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

sample188.0ms

Algorithm

intervals

Results

72.0ms	134×	body	1280	valid
59.0ms	61×	body	2560	valid
10.0ms	24×	body	1280	overflowed
10.0ms	31×	body	640	valid
7.0ms	11×	body	2560	overflowed
6.0ms	319×	pre	80	true
5.0ms	17×	body	640	overflowed
2.0ms	11×	body	320	valid
1.0ms	15×	body	80	valid
1.0ms	4×	body	160	valid
0.0ms	7×	body	80	overflowed
0.0ms	2×	body	320	overflowed
0.0ms	2×	body	160	overflowed

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	5221	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: 60.6b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
3.3b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.3b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.3b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
8×	`associate-/r/_binary64`
6×	`difference-of-squares_binary64`
4×	`pow1_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `associate-*l/_binary64`
1×	`associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 76

Calls

4 calls:

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

series99.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
7.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
7.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
15.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5029	1449

prune75.0ms

Filtered

65 candidates to 88 candidates (-35.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	3	89

Merged error: 0.2b

Counts

89 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

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:

13.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify79.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4881	196
1	4881	196

prune23.0ms

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: 0.2b

Counts

25 → 5

localize8.0ms

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)))

rewrite85.0ms

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:

36.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
26.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
22.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
22.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5059	2572

prune137.0ms

Filtered

96 candidates to 171 candidates (-78.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	171	5	176

Merged error: 0.2b

Counts

176 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
40×	`cbrt-prod_binary64`
28×	`distribute-lft-out_binary64`
24×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `div-inv_binary64`
12×	`cbrt-div_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `pow1/3_binary64` `frac-add_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`

Counts

4 → 84

Calls

4 calls:

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

series88.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
24.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
22.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
22.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4902	1256
1	4902	1256

prune143.0ms

Filtered

68 candidates to 96 candidates (-41.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	96	5	101

Merged error: 0.2b

Counts

101 → 5

regimes115.0ms

Accuracy

0% (3.1b remaining)

Error of 3.3b against oracle of 0.1b and baseline of 3.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.7s	2568×	body	2560	valid
1.9s	3429×	body	1280	valid
355.0ms	1083×	body	640	valid
287.0ms	689×	body	1280	overflowed
194.0ms	9728×	pre	80	true
103.0ms	381×	body	640	overflowed
100.0ms	160×	body	2560	overflowed
81.0ms	358×	body	320	valid
40.0ms	188×	body	320	overflowed
31.0ms	439×	body	80	valid
21.0ms	123×	body	160	valid
15.0ms	223×	body	80	overflowed
12.0ms	87×	body	160	overflowed

Details

analyze1.7s

sample188.0ms

simplify17.0ms

prune7.0ms

localize15.0ms

rewrite33.0ms

series99.0ms

simplify43.0ms

prune75.0ms

localize5.0ms

rewrite14.0ms

series3.0ms

simplify79.0ms

prune23.0ms

localize8.0ms

rewrite85.0ms

series100.0ms

simplify61.0ms

prune137.0ms

localize14.0ms

rewrite57.0ms

series88.0ms

simplify57.0ms

prune143.0ms

regimes115.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.1s

Profiling