Details

analyze117.0ms (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)

sample19.0ms (0.3%)

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)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.8b

Counts

1 → 1

Alt Table

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

Compiler

Compiled 20 to 12 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
0.7b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

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

Counts

2 → 45

Calls

2 calls:

5.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 676 to 135 computations (80% saved)

series55.0ms (0.9%)

Error

0.4b

Counts

2 → 24

Calls

2 calls:

31.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
10.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 1199 to 779 computations (35% saved)

simplify110.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

536×	`times-frac_binary64`
389×	`associate-/l*_binary64`
245×	`associate-/r*_binary64`
241×	`associate--l+_binary64`
209×	`associate--r+_binary64`

Counts

69 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	1707
1	428	1601
2	1327	1577
3	4721	1574
4	4983	1574
5	4965	1574

prune47.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	5	50

Error

0.4b

Counts

50 → 5

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
	1.1b	(/.f64 (/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a)))) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
	9.8b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))))) (+.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) (.f64 3/2 (*.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) a))))
	15.0b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
▶	0.8b	(/.f64 (exp.f64 a) (cbrt.f64 (pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3)))

Compiler

Compiled 1144 to 510 computations (55.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 b) (exp.f64 a))
0.0b	(pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3)
0.0b	(cbrt.f64 (pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3))
0.7b	(/.f64 (exp.f64 a) (cbrt.f64 (pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3)))

rewrite156.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

70×	`*-un-lft-identity_binary64`
70×	`cbrt-prod_binary64`
51×	`times-frac_binary64`
44×	`add-sqr-sqrt_binary64`
44×	`add-cube-cbrt_binary64`

Counts

4 → 149

Calls

4 calls:

10.0ms	(/.f64 (exp.f64 a) (cbrt.f64 (pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3)))
6.0ms	(pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3)
4.0ms	(cbrt.f64 (pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3))
3.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

Compiler

Compiled 2558 to 962 computations (62.4% saved)

series122.0ms (2.1%)

Error

0.4b

Counts

4 → 48

Calls

4 calls:

31.0ms	(/.f64 (exp.f64 a) (cbrt.f64 (pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3)))
27.0ms	(pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3)
13.0ms	(+.f64 (exp.f64 b) (exp.f64 a))
12.0ms	(cbrt.f64 (pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3))

Compiler

Compiled 2562 to 1719 computations (32.9% saved)

simplify173.0ms (3%)

Algorithm

1×	egg-herbie

Rules

909×	`times-frac_binary64`
317×	`associate-+r+_binary64`
298×	`unswap-sqr_binary64`
209×	`+-commutative_binary64`
189×	`associate-+l+_binary64`

Counts

197 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	325	4865
1	789	4483
2	2910	4464
3	4807	4464
4	5084	4464

prune92.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	151	5	156

Error

0.4b

Counts

156 → 5

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
▶	1.1b	(/.f64 (/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a)))) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
	9.8b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))))) (+.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) (.f64 3/2 (*.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) a))))
	15.0b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
✓	0.8b	(/.f64 (exp.f64 a) (cbrt.f64 (pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3)))

Compiler

Compiled 2065 to 969 computations (53.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
0.0b	(+.f64 (exp.f64 b) (exp.f64 a))
0.7b	(/.f64 (/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a)))) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
0.9b	(/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a))))

rewrite240.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

378×	`times-frac_binary64`
304×	`*-un-lft-identity_binary64`
224×	`sqrt-prod_binary64`
188×	`add-sqr-sqrt_binary64`
188×	`add-cube-cbrt_binary64`

Counts

4 → 309

Calls

4 calls:

21.0ms	(/.f64 (/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a)))) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
6.0ms	(/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a))))
5.0ms	(+.f64 (exp.f64 b) (exp.f64 a))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 6878 to 923 computations (86.6% saved)

series151.0ms (2.6%)

Error

0.4b

Counts

4 → 48

Calls

4 calls:

53.0ms	(/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a))))
33.0ms	(/.f64 (/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a)))) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
11.0ms	(+.f64 (exp.f64 b) (exp.f64 a))
11.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 3470 to 2191 computations (36.9% saved)

simplify420.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

448×	`cancel-sign-sub-inv_binary64`
282×	`associate-/l/_binary64`
219×	`neg-mul-1_binary64`
218×	`neg-sub0_binary64`
200×	`sub-neg_binary64`

Counts

357 → 297

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	491	14928
1	1150	14327
2	3157	13342
3	4687	13099
4	5063	13099

prune124.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	297	5	302

Error

0.4b

Counts

302 → 5

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
✓	1.1b	(/.f64 (/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a)))) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
▶	9.8b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))))) (+.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) (.f64 3/2 (*.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) a))))
	15.0b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
✓	0.8b	(/.f64 (exp.f64 a) (cbrt.f64 (pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3)))

Compiler

Compiled 4291 to 1301 computations (69.7% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 1/2 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (*.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))))
0.1b	(.f64 3/2 (.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) a))
1.7b	(/.f64 (*.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))
8.9b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))))) (+.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) (.f64 3/2 (*.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) a))))

rewrite541.0ms (9.3%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

41×	`add-log-exp_binary64`
38×	`frac-add_binary64`
33×	`add-exp-log_binary64`
27×	`*-un-lft-identity_binary64`
21×	`frac-sub_binary64`

Counts

4 → 136

Calls

4 calls:

54.0ms	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))))) (+.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) (.f64 3/2 (*.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) a))))
32.0ms	(+.f64 (.f64 1/2 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (*.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))))
10.0ms	(.f64 3/2 (.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) a))
9.0ms	(/.f64 (*.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))

Compiler

Compiled 13586 to 8592 computations (36.8% saved)

series342.0ms (5.9%)

Error

0.4b

Counts

4 → 36

Calls

4 calls:

155.0ms	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))))) (+.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) (.f64 3/2 (*.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) a))))
74.0ms	(+.f64 (.f64 1/2 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (*.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))))
39.0ms	(/.f64 (*.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))
35.0ms	(.f64 3/2 (.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) a))

Compiler

Compiled 4579 to 3224 computations (29.6% saved)

simplify235.0ms (4%)

Algorithm

1×	egg-herbie

Rules

636×	`distribute-rgt-in_binary64`
619×	`distribute-lft-in_binary64`
177×	`times-frac_binary64`
150×	`*-commutative_binary64`
142×	`cancel-sign-sub-inv_binary64`

Counts

172 → 142

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	444	14940
1	1519	13781
2	4984	13781

prune198.0ms (3.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	142	5	147

Error

0.4b

Counts

147 → 5

Alt Table

Status	Error	Program
	44.9b	(-.f64 (+.f64 (/.f64 (.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3)) (+.f64 (.f64 1/2 (/.f64 (.f64 a a) (+.f64 1 (exp.f64 b)))) (/.f64 a (+.f64 1 (exp.f64 b))))) (+.f64 (.f64 3/2 (/.f64 (.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 2))) (/.f64 a (+.f64 1 (.f64 (exp.f64 b) (+.f64 2 (exp.f64 b)))))))
	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
	1.1b	(/.f64 (/.f64 (exp.f64 a) (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a)))) (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
	9.8b	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (+.f64 (.f64 1/2 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 (.f64 a a) (pow.f64 (+.f64 1 (exp.f64 b)) 3))))) (+.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) (.f64 3/2 (*.f64 (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)) a))))
	0.8b	(/.f64 (exp.f64 a) (cbrt.f64 (pow.f64 (+.f64 (exp.f64 b) (exp.f64 a)) 3)))

Compiler

Compiled 9284 to 5688 computations (38.7% saved)

regimes1.3s (22.1%)

Accuracy

Total 0.3b remaining (46.5%)

Threshold costs 0.3b (46.5%)

Compiler

Compiled 23270 to 15222 computations (34.6% saved)

simplify8.0ms (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

end1.0ms (0%)

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

sample1.3s (21.9%)

Algorithm

1×

intervals

Results

602.0ms	8000×	body	128	valid
40.0ms	681×	body	128	overflowed

Compiler

Compiled 179 to 116 computations (35.2% saved)

Details

analyze117.0ms (2%)

sample19.0ms (0.3%)

simplify11.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.1%)

rewrite40.0ms (0.7%)

series55.0ms (0.9%)

simplify110.0ms (1.9%)

prune47.0ms (0.8%)

localize8.0ms (0.1%)

rewrite156.0ms (2.7%)

series122.0ms (2.1%)

simplify173.0ms (3%)

prune92.0ms (1.6%)

localize9.0ms (0.2%)

rewrite240.0ms (4.1%)

series151.0ms (2.6%)

simplify420.0ms (7.2%)

prune124.0ms (2.1%)

localize25.0ms (0.4%)

rewrite541.0ms (9.3%)

series342.0ms (5.9%)

simplify235.0ms (4%)

prune198.0ms (3.4%)

regimes1.3s (22.1%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample1.3s (21.9%)

Profiling