Details

analyze95.0ms (2.3%)

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)

sample35.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	22×	body	128	overflowed

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify6.0ms (0.2%)

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

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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.3b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series38.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

34.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite12.0ms (0.3%)

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:

7.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify87.0ms (2.1%)

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

prune107.0ms (2.5%)

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

Counts

109 → 3

Alt Table

Status	Error	Program
	20.1b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
	9.8b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a 2) (+.f64 1 (exp.f64 b)))) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (pow.f64 a 2) (.f64 (pow.f64 (+.f64 1 (exp.f64 b)) 2) (+.f64 (exp.f64 b) 1)))))) (+.f64 (.f64 3/2 (/.f64 (pow.f64 a 2) (.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))) (/.f64 a (*.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))))
▶	0.6b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))

Compiler

Compiled 2405 to 939 computations (61% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 b) (exp.f64 a))
✓	0.0b	(pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3)
✓	0.3b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))
✓	0.4b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))

series151.0ms (3.6%)

Counts

4 → 64

Calls

4 calls:

81.0ms	(pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3)
33.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))
31.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))
5.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
48×	`add-sqr-sqrt_binary64`
48×	`add-cube-cbrt_binary64`
42×	`cbrt-prod_binary64`

Counts

4 → 164

Calls

4 calls:

8.0ms	(pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3)
6.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))
5.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))
3.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

simplify142.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

434×	`unswap-sqr_binary64`
198×	`sub-neg_binary64`
178×	`associate-/l*_binary64`
173×	`associate-+r+_binary64`
163×	`fma-def_binary64`

Counts

228 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	6527
1	1015	6054
2	3734	5934
3	5189	5934

prune167.0ms (4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	183	3	186

Error

Counts

186 → 3

Alt Table

Status	Error	Program
	20.1b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
▶	9.8b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a 2) (+.f64 1 (exp.f64 b)))) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (pow.f64 a 2) (.f64 (pow.f64 (+.f64 1 (exp.f64 b)) 2) (+.f64 (exp.f64 b) 1)))))) (+.f64 (.f64 3/2 (/.f64 (pow.f64 a 2) (.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))) (/.f64 a (*.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))))
✓	0.6b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))

Compiler

Compiled 5351 to 2511 computations (53.1% saved)

localize24.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.5b	(/.f64 (pow.f64 a 2) (*.f64 (pow.f64 (+.f64 1 (exp.f64 b)) 2) (+.f64 (exp.f64 b) 1)))
✓	2.5b	(/.f64 (pow.f64 a 2) (+.f64 1 (exp.f64 b)))
✓	2.5b	(/.f64 (pow.f64 a 2) (*.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))
✓	7.3b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a 2) (+.f64 1 (exp.f64 b)))) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (pow.f64 a 2) (.f64 (pow.f64 (+.f64 1 (exp.f64 b)) 2) (+.f64 (exp.f64 b) 1)))))) (+.f64 (.f64 3/2 (/.f64 (pow.f64 a 2) (.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))) (/.f64 a (*.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))))

series360.0ms (8.6%)

Counts

4 → 80

Calls

4 calls:

188.0ms	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a 2) (+.f64 1 (exp.f64 b)))) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (pow.f64 a 2) (.f64 (pow.f64 (+.f64 1 (exp.f64 b)) 2) (+.f64 (exp.f64 b) 1)))))) (+.f64 (.f64 3/2 (/.f64 (pow.f64 a 2) (.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))) (/.f64 a (*.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))))
87.0ms	(/.f64 (pow.f64 a 2) (*.f64 (pow.f64 (+.f64 1 (exp.f64 b)) 2) (+.f64 (exp.f64 b) 1)))
61.0ms	(/.f64 (pow.f64 a 2) (*.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))
24.0ms	(/.f64 (pow.f64 a 2) (+.f64 1 (exp.f64 b)))

rewrite115.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
48×	`add-exp-log_binary64`
43×	`add-sqr-sqrt_binary64`
41×	`add-cube-cbrt_binary64`

Counts

4 → 222

Calls

4 calls:

51.0ms	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a 2) (+.f64 1 (exp.f64 b)))) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (pow.f64 a 2) (.f64 (pow.f64 (+.f64 1 (exp.f64 b)) 2) (+.f64 (exp.f64 b) 1)))))) (+.f64 (.f64 3/2 (/.f64 (pow.f64 a 2) (.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))) (/.f64 a (*.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))))
9.0ms	(/.f64 (pow.f64 a 2) (*.f64 (pow.f64 (+.f64 1 (exp.f64 b)) 2) (+.f64 (exp.f64 b) 1)))
8.0ms	(/.f64 (pow.f64 a 2) (*.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))
6.0ms	(/.f64 (pow.f64 a 2) (+.f64 1 (exp.f64 b)))

simplify294.0ms (7%)

Algorithm

1×	egg-herbie

Rules

782×	`distribute-rgt-in_binary64`
761×	`distribute-lft-in_binary64`
437×	`fma-def_binary64`
180×	`cancel-sign-sub-inv_binary64`
153×	`*-commutative_binary64`

Counts

302 → 378

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	579	21441
1	1859	17238
2	5946	17238

prune793.0ms (18.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	378	0	378
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	378	3	381

Error

Counts

381 → 3

Alt Table

Status	Error	Program
▶	20.1b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
✓	9.8b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a 2) (+.f64 1 (exp.f64 b)))) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (pow.f64 a 2) (.f64 (pow.f64 (+.f64 1 (exp.f64 b)) 2) (+.f64 (exp.f64 b) 1)))))) (+.f64 (.f64 3/2 (/.f64 (pow.f64 a 2) (.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))) (/.f64 a (*.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))))
✓	0.6b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))

Compiler

Compiled 39596 to 25738 computations (35% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 b (exp.f64 a))
✓	0.0b	(pow.f64 (+.f64 1 (exp.f64 a)) 2)
✓	0.3b	(/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2))
✓	0.3b	(/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a)))

series112.0ms (2.7%)

Counts

4 → 44

Calls

4 calls:

91.0ms	(/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2))
9.0ms	(/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a)))
8.0ms	(*.f64 b (exp.f64 a))
4.0ms	(pow.f64 (+.f64 1 (exp.f64 a)) 2)

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`
17×	`add-exp-log_binary64`

Counts

4 → 115

Calls

4 calls:

7.0ms	(pow.f64 (+.f64 1 (exp.f64 a)) 2)
7.0ms	(/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2))
5.0ms	(/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a)))
4.0ms	(*.f64 b (exp.f64 a))

simplify91.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

502×	`fma-def_binary64`
448×	`associate-/r*_binary64`
351×	`associate-*l/_binary64`
343×	`associate-/l/_binary64`
255×	`associate-*r/_binary64`

Counts

159 → 201

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	2530
1	486	2217
2	1573	2165
3	4346	2165
4	4953	2165

prune168.0ms (4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	201	3	204

Error

Counts

204 → 3

Alt Table

Status	Error	Program
✓	20.1b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
✓	9.8b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a 2) (+.f64 1 (exp.f64 b)))) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (pow.f64 a 2) (.f64 (pow.f64 (+.f64 1 (exp.f64 b)) 2) (+.f64 (exp.f64 b) 1)))))) (+.f64 (.f64 3/2 (/.f64 (pow.f64 a 2) (.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))) (/.f64 a (*.f64 (+.f64 1 (exp.f64 b)) (+.f64 (exp.f64 b) 1)))))
✓	0.6b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))

Compiler

Compiled 5175 to 2756 computations (46.7% saved)

regimes712.0ms (16.9%)

Accuracy

Total 0.3b remaining (55.7%)

Threshold costs 0.3b (55.7%)

Counts

141 → 1

Compiler

Compiled 20233 to 13508 computations (33.2% saved)

simplify3.0ms (0.1%)

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

end0.0ms (0%)

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

sample609.0ms (14.5%)

Algorithm

1×

intervals

Results

293.0ms	8000×	body	128	valid
20.0ms	662×	body	128	overflowed

Compiler

Compiled 128 to 87 computations (32% saved)

Details

analyze95.0ms (2.3%)

sample35.0ms (0.8%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series38.0ms (0.9%)

rewrite12.0ms (0.3%)

simplify87.0ms (2.1%)

prune107.0ms (2.5%)

localize8.0ms (0.2%)

series151.0ms (3.6%)

rewrite35.0ms (0.8%)

simplify142.0ms (3.4%)

prune167.0ms (4%)

localize24.0ms (0.6%)

series360.0ms (8.6%)

rewrite115.0ms (2.7%)

simplify294.0ms (7%)

prune793.0ms (18.9%)

localize10.0ms (0.2%)

series112.0ms (2.7%)

rewrite27.0ms (0.6%)

simplify91.0ms (2.2%)

prune168.0ms (4%)

regimes712.0ms (16.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample609.0ms (14.5%)

Profiling