Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

sample42.0ms

Algorithm

intervals

Results

19.0ms	256×	body	128	valid
8.0ms	97×	body	128	invalid
3.0ms	66×	body	128	nan

simplify118.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	5018	19

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 1.7b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 k (+.f64 k 10))
0.0b	(*.f64 a (pow.f64 k m))
1.7b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log_binary64`
17×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cbrt-cube_binary64`
11×	`associate-r_binary64`
10×	`add-cube-cbrt_binary64`
7×	`prod-exp_binary64`
6×	`associate-l_binary64`
5×	`pow1_binary64`
4×	`unswap-sqr_binary64` `unpow-prod-down_binary64` `div-exp_binary64`
3×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `times-frac_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `flip-+_binary64` `pow-exp_binary64` `-commutative_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

3 → 73

Calls

3 calls:

7.0ms	(*.f64 k (+.f64 k 10))
6.0ms	(*.f64 a (pow.f64 k m))
7.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

series428.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(*.f64 k (+.f64 k 10))
113.0ms	(*.f64 a (pow.f64 k m))
256.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

simplify69.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4956	1226
1	4956	1226

prune67.0ms

Filtered

57 candidates to 82 candidates (-43.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 1.6b

Counts

83 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (pow.f64 k m))
0.0b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (pow.f64 k m)) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
13.0b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
13.0b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
38×	`add-exp-log_binary64`
30×	`times-frac_binary64`
25×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
24×	`associate-l_binary64` `sqrt-prod_binary64`
18×	`add-cbrt-cube_binary64`
13×	`div-exp_binary64`
12×	`prod-exp_binary64`
9×	`unswap-sqr_binary64`
8×	`sqrt-div_binary64`
7×	`associate-r_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `unpow-prod-down_binary64`
5×	`cbrt-undiv_binary64`
4×	`pow-to-exp_binary64` `flip3-+_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `flip-+_binary64` `pow-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `associate-*l/_binary64`
1×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `-commutative_binary64`

Counts

4 → 123

Calls

4 calls:

15.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (pow.f64 k m))
15.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (pow.f64 k m)) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

series611.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (pow.f64 k m))
261.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (pow.f64 k m)) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
28.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
31.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

simplify58.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5119	3461

prune156.0ms

Filtered

98 candidates to 135 candidates (-37.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	134	6	140

Merged error: 1.6b

Counts

140 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 k (+.f64 k 10))
0.0b	(*.f64 a (pow.f64 k m))
0.1b	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
1.7b	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log_binary64`
36×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
22×	`add-cbrt-cube_binary64`
17×	`div-exp_binary64`
13×	`prod-exp_binary64`
11×	`associate-r_binary64`
8×	`associate-/r*_binary64`
7×	`pow1_binary64` `cbrt-undiv_binary64`
6×	`associate-l_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`rec-exp_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `pow-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-r/_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `-commutative_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 130

Calls

4 calls:

7.0ms	(*.f64 k (+.f64 k 10))
6.0ms	(*.f64 a (pow.f64 k m))
9.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
8.0ms	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))

series562.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(*.f64 k (+.f64 k 10))
92.0ms	(*.f64 a (pow.f64 k m))
200.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
215.0ms	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))

simplify90.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4947	2875
1	4947	2875

prune107.0ms

Filtered

91 candidates to 142 candidates (-56.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	143	5	148

Merged error: 0.0b

Counts

148 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (pow.f64 k (neg.f64 m)) a)
0.0b	(+.f64 (/.f64 k a) (/.f64 10 a))
0.1b	(*.f64 (/.f64 k (pow.f64 k m)) (+.f64 (/.f64 k a) (/.f64 10 a)))
0.1b	(/.f64 1 (+.f64 (/.f64 (pow.f64 k (neg.f64 m)) a) (*.f64 (/.f64 k (pow.f64 k m)) (+.f64 (/.f64 k a) (/.f64 10 a)))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac_binary64`
63×	`*-un-lft-identity_binary64`
57×	`add-sqr-sqrt_binary64`
47×	`add-cube-cbrt_binary64`
25×	`associate-l_binary64`
22×	`add-exp-log_binary64` `unpow-prod-down_binary64`
13×	`add-cbrt-cube_binary64`
12×	`frac-add_binary64`
10×	`associate-/l*_binary64`
9×	`associate-/r/_binary64`
8×	`distribute-lft-out_binary64` `associate-r_binary64` `sqr-pow_binary64`
7×	`pow1_binary64` `div-inv_binary64` `div-exp_binary64`
6×	`flip3-+_binary64` `associate-/r_binary64` `add-log-exp_binary64` `associate-r/_binary64` `flip-+_binary64` `frac-times_binary64`
4×	`unswap-sqr_binary64` `prod-exp_binary64`
3×	`cbrt-undiv_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-rgt-out_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `neg-sub0_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-sub_binary64` `inv-pow_binary64` `rec-exp_binary64` `pow-neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 164

Calls

4 calls:

5.0ms	(/.f64 (pow.f64 k (neg.f64 m)) a)
17.0ms	(+.f64 (/.f64 k a) (/.f64 10 a))
26.0ms	(*.f64 (/.f64 k (pow.f64 k m)) (+.f64 (/.f64 k a) (/.f64 10 a)))
15.0ms	(/.f64 1 (+.f64 (/.f64 (pow.f64 k (neg.f64 m)) a) (*.f64 (/.f64 k (pow.f64 k m)) (+.f64 (/.f64 k a) (/.f64 10 a)))))

series845.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/.f64 (pow.f64 k (neg.f64 m)) a)
36.0ms	(+.f64 (/.f64 k a) (/.f64 10 a))
229.0ms	(*.f64 (/.f64 k (pow.f64 k m)) (+.f64 (/.f64 k a) (/.f64 10 a)))
467.0ms	(/.f64 1 (+.f64 (/.f64 (pow.f64 k (neg.f64 m)) a) (*.f64 (/.f64 k (pow.f64 k m)) (+.f64 (/.f64 k a) (/.f64 10 a)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5564	4354

prune163.0ms

Filtered

138 candidates to 176 candidates (-27.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	176	5	181

Merged error: 0.0b

Counts

181 → 5

regimes54.0ms

Accuracy

91.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 2.1b

bsearch20.0ms

Steps

Iters	Range		Point
6	2.6602592073498244e+26	4.1954436430461596e+27	4.820871725571901e+26

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	74
1	42	74

end0.0ms

sample1.3s

Algorithm

intervals

Results

547.0ms	8000×	body	128	valid
288.0ms	3225×	body	128	invalid
92.0ms	2022×	body	128	nan

Details

analyze1.0s

sample42.0ms

simplify118.0ms

prune4.0ms

localize9.0ms

rewrite25.0ms

series428.0ms

simplify69.0ms

prune67.0ms

localize14.0ms

rewrite50.0ms

series611.0ms

simplify58.0ms

prune156.0ms

localize10.0ms

rewrite41.0ms

series562.0ms

simplify90.0ms

prune107.0ms

localize16.0ms

rewrite84.0ms

series845.0ms

simplify82.0ms

prune163.0ms

regimes54.0ms

bsearch20.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling