Details

analyze1.6s (9.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 31 to 24 computations (22.6% saved)

sample181.0ms (1.1%)

Algorithm

1×

intervals

Results

105.0ms	129×	body	2048	valid
30.0ms	71×	body	1024	valid
8.0ms	15×	body	2048	overflowed
7.0ms	314×	pre	128	true
6.0ms	20×	body	1024	overflowed
5.0ms	23×	body	512	valid
2.0ms	16×	body	256	valid
1.0ms	1×	body	4096	valid
1.0ms	17×	body	128	overflowed
1.0ms	16×	body	128	valid
1.0ms	1×	body	2048	invalid
0.0ms	2×	body	512	overflowed
0.0ms	3×	body	256	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5217	37

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 60.9b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.7b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.0b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.4b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64`
9×	`flip3--_binary64` `flip--_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`sub-neg_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
4×	`frac-times_binary64`
3×	`diff-log_binary64`
2×	`associate-r/_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

12.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

series248.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
75.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
43.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
41.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5130	1893

prune128.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	5	94

Merged error: 48.5b

Counts

94 → 5

Compiler

Compiled 3098 to 1333 computations (57% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.4b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
3.4b	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
4.4b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
14.5b	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

rewrite54.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
26×	`add-cbrt-cube_binary64`
14×	`prod-exp_binary64`
11×	`pow1_binary64` `add-sqr-sqrt_binary64`
10×	`cbrt-unprod_binary64`
9×	`*-un-lft-identity_binary64`
8×	`associate-/r/_binary64`
6×	`add-log-exp_binary64` `associate-*r/_binary64` `add-cube-cbrt_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64` `flip-+_binary64` `frac-times_binary64`
2×	`associate-/l/_binary64` `difference-of-squares_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 88

Calls

4 calls:

16.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
12.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
7.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series8.2s (48.3%)

Counts

4 → 12

Calls

4 calls:

7.9s	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
180.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
79.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
78.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify104.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4953	3679
1	4953	3679

prune222.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	101	4	105

Merged error: 0.1b

Counts

105 → 4

Compiler

Compiled 5155 to 2536 computations (50.8% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
7×	`distribute-lft-out_binary64`
6×	`times-frac_binary64`
4×	`div-inv_binary64`
3×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
1×	`flip3-+_binary64` `pow1_binary64` `frac-add_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

1 → 19

Calls

1 calls:

13.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

series21.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

21.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

simplify84.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5088	287

prune25.0ms (0.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	20	6	26

Merged error: 0.1b

Counts

26 → 6

Compiler

Compiled 357 to 280 computations (21.6% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

14.0b

(/.f64 (+.f64 b a) (*.f64 b a))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/l*_binary64` `times-frac_binary64`
3×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
2×	`associate-/l/_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip-+_binary64`

Counts

1 → 25

Calls

1 calls:

7.0ms

(/.f64 (+.f64 b a) (*.f64 b a))

series61.0ms (0.4%)

Counts

1 → 3

Calls

1 calls:

61.0ms

(/.f64 (+.f64 b a) (*.f64 b a))

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4975	354
1	4975	354

prune21.0ms (0.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	28	6	34

Merged error: 0.0b

Counts

34 → 6

Compiler

Compiled 316 to 94 computations (70.3% saved)

regimes46.0ms (0.3%)

Compiler: Compiled 339 to 297 computations (12.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms (0%)

sample5.8s (33.8%)

Algorithm

1×

intervals

Results

3.4s	4132×	body	2048	valid
930.0ms	2296×	body	1024	valid
218.0ms	412×	body	2048	overflowed
217.0ms	9680×	pre	128	true
182.0ms	578×	body	1024	overflowed
179.0ms	730×	body	512	valid
53.0ms	265×	body	512	overflowed
41.0ms	275×	body	256	valid
38.0ms	552×	body	128	valid
21.0ms	161×	body	256	overflowed
19.0ms	15×	body	4096	valid
18.0ms	262×	body	128	overflowed
2.0ms	2×	body	2048	invalid

Compiler

Compiled 156 to 134 computations (14.1% saved)

Details

analyze1.6s (9.4%)

sample181.0ms (1.1%)

simplify23.0ms (0.1%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite34.0ms (0.2%)

series248.0ms (1.4%)

simplify68.0ms (0.4%)

prune128.0ms (0.7%)

localize24.0ms (0.1%)

rewrite54.0ms (0.3%)

series8.2s (48.3%)

simplify104.0ms (0.6%)

prune222.0ms (1.3%)

localize4.0ms (0%)

rewrite15.0ms (0.1%)

series21.0ms (0.1%)

simplify84.0ms (0.5%)

prune25.0ms (0.1%)

localize4.0ms (0%)

rewrite9.0ms (0.1%)

series61.0ms (0.4%)

simplify63.0ms (0.4%)

prune21.0ms (0.1%)

regimes46.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.8s (33.8%)

Profiling