations (25% saved)

Details

analyze111.0ms (4.5%)

sample19.0ms (0.8%)

simplify8.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series36.0ms (1.5%)

rewrite11.0ms (0.4%)

simplify86.0ms (3.5%)

prune100.0ms (4.1%)

localize6.0ms (0.2%)

series48.0ms (1.9%)

rewrite27.0ms (1.1%)

simplify142.0ms (5.8%)

prune193.0ms (7.8%)

localize6.0ms (0.3%)

series61.0ms (2.5%)

rewrite20.0ms (0.8%)

simplify107.0ms (4.4%)

prune168.0ms (6.8%)

localize4.0ms (0.1%)

series9.0ms (0.4%)

rewrite9.0ms (0.4%)

simplify74.0ms (3%)

prune51.0ms (2.1%)

regimes546.0ms (22.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample603.0ms (24.6%)

Profiling