Details

analyze1.8s

Algorithm

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

sample201.0ms

Algorithm

intervals

Results

81.0ms	73×	body	2560	valid
64.0ms	111×	body	1280	valid
12.0ms	34×	body	640	valid
9.0ms	20×	body	1280	overflowed
7.0ms	315×	pre	80	true
5.0ms	6×	body	2560	overflowed
4.0ms	14×	body	640	overflowed
4.0ms	15×	body	320	valid
1.0ms	20×	body	80	valid
1.0ms	13×	body	80	overflowed
1.0ms	5×	body	160	overflowed
1.0ms	3×	body	160	valid
0.0ms	1×	body	320	overflowed

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5218	37

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 58.8b

Counts

2 → 1

localize20.0ms

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))
2.0b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
2.1b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite26.0ms

Algorithm

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:

11.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series151.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
28.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
24.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
45.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify89.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4976	1893
1	4976	1893

prune105.0ms

Filtered

70 candidates to 93 candidates (-32.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 48.0b

Counts

94 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

3.0b	(+.f64 (.f64 1/6 (.f64 (pow.f64 a 3) (pow.f64 eps 3))) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))))
3.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
7.9b	(.f64 eps (.f64 1/2 (*.f64 a a)))
15.9b	(*.f64 (pow.f64 a 3) (pow.f64 eps 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

9.0ms	(+.f64 (.f64 1/6 (.f64 (pow.f64 a 3) (pow.f64 eps 3))) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
9.0ms	(*.f64 (pow.f64 a 3) (pow.f64 eps 3))

series198.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+.f64 (.f64 1/6 (.f64 (pow.f64 a 3) (pow.f64 eps 3))) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))))
41.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
28.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
52.0ms	(*.f64 (pow.f64 a 3) (pow.f64 eps 3))

simplify86.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5313	2064

prune153.0ms

Filtered

76 candidates to 120 candidates (-57.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	117	7	124

Merged error: 47.2b

Counts

124 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

2.1b	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
2.4b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2)))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
3.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
7.9b	(.f64 eps (.f64 (*.f64 a a) 1/2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
15×	`pow1_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`associate-*r/_binary64`
10×	`*-un-lft-identity_binary64`
8×	`associate-/r/_binary64`
7×	`pow-prod-down_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`flip3-+_binary64` `associate-r_binary64` `flip-+_binary64` `frac-times_binary64`
2×	`associate-/l/_binary64` `difference-of-squares_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`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`

Counts

4 → 93

Calls

4 calls:

6.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
17.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2)))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
7.0ms	(.f64 eps (.f64 (*.f64 a a) 1/2))

series996.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
866.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2)))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
42.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
32.0ms	(.f64 eps (.f64 (*.f64 a a) 1/2))

simplify77.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5232	2927

prune118.0ms

Filtered

67 candidates to 105 candidates (-56.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	109	3	112

Merged error: 0.1b

Counts

112 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm

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:

12.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify79.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4951	287
1	4951	287

prune12.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	20	5	25

Merged error: 0.0b

Counts

25 → 5

regimes50.0ms

Accuracy

-15.4% (4.0b remaining)

Error of 4.1b against oracle of 0.1b and baseline of 3.5b

bsearch165.0ms

Steps

Iters	Range		Point
8	-2.0325578823603266e-63	-3.223307977229915e-66	-2.010446323295612e-63
7	-2.9491511367669586e-55	-8.90867569140479e-57	-9.009444801518506e-57

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	65
1	48	65

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.7s	2496×	body	2560	valid
2.0s	3480×	body	1280	valid
371.0ms	1072×	body	640	valid
293.0ms	660×	body	1280	overflowed
207.0ms	9711×	pre	80	true
109.0ms	361×	body	640	overflowed
105.0ms	155×	body	2560	overflowed
84.0ms	350×	body	320	valid
41.0ms	190×	body	320	overflowed
37.0ms	479×	body	80	valid
19.0ms	258×	body	80	overflowed
19.0ms	123×	body	160	valid
12.0ms	83×	body	160	overflowed
4.0ms	2×	body	2560	invalid
1.0ms	2×	body	1280	invalid

Details

analyze1.8s

sample201.0ms

simplify30.0ms

prune3.0ms

localize20.0ms

rewrite26.0ms

series151.0ms

simplify89.0ms

prune105.0ms

localize26.0ms

rewrite34.0ms

series198.0ms

simplify86.0ms

prune153.0ms

localize22.0ms

rewrite38.0ms

series996.0ms

simplify77.0ms

prune118.0ms

localize5.0ms

rewrite12.0ms

series10.0ms

simplify79.0ms

prune12.0ms

regimes50.0ms

bsearch165.0ms

simplify4.0ms

end0.0ms

sample6.3s

Profiling