Details

analyze201.0ms (2.2%)

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)

sample36.0ms (0.4%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
1.0ms	22×	body	128	overflowed

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify13.0ms (0.1%)

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

prune3.0ms (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

0.8b

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)

localize10.0ms (0.1%)

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)))

series78.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

69.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
8.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite22.0ms (0.2%)

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:

10.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
6.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify167.0ms (1.9%)

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

prune181.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	3	109

Error

0.2b

Counts

109 → 3

Alt Table

Status	Error	Program
	23.6b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
	13.6b	(/.f64 1 (+.f64 1 (exp.f64 b)))
▶	0.8b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))

Compiler

Compiled 2285 to 855 computations (62.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 b) (exp.f64 a))
✓	0.1b	(sqrt.f64 (exp.f64 a))
✓	0.5b	(/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a)))
✓	0.7b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))

series164.0ms (1.8%)

Counts

4 → 60

Calls

4 calls:

82.0ms	(/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a)))
68.0ms	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
8.0ms	(+.f64 (exp.f64 b) (exp.f64 a))
5.0ms	(sqrt.f64 (exp.f64 a))

rewrite77.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
52×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
38×	`sqrt-prod_binary64`

Counts

4 → 143

Calls

4 calls:

31.0ms	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
14.0ms	(/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a)))
6.0ms	(+.f64 (exp.f64 b) (exp.f64 a))
3.0ms	(sqrt.f64 (exp.f64 a))

simplify279.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

480×	`fma-neg_binary64`
329×	`associate-/l/_binary64`
271×	`cancel-sign-sub-inv_binary64`
183×	`sub-neg_binary64`
166×	`distribute-rgt-in_binary64`

Counts

203 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	291	4802
1	780	4419
2	2855	4329
3	4821	4329
4	5061	4329

prune302.0ms (3.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	230	3	233

Error

0.2b

Counts

233 → 3

Alt Table

Status	Error	Program
	23.6b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
	13.6b	(/.f64 1 (+.f64 1 (exp.f64 b)))
▶	0.8b	(.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (fma.f64 (.f64 (cbrt.f64 (exp.f64 b)) (cbrt.f64 (exp.f64 b))) (cbrt.f64 (exp.f64 b)) (exp.f64 a))))

Compiler

Compiled 5855 to 1819 computations (68.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (exp.f64 b))
	0.1b	(sqrt.f64 (exp.f64 a))
✓	0.5b	(/.f64 (sqrt.f64 (exp.f64 a)) (fma.f64 (*.f64 (cbrt.f64 (exp.f64 b)) (cbrt.f64 (exp.f64 b))) (cbrt.f64 (exp.f64 b)) (exp.f64 a)))
✓	0.7b	(.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (fma.f64 (.f64 (cbrt.f64 (exp.f64 b)) (cbrt.f64 (exp.f64 b))) (cbrt.f64 (exp.f64 b)) (exp.f64 a))))

series4.1s (45.8%)

Counts

3 → 60

Calls

3 calls:

2.0s

(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (fma.f64 (*.f64 (cbrt.f64 (exp.f64 b)) (cbrt.f64 (exp.f64 b))) (cbrt.f64 (exp.f64 b)) (exp.f64 a))))

1.7s

(/.f64 (sqrt.f64 (exp.f64 a)) (fma.f64 (*.f64 (cbrt.f64 (exp.f64 b)) (cbrt.f64 (exp.f64 b))) (cbrt.f64 (exp.f64 b)) (exp.f64 a)))

320.0ms

(cbrt.f64 (exp.f64 b))

rewrite61.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
29×	`sqrt-prod_binary64`

Counts

3 → 104

Calls

3 calls:

25.0ms

(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (fma.f64 (*.f64 (cbrt.f64 (exp.f64 b)) (cbrt.f64 (exp.f64 b))) (cbrt.f64 (exp.f64 b)) (exp.f64 a))))

9.0ms

(/.f64 (sqrt.f64 (exp.f64 a)) (fma.f64 (*.f64 (cbrt.f64 (exp.f64 b)) (cbrt.f64 (exp.f64 b))) (cbrt.f64 (exp.f64 b)) (exp.f64 a)))

2.0ms

(cbrt.f64 (exp.f64 b))

simplify285.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

925×	`times-frac_binary64`
846×	`fma-def_binary64`
503×	`fma-neg_binary64`
171×	`sub-neg_binary64`
130×	`associate-/l*_binary64`

Counts

164 → 192

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	5040
1	658	4668
2	2471	4521
3	4637	4521
4	4963	4521

prune436.0ms (4.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	290	0	290
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	290	3	293

Error

0.2b

Counts

293 → 3

Alt Table

Status	Error	Program
	23.6b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
▶	13.6b	(/.f64 1 (+.f64 1 (exp.f64 b)))
✓	0.8b	(.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (fma.f64 (.f64 (cbrt.f64 (exp.f64 b)) (cbrt.f64 (exp.f64 b))) (cbrt.f64 (exp.f64 b)) (exp.f64 a))))

Compiler

Compiled 9605 to 2526 computations (73.7% saved)

localize7.0ms (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)))

series20.0ms (0.2%)

Counts

2 → 8

Calls

2 calls:

17.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
3.0ms	(+.f64 1 (exp.f64 b))

rewrite20.0ms (0.2%)

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:

8.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
7.0ms	(+.f64 1 (exp.f64 b))

simplify119.0ms (1.3%)

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

prune127.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	75	3	78

Error

0.2b

Counts

78 → 3

Alt Table

Status	Error	Program
	23.6b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
	13.9b	(/.f64 1 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 b)))))
✓	0.8b	(.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (fma.f64 (.f64 (cbrt.f64 (exp.f64 b)) (cbrt.f64 (exp.f64 b))) (cbrt.f64 (exp.f64 b)) (exp.f64 a))))

Compiler

Compiled 924 to 667 computations (27.8% saved)

regimes1.2s (13.7%)

Accuracy

Total 0.4b remaining (66.6%)

Threshold costs 0.4b (66.6%)

Counts

154 → 1

Compiler

Compiled 13175 to 8801 computations (33.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	12	15
2	17	15
3	19	15
4	20	15
5	20	15

end1.0ms (0%)

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

sample978.0ms (10.9%)

Algorithm

1×

intervals

Results

483.0ms	8000×	body	128	valid
31.0ms	650×	body	128	overflowed

Compiler

Compiled 78 to 49 computations (37.2% saved)

Details

analyze201.0ms (2.2%)

sample36.0ms (0.4%)

simplify13.0ms (0.1%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series78.0ms (0.9%)

rewrite22.0ms (0.2%)

simplify167.0ms (1.9%)

prune181.0ms (2%)

localize13.0ms (0.1%)

series164.0ms (1.8%)

rewrite77.0ms (0.9%)

simplify279.0ms (3.1%)

prune302.0ms (3.4%)

localize19.0ms (0.2%)

series4.1s (45.8%)

rewrite61.0ms (0.7%)

simplify285.0ms (3.2%)

prune436.0ms (4.9%)

localize7.0ms (0.1%)

series20.0ms (0.2%)

rewrite20.0ms (0.2%)

simplify119.0ms (1.3%)

prune127.0ms (1.4%)

regimes1.2s (13.7%)

simplify4.0ms (0%)

end1.0ms (0%)

sample978.0ms (10.9%)

Profiling