Details

analyze12.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

sample27.0ms

Algorithm

intervals

Results

8.0ms	57×	body	640	valid
5.0ms	136×	body	80	valid
4.0ms	24×	body	1280	valid
2.0ms	22×	body	320	valid
1.0ms	17×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	880	15
1	880	15

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: 8.7b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1.0 (+.f64 x 1.0))
0.0b	(-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x))
0.0b	(/.f64 1.0 (-.f64 x 1.0))
1.6b	(+.f64 (-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x)) (/.f64 1.0 (-.f64 x 1.0)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity_binary64`
47×	`times-frac_binary64`
43×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
14×	`distribute-lft-out--_binary64`
13×	`distribute-lft-out_binary64`
11×	`add-log-exp_binary64`
9×	`associate-/r*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
6×	`associate-/l*_binary64`
4×	`pow1_binary64` `associate-/r/_binary64`
3×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64`

Counts

4 → 112

Calls

4 calls:

6.0ms	(/.f64 1.0 (+.f64 x 1.0))
18.0ms	(-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x))
6.0ms	(/.f64 1.0 (-.f64 x 1.0))
36.0ms	(+.f64 (-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x)) (/.f64 1.0 (-.f64 x 1.0)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/.f64 1.0 (+.f64 x 1.0))
4.0ms	(-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x))
3.0ms	(/.f64 1.0 (-.f64 x 1.0))
18.0ms	(+.f64 (-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x)) (/.f64 1.0 (-.f64 x 1.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4954	1594
1	4954	1594

prune155.0ms

Filtered

95 candidates to 124 candidates (-30.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	121	4	125

Merged error: 0.3b

Counts

125 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))
0.1b	(+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))
6.0b	(+.f64 (*.f64 (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)) (-.f64 x 1.0)) 1.0)
16.3b	(/.f64 (.f64 (+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)) (+.f64 (.f64 (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)) (-.f64 x 1.0)) 1.0)) (*.f64 (-.f64 x 1.0) (+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`flip3-+_binary64` `flip-+_binary64`
12×	`frac-times_binary64`
11×	`associate-/l/_binary64` `associate-/r/_binary64`
10×	`add-log-exp_binary64`
9×	`times-frac_binary64`
8×	`distribute-lft-out_binary64` `frac-add_binary64`
5×	`associate-r/_binary64` `associate-l/_binary64`
4×	`pow1_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64` `div-exp_binary64` `flip--_binary64`
3×	`+-commutative_binary64` `sum-log_binary64`
2×	`sub-neg_binary64` `associate-+l+_binary64`
1×	`associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64`

Counts

4 → 86

Calls

4 calls:

20.0ms	(+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))
17.0ms	(+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))
26.0ms	(+.f64 (*.f64 (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)) (-.f64 x 1.0)) 1.0)
71.0ms	(/.f64 (.f64 (+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)) (+.f64 (.f64 (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)) (-.f64 x 1.0)) 1.0)) (*.f64 (-.f64 x 1.0) (+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))
4.0ms	(+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))
8.0ms	(+.f64 (*.f64 (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)) (-.f64 x 1.0)) 1.0)
23.0ms	(/.f64 (.f64 (+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)) (+.f64 (.f64 (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)) (-.f64 x 1.0)) 1.0)) (*.f64 (-.f64 x 1.0) (+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))))

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5847	2223

prune190.0ms

Filtered

79 candidates to 98 candidates (-24.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	97	5	102

Merged error: 0.0b

Counts

102 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))
0.1b	(+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))
0.6b	(/.f64 2.0 (*.f64 x x))
4.5b	(/.f64 (.f64 (+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)) (/.f64 2.0 (.f64 x x))) (*.f64 (-.f64 x 1.0) (+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
28×	`*-un-lft-identity_binary64`
14×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`times-frac_binary64`
11×	`associate-/r/_binary64`
9×	`frac-times_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out_binary64`
7×	`flip3-+_binary64` `associate-/l/_binary64` `frac-add_binary64` `flip-+_binary64`
6×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`associate-*l/_binary64`
4×	`pow1_binary64` `flip3--_binary64` `associate-r/_binary64` `associate-/l_binary64` `flip--_binary64`
2×	`associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

17.0ms	(+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))
17.0ms	(+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))
5.0ms	(/.f64 2.0 (*.f64 x x))
49.0ms	(/.f64 (.f64 (+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)) (/.f64 2.0 (.f64 x x))) (*.f64 (-.f64 x 1.0) (+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))))

series17.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))
4.0ms	(+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))
4.0ms	(/.f64 2.0 (*.f64 x x))
5.0ms	(/.f64 (.f64 (+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)) (/.f64 2.0 (.f64 x x))) (*.f64 (-.f64 x 1.0) (+.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))))

simplify39.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4963	1577
1	4963	1577

prune144.0ms

Filtered

77 candidates to 110 candidates (-42.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	107	8	115

Merged error: 0b

Counts

115 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 2.0 (*.f64 x x)) (-.f64 x 1.0))
0.2b	(.f64 (/.f64 (.f64 1 (/.f64 (/.f64 2.0 (*.f64 x x)) (-.f64 x 1.0))) (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))) (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)))
0.6b	(/.f64 2.0 (*.f64 x x))
21.7b	(/.f64 (.f64 1 (/.f64 (/.f64 2.0 (.f64 x x)) (-.f64 x 1.0))) (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac_binary64`
97×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
91×	`*-un-lft-identity_binary64`
65×	`add-cbrt-cube_binary64`
45×	`div-exp_binary64`
32×	`prod-exp_binary64`
31×	`add-cube-cbrt_binary64`
27×	`cbrt-undiv_binary64`
24×	`difference-of-squares_binary64`
20×	`distribute-lft-out--_binary64`
18×	`cbrt-unprod_binary64`
17×	`associate-l_binary64`
16×	`associate-/r*_binary64`
11×	`associate-/l*_binary64`
10×	`associate-r_binary64` `div-inv_binary64`
8×	`1-exp_binary64` `associate-/r/_binary64`
6×	`pow1_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `frac-sub_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 198

Calls

4 calls:

10.0ms	(/.f64 (/.f64 2.0 (*.f64 x x)) (-.f64 x 1.0))
58.0ms	(.f64 (/.f64 (.f64 1 (/.f64 (/.f64 2.0 (*.f64 x x)) (-.f64 x 1.0))) (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))) (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)))
5.0ms	(/.f64 2.0 (*.f64 x x))
31.0ms	(/.f64 (.f64 1 (/.f64 (/.f64 2.0 (.f64 x x)) (-.f64 x 1.0))) (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/.f64 (/.f64 2.0 (*.f64 x x)) (-.f64 x 1.0))
5.0ms	(.f64 (/.f64 (.f64 1 (/.f64 (/.f64 2.0 (*.f64 x x)) (-.f64 x 1.0))) (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x))) (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)))
4.0ms	(/.f64 2.0 (*.f64 x x))
15.0ms	(/.f64 (.f64 1 (/.f64 (/.f64 2.0 (.f64 x x)) (-.f64 x 1.0))) (-.f64 (/.f64 1.0 (+.f64 1.0 x)) (/.f64 2.0 x)))

simplify56.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5030	3610

prune280.0ms

Filtered

138 candidates to 210 candidates (-52.2%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	210	8	218

Merged error: 0b

Counts

218 → 8

regimes107.0ms

Accuracy

95.2% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 9.6b

bsearch43.0ms

Steps

Iters	Range		Point
11	1.5553778562738503e-12	1.7474571606456e+21	299129.8760379891
9	-45653906.43056792	-0.011514006144460328	-218778.51422173358

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	81
1	60	81

end0.0ms

sample780.0ms

Algorithm

intervals

Results

280.0ms	1882×	body	640	valid
165.0ms	4217×	body	80	valid
101.0ms	914×	body	320	valid
99.0ms	524×	body	1280	valid
34.0ms	463×	body	160	valid

Details

analyze12.0ms

sample27.0ms

simplify67.0ms

prune5.0ms

localize9.0ms

rewrite70.0ms

series27.0ms

simplify52.0ms

prune155.0ms

localize14.0ms

rewrite138.0ms

series40.0ms

simplify46.0ms

prune190.0ms

localize12.0ms

rewrite96.0ms

series17.0ms

simplify39.0ms

prune144.0ms

localize14.0ms

rewrite115.0ms

series28.0ms

simplify56.0ms

prune280.0ms

regimes107.0ms

bsearch43.0ms

simplify3.0ms

end0.0ms

sample780.0ms

Profiling