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

sample190.0ms

Algorithm

intervals

Results

114.0ms	131×	body	2048	valid
31.0ms	74×	body	1024	valid
12.0ms	27×	body	512	valid
6.0ms	12×	body	2048	overflowed
6.0ms	301×	pre	128	true
5.0ms	16×	body	1024	overflowed
1.0ms	18×	body	128	valid
1.0ms	6×	body	256	valid
1.0ms	4×	body	512	overflowed
1.0ms	1×	body	2048	invalid
1.0ms	8×	body	128	overflowed
1.0ms	4×	body	256	overflowed

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5217	37

prune5.0ms

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: 60.1b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.3b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.2b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
5.6b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite34.0ms

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:

12.0ms	(.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)

series274.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
44.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
45.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
83.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify70.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4979	1893
1	4979	1893

prune104.0ms

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: 48.8b

Counts

94 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

4.2b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
5.2b	(/.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)))))))
5.6b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
11.6b	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
9×	`pow1_binary64`
8×	`add-log-exp_binary64` `associate-/r/_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`flip3--_binary64` `associate-*r/_binary64` `flip--_binary64`
5×	`add-cube-cbrt_binary64`
4×	`flip3-+_binary64` `cbrt-undiv_binary64` `difference-of-squares_binary64` `div-exp_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `associate-r_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `associate-*l/_binary64`
1×	`associate-/r_binary64` `distribute-lft-in_binary64` `associate-l_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 → 84

Calls

4 calls:

4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
17.0ms	(/.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)))))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
16.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

series8.4s

Counts

4 → 12

Calls

4 calls:

43.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
8.1s	(/.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)))))))
73.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
183.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

simplify86.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5124	3711

prune158.0ms

Filtered

68 candidates to 96 candidates (-41.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	97	3	100

Merged error: 0.4b

Counts

100 → 3

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite16.0ms

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:

15.0ms

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

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

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

simplify66.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4953	287
1	4953	287

prune30.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	19	6	25

Merged error: 0.3b

Counts

25 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity_binary64`
114×	`cbrt-prod_binary64`
81×	`distribute-lft-out_binary64`
60×	`div-inv_binary64`
42×	`times-frac_binary64`
37×	`add-sqr-sqrt_binary64`
33×	`cbrt-div_binary64` `swap-sqr_binary64`
29×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64` `associate-l_binary64`
11×	`flip3-+_binary64` `pow1_binary64` `frac-add_binary64` `flip-+_binary64`
9×	`pow1/3_binary64` `frac-times_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 159

Calls

4 calls:

55.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
21.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
21.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
24.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

series641.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
135.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
151.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
192.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

simplify105.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4909	3950
1	4909	3950

prune175.0ms

Filtered

96 candidates to 171 candidates (-78.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	170	7	177

Merged error: 0.3b

Counts

177 → 7

regimes54.0ms

Accuracy

0% (3.7b remaining)

Error of 3.8b against oracle of 0.1b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	8	10

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.5s	4110×	body	2048	valid
964.0ms	2305×	body	1024	valid
210.0ms	397×	body	2048	overflowed
198.0ms	9772×	pre	128	true
196.0ms	597×	body	1024	overflowed
193.0ms	759×	body	512	valid
70.0ms	330×	body	512	overflowed
40.0ms	584×	body	128	valid
36.0ms	232×	body	256	valid
21.0ms	302×	body	128	overflowed
19.0ms	141×	body	256	overflowed
16.0ms	10×	body	4096	valid
4.0ms	5×	body	2048	invalid

Details

analyze1.7s

sample190.0ms

simplify23.0ms

prune5.0ms

localize16.0ms

rewrite34.0ms

series274.0ms

simplify70.0ms

prune104.0ms

localize24.0ms

rewrite54.0ms

series8.4s

simplify86.0ms

prune158.0ms

localize7.0ms

rewrite16.0ms

series20.0ms

simplify66.0ms

prune30.0ms

localize14.0ms

rewrite161.0ms

series641.0ms

simplify105.0ms

prune175.0ms

regimes54.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.7s

Profiling