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

sample203.0ms

Algorithm

intervals

Results

83.0ms	77×	body	2560	valid
56.0ms	103×	body	1280	valid
14.0ms	44×	body	640	valid
11.0ms	26×	body	1280	overflowed
8.0ms	6×	body	2560	overflowed
7.0ms	317×	pre	80	true
4.0ms	16×	body	640	overflowed
2.0ms	10×	body	320	valid
1.0ms	19×	body	80	valid
1.0ms	3×	body	320	overflowed
1.0ms	4×	body	160	overflowed
0.0ms	3×	body	160	valid
0.0ms	6×	body	80	overflowed

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4855	24
1	4855	24

prune7.0ms

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: 59.1b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (-.f64 (exp.f64 (*.f64 b eps)) 1.0))
2.0b	(-.f64 (exp.f64 (*.f64 b eps)) 1.0)
2.8b	(-.f64 (exp.f64 (*.f64 a eps)) 1.0)
4.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)

rewrite27.0ms

Algorithm

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

series50.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(.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)
17.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4887	1142
1	4887	1142

prune98.0ms

Filtered

61 candidates to 83 candidates (-36.1%)

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: 48.1b

Counts

84 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

4.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)
4.5b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1.0)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 b 3))) (.f64 b (+.f64 eps (.f64 b (.f64 1/2 (.f64 eps eps))))))))
7.0b	(.f64 b (.f64 1/2 (*.f64 eps eps)))
16.2b	(*.f64 (pow.f64 eps 3) (pow.f64 b 3))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
27×	`add-cbrt-cube_binary64`
19×	`prod-exp_binary64`
16×	`unswap-sqr_binary64`
15×	`associate-l_binary64`
14×	`unpow-prod-down_binary64` `cube-prod_binary64`
13×	`-un-lft-identity_binary64` `pow1_binary64` `associate-r*_binary64`
11×	`cbrt-unprod_binary64` `add-cube-cbrt_binary64`
10×	`sqr-pow_binary64`
8×	`associate-/r/_binary64`
7×	`pow-prod-down_binary64`
6×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow-exp_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`cbrt-undiv_binary64` `associate-*r/_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `unpow3_binary64` `associate-l/_binary64` `-commutative_binary64` `cube-mult_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 124

Calls

4 calls:

5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)
21.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1.0)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 b 3))) (.f64 b (+.f64 eps (.f64 b (.f64 1/2 (.f64 eps eps))))))))
8.0ms	(.f64 b (.f64 1/2 (*.f64 eps eps)))
10.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 b 3))

series1.0s

Counts

4 → 12

Calls

4 calls:

17.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)
917.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1.0)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 b 3))) (.f64 b (+.f64 eps (.f64 b (.f64 1/2 (.f64 eps eps))))))))
77.0ms	(.f64 b (.f64 1/2 (*.f64 eps eps)))
10.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 b 3))

simplify64.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5169	2567

prune189.0ms

Filtered

87 candidates to 136 candidates (-56.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	136	4	140

Merged error: 0.0b

Counts

140 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

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

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 a) (/.f64 1 b))

series3.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify77.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4881	196
1	4881	196

prune36.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	19	7	26

Merged error: 0.0b

Counts

26 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b)))
0.6b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b))) (cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b))))

rewrite83.0ms

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:

15.0ms	(cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b)))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b)))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b)))
33.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b))) (cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b))))

series112.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b)))
28.0ms	(cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b)))
24.0ms	(cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b)))
35.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b))) (cbrt.f64 (+.f64 (/.f64 1 a) (/.f64 1 b))))

simplify61.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5017	2572

prune173.0ms

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	1	4	5
Picked	0	1	1
Done	0	1	1
Total	171	7	178

Merged error: 0.0b

Counts

178 → 7

regimes173.0ms

Accuracy

0% (3.5b remaining)

Error of 3.6b against oracle of 0.1b and baseline of 3.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.8s	2597×	body	2560	valid
1.9s	3401×	body	1280	valid
351.0ms	1042×	body	640	valid
277.0ms	650×	body	1280	overflowed
203.0ms	9712×	pre	80	true
110.0ms	166×	body	2560	overflowed
101.0ms	362×	body	640	overflowed
82.0ms	351×	body	320	valid
43.0ms	208×	body	320	overflowed
34.0ms	482×	body	80	valid
19.0ms	127×	body	160	valid
18.0ms	240×	body	80	overflowed
11.0ms	84×	body	160	overflowed
2.0ms	2×	body	2560	invalid

Details

analyze1.7s

sample203.0ms

simplify48.0ms

prune7.0ms

localize18.0ms

rewrite27.0ms

series50.0ms

simplify38.0ms

prune98.0ms

localize27.0ms

rewrite49.0ms

series1.0s

simplify64.0ms

prune189.0ms

localize5.0ms

rewrite16.0ms

series3.0ms

simplify77.0ms

prune36.0ms

localize11.0ms

rewrite83.0ms

series112.0ms

simplify61.0ms

prune173.0ms

regimes173.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling