Details

analyze233.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample67.0ms

Algorithm

intervals

Results

23.0ms	42×	body	1280	valid
15.0ms	43×	body	640	valid
13.0ms	141×	body	80	valid
4.0ms	16×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	8×	body	80	invalid
1.0ms	1×	body	1280	invalid
0.0ms	6×	body	80	overflowed
0.0ms	1×	body	640	invalid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5443	27

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: 26.8b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
2.4b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub_binary64`
78×	`exp-neg_binary64`
76×	`frac-times_binary64`
59×	`neg-sub0_binary64` `exp-diff_binary64`
38×	`associate-r/_binary64` `associate-l/_binary64`
31×	`flip3--_binary64` `flip--_binary64`
27×	`flip3-+_binary64` `flip-+_binary64`
25×	`add-sqr-sqrt_binary64`
19×	`un-div-inv_binary64`
17×	`*-un-lft-identity_binary64`
14×	`associate-l_binary64`
12×	`exp-prod_binary64`
10×	`add-log-exp_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `times-frac_binary64`
5×	`add-exp-log_binary64`
4×	`rem-exp-log_binary64`
3×	`associate-r_binary64` `difference-of-sqr-1_binary64`
2×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64` `distribute-lft-out--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 164

Calls

4 calls:

16.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
6.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
3.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
19.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
5.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
6.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
33.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5507	5772

prune200.0ms

Filtered

96 candidates to 176 candidates (-83.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	2	177

Merged error: 0.7b

Counts

177 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(*.f64 2/3 (pow.f64 x 3))
7.2b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
7×	`add-log-exp_binary64` `add-exp-log_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`associate-l_binary64` `prod-exp_binary64`
2×	`pow1_binary64` `diff-log_binary64` `sqr-pow_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `difference-of-squares_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 45

Calls

2 calls:

7.0ms	(*.f64 2/3 (pow.f64 x 3))
9.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(*.f64 2/3 (pow.f64 x 3))
4.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

simplify33.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5491	454

prune38.0ms

Filtered

31 candidates to 51 candidates (-64.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	50	3	53

Merged error: 0.7b

Counts

53 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 2/3 (.f64 x x))
0.6b	(cbrt.f64 x)
0.8b	(pow.f64 (cbrt.f64 x) 3)
7.2b	(-.f64 (+.f64 (.f64 (.f64 2/3 (.f64 x x)) (pow.f64 (cbrt.f64 x) 3)) 2) (.f64 x x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1_binary64` `add-exp-log_binary64`
9×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
6×	`unpow-prod-down_binary64` `cube-prod_binary64`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`diff-log_binary64` `pow1/3_binary64` `pow-pow_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `associate-r_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `difference-of-squares_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 74

Calls

4 calls:

8.0ms	(.f64 2/3 (.f64 x x))
1.0ms	(cbrt.f64 x)
3.0ms	(pow.f64 (cbrt.f64 x) 3)
14.0ms	(-.f64 (+.f64 (.f64 (.f64 2/3 (.f64 x x)) (pow.f64 (cbrt.f64 x) 3)) 2) (.f64 x x))

series49.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(.f64 2/3 (.f64 x x))
14.0ms	(cbrt.f64 x)
24.0ms	(pow.f64 (cbrt.f64 x) 3)
7.0ms	(-.f64 (+.f64 (.f64 (.f64 2/3 (.f64 x x)) (pow.f64 (cbrt.f64 x) 3)) 2) (.f64 x x))

simplify54.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5263	529

prune45.0ms

Filtered

49 candidates to 86 candidates (-75.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	85	4	89

Merged error: 0.7b

Counts

89 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
0.6b	(cbrt.f64 (*.f64 x (-.f64 -1 eps)))
0.6b	(cbrt.f64 (*.f64 x (-.f64 -1 eps)))
3.2b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 -1 eps))) (cbrt.f64 (.f64 x (-.f64 -1 eps))))) (cbrt.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-*l/_binary64`
18×	`frac-sub_binary64`
12×	`flip3--_binary64` `flip--_binary64`
8×	`associate-*r/_binary64` `exp-neg_binary64` `frac-times_binary64` `cbrt-prod_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64` `neg-sub0_binary64` `exp-diff_binary64`
5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`
2×	`distribute-neg-frac_binary64` `un-div-inv_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`

Counts

4 → 67

Calls

4 calls:

2.0ms	(cbrt.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
5.0ms	(cbrt.f64 (*.f64 x (-.f64 -1 eps)))
5.0ms	(cbrt.f64 (*.f64 x (-.f64 -1 eps)))
16.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 -1 eps))) (cbrt.f64 (.f64 x (-.f64 -1 eps))))) (cbrt.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))))

series385.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
25.0ms	(cbrt.f64 (*.f64 x (-.f64 -1 eps)))
22.0ms	(cbrt.f64 (*.f64 x (-.f64 -1 eps)))
316.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 -1 eps))) (cbrt.f64 (.f64 x (-.f64 -1 eps))))) (cbrt.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5184	3008

prune164.0ms

Filtered

68 candidates to 79 candidates (-16.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	79	4	83

Merged error: 0.7b

Counts

83 → 4

regimes117.0ms

Accuracy

96.5% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.8b

bsearch68.0ms

Steps

Iters	Range		Point
8	70.13742852675067	26207.825739476375	226.99331786434493

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	210	64
1	210	64

end0.0ms

sample2.1s

Algorithm

intervals

Results

916.0ms	1675×	body	1280	valid
445.0ms	1290×	body	640	valid
322.0ms	4093×	body	80	valid
143.0ms	604×	body	320	valid
51.0ms	338×	body	160	valid
21.0ms	216×	body	80	invalid
13.0ms	177×	body	80	overflowed
10.0ms	18×	body	1280	invalid
5.0ms	14×	body	640	invalid
1.0ms	5×	body	320	invalid
1.0ms	4×	body	160	invalid

Details

analyze233.0ms

sample67.0ms

simplify67.0ms

prune6.0ms

localize17.0ms

rewrite55.0ms

series54.0ms

simplify66.0ms

prune200.0ms

localize8.0ms

rewrite17.0ms

series9.0ms

simplify33.0ms

prune38.0ms

localize11.0ms

rewrite28.0ms

series49.0ms

simplify54.0ms

prune45.0ms

localize27.0ms

rewrite33.0ms

series385.0ms

simplify65.0ms

prune164.0ms

regimes117.0ms

bsearch68.0ms

simplify5.0ms

end0.0ms

sample2.1s

Profiling