Details

analyze1.7s (16.9%)

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

sample197.0ms (2%)

Algorithm

1×

intervals

Results

79.0ms	77×	body	2560	valid
57.0ms	102×	body	1280	valid
17.0ms	43×	body	640	valid
11.0ms	25×	body	1280	overflowed
7.0ms	315×	pre	80	true
3.0ms	12×	body	640	overflowed
3.0ms	15×	body	320	valid
2.0ms	4×	body	2560	overflowed
1.0ms	5×	body	320	overflowed
1.0ms	14×	body	80	valid
1.0ms	5×	body	160	valid
1.0ms	9×	body	80	overflowed
1.0ms	4×	body	160	overflowed

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4855	24
1	4855	24

prune7.0ms (0.1%)

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: 60.2b

Counts

2 → 1

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (-.f64 (exp.f64 (*.f64 b eps)) 1.0))
2.2b	(-.f64 (exp.f64 (*.f64 b eps)) 1.0)
3.5b	(-.f64 (exp.f64 (*.f64 a eps)) 1.0)
4.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`flip3--_binary64` `flip--_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`sub-neg_binary64` `associate-r_binary64` `associate-l_binary64` `difference-of-squares_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 → 71

Calls

4 calls:

11.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (-.f64 (exp.f64 (*.f64 b eps)) 1.0))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1.0)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1.0)

series47.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)
15.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (-.f64 (exp.f64 (*.f64 b eps)) 1.0))
8.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1.0)
8.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1.0)

simplify39.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4887	1142
1	4887	1142

prune130.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	4	84

Merged error: 49.5b

Counts

84 → 4

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.5b	(.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))
4.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)
6.5b	(.f64 eps (.f64 1/2 (*.f64 a a)))
15.5b	(*.f64 (pow.f64 a 3) (pow.f64 eps 3))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
27×	`add-exp-log_binary64`
18×	`associate-l_binary64`
17×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
16×	`associate-r_binary64` `prod-exp_binary64`
15×	`*-un-lft-identity_binary64` `pow1_binary64`
14×	`unpow-prod-down_binary64` `cube-prod_binary64`
13×	`add-cube-cbrt_binary64`
10×	`sqr-pow_binary64`
8×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
6×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow-exp_binary64`
3×	`*-commutative_binary64`
2×	`associate-*r/_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 115

Calls

4 calls:

11.0ms	(*.f64 (pow.f64 a 3) (pow.f64 eps 3))
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
6.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)

series53.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)
15.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))
13.0ms	(*.f64 (pow.f64 a 3) (pow.f64 eps 3))
9.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5173	1262

prune454.0ms (4.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	122	5	127
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	123	8	131

Merged error: 49.5b

Counts

131 → 8

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.9b	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1.0))
3.5b	(.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))
4.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)
6.5b	(.f64 eps (.f64 1/2 (*.f64 a a)))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

12.0ms	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1.0))
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
6.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)

series77.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1.0))
16.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)
15.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))
9.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))

simplify51.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4998	1857
1	4998	1857

prune186.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	99	7	106

Merged error: 49.0b

Counts

106 → 7

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.2b	(-.f64 (exp.f64 (*.f64 b eps)) 1.0)
2.4b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1.0)) (.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps a)) (-.f64 (exp.f64 (*.f64 b eps)) 1.0)))
2.9b	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps a)) (-.f64 (exp.f64 (*.f64 b eps)) 1.0))
4.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

17.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1.0)) (.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps a)) (-.f64 (exp.f64 (*.f64 b eps)) 1.0)))
12.0ms	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps a)) (-.f64 (exp.f64 (*.f64 b eps)) 1.0))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1.0)

series148.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1.0)) (.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps a)) (-.f64 (exp.f64 (*.f64 b eps)) 1.0)))
24.0ms	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps a)) (-.f64 (exp.f64 (*.f64 b eps)) 1.0))
18.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)
8.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1.0)

simplify39.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5159	2194

prune154.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	99	7	106

Merged error: 3.0b

Counts

106 → 7

regimes181.0ms (1.8%)

Accuracy

Total 8.2b remaining (74.2%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	15
1	17	15

end0.0ms (0%)

sample6.2s (62%)

Algorithm

1×

intervals

Results

2.7s	2618×	body	2560	valid
1.9s	3416×	body	1280	valid
339.0ms	1033×	body	640	valid
295.0ms	693×	body	1280	overflowed
211.0ms	9773×	pre	80	true
103.0ms	159×	body	2560	overflowed
100.0ms	366×	body	640	overflowed
78.0ms	343×	body	320	valid
45.0ms	221×	body	320	overflowed
32.0ms	468×	body	80	valid
18.0ms	122×	body	160	valid
17.0ms	247×	body	80	overflowed
12.0ms	87×	body	160	overflowed

Details

analyze1.7s (16.9%)

sample197.0ms (2%)

simplify48.0ms (0.5%)

prune7.0ms (0.1%)

localize18.0ms (0.2%)

rewrite27.0ms (0.3%)

series47.0ms (0.5%)

simplify39.0ms (0.4%)

prune130.0ms (1.3%)

localize25.0ms (0.3%)

rewrite34.0ms (0.3%)

series53.0ms (0.5%)

simplify53.0ms (0.5%)

prune454.0ms (4.6%)

localize27.0ms (0.3%)

rewrite34.0ms (0.3%)

series77.0ms (0.8%)

simplify51.0ms (0.5%)

prune186.0ms (1.9%)

localize18.0ms (0.2%)

rewrite41.0ms (0.4%)

series148.0ms (1.5%)

simplify39.0ms (0.4%)

prune154.0ms (1.6%)

regimes181.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.2s (62%)

Profiling