Details

analyze1.7s

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

sample200.0ms

Algorithm

intervals

Results

81.0ms	77×	body	2560	valid
61.0ms	102×	body	1280	valid
14.0ms	43×	body	640	valid
11.0ms	25×	body	1280	overflowed
6.0ms	315×	pre	80	true
4.0ms	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

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	5221	24

prune6.0ms

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: 60.2b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.2b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.5b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
4.2b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite29.0ms

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))
6.0ms	(-.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)

series48.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
8.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
8.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
16.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify64.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5017	1225

prune128.0ms

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: 49.5b

Counts

94 → 4

localize25.0ms

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)
6.5b	(.f64 eps (.f64 1/2 (*.f64 a a)))
15.5b	(*.f64 (pow.f64 a 3) (pow.f64 eps 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
27×	`add-exp-log_binary64`
18×	`associate-l_binary64`
17×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
16×	`-un-lft-identity_binary64` `associate-r*_binary64` `prod-exp_binary64`
15×	`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` `difference-of-squares_binary64` `unpow3_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` `flip--_binary64` `flip-+_binary64`

Counts

4 → 117

Calls

4 calls:

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)
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
10.0ms	(*.f64 (pow.f64 a 3) (pow.f64 eps 3))

series57.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify49.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5181	1289

prune164.0ms

Filtered

81 candidates to 129 candidates (-59.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	125	8	133

Merged error: 49.5b

Counts

133 → 8

localize24.0ms

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))
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)
6.5b	(.f64 eps (.f64 1/2 (*.f64 a a)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
17×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
11×	`associate-r_binary64`
9×	`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` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `*-commutative_binary64`
2×	`difference-of-sqr-1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `associate-*l/_binary64`
1×	`diff-log_binary64`

Counts

4 → 90

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))
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)
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(.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))
28.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))
16.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
9.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4991	1915
1	4991	1915

prune163.0ms

Filtered

71 candidates to 102 candidates (-43.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	103	7	110

Merged error: 49.0b

Counts

110 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`add-log-exp_binary64` `associate-/r/_binary64` `frac-times_binary64`
7×	`associate-r_binary64`
6×	`flip3-+_binary64` `pow1_binary64` `associate-*r/_binary64` `add-cube-cbrt_binary64` `difference-of-squares_binary64` `flip-+_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`sub-neg_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `associate-*l/_binary64`
3×	`difference-of-sqr-1_binary64` `associate-l_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 → 93

Calls

4 calls:

4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
17.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps a)) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
13.0ms	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps a)) (-.f64 (exp.f64 (*.f64 b eps)) 1))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series156.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
106.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps a)) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
25.0ms	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 a eps) 3)) (.f64 eps a)) (-.f64 (exp.f64 (*.f64 b eps)) 1))
16.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify38.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5002	2243

prune136.0ms

Filtered

80 candidates to 105 candidates (-31.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	105	7	112

Merged error: 3.0b

Counts

112 → 7

regimes196.0ms

Accuracy

0% (8.2b remaining)

Error of 11.0b against oracle of 2.8b and baseline of 11.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	15
1	17	15

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.8s	2618×	body	2560	valid
1.9s	3416×	body	1280	valid
355.0ms	1033×	body	640	valid
303.0ms	693×	body	1280	overflowed
205.0ms	9773×	pre	80	true
107.0ms	159×	body	2560	overflowed
104.0ms	366×	body	640	overflowed
80.0ms	343×	body	320	valid
45.0ms	221×	body	320	overflowed
36.0ms	468×	body	80	valid
19.0ms	122×	body	160	valid
18.0ms	247×	body	80	overflowed
12.0ms	87×	body	160	overflowed

Details

analyze1.7s

sample200.0ms

simplify16.0ms

prune6.0ms

localize16.0ms

rewrite29.0ms

series48.0ms

simplify64.0ms

prune128.0ms

localize25.0ms

rewrite32.0ms

series57.0ms

simplify49.0ms

prune164.0ms

localize24.0ms

rewrite34.0ms

series106.0ms

simplify51.0ms

prune163.0ms

localize22.0ms

rewrite43.0ms

series156.0ms

simplify38.0ms

prune136.0ms

regimes196.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling