Details

analyze268.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample63.0ms

Algorithm

intervals

Results

32.0ms	80×	body	1024	valid
11.0ms	34×	body	2048	valid
6.0ms	33×	body	512	valid
4.0ms	88×	body	128	valid
2.0ms	19×	body	256	valid
1.0ms	2×	body	4096	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	10	14

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 52.2b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
4.1b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`flip3-+_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 42

Calls

3 calls:

7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
10.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series192.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
98.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
36.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify103.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4839	862
1	4839	862

prune71.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Merged error: 0b

Counts

52 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
18.2b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

3.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
6.0ms	(*.f64 3/40 (pow.f64 x 5))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
7.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

series357.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
61.0ms	(*.f64 3/40 (pow.f64 x 5))
60.0ms	(*.f64 (pow.f64 x 3) 1/6)
58.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

simplify79.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5084	1210

prune76.0ms

Filtered

60 candidates to 92 candidates (-53.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	92	5	97

Merged error: 0b

Counts

97 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 1/2 x))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.2b	(/.f64 1/8 (pow.f64 x 3))
11.4b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
15×	`add-log-exp_binary64`
12×	`associate-/r*_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
10×	`add-exp-log_binary64`
9×	`distribute-lft-out_binary64`
6×	`log-prod_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `sum-log_binary64`
4×	`sqr-pow_binary64` `distribute-lft-out--_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`diff-log_binary64` `log-div_binary64` `+-commutative_binary64` `associate-+r+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-+r-_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-exp_binary64` `associate--l+_binary64`

Counts

4 → 113

Calls

4 calls:

8.0ms	(+.f64 x (/.f64 1/2 x))
26.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
29.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

series225.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+.f64 x (/.f64 1/2 x))
46.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
50.0ms	(/.f64 1/8 (pow.f64 x 3))
74.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

simplify77.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4890	2077
1	4890	2077

prune90.0ms

Filtered

73 candidates to 125 candidates (-71.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	125	5	130

Merged error: 0b

Counts

130 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/16 (pow.f64 x 5))
0.2b	(/.f64 1/8 (pow.f64 x 3))
13.1b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
18.7b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
71×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
26×	`unpow-prod-down_binary64`
19×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
11×	`log-prod_binary64`
10×	`sqr-pow_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-sub_binary64`
5×	`pow1_binary64` `log-div_binary64`
4×	`distribute-lft-out_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sum-log_binary64`

Counts

4 → 159

Calls

4 calls:

5.0ms	(/.f64 1/16 (pow.f64 x 5))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
38.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
46.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/.f64 1/16 (pow.f64 x 5))
42.0ms	(/.f64 1/8 (pow.f64 x 3))
73.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
54.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

simplify97.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4864	3605
1	4864	3605

prune176.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	171	5	176

Merged error: 0b

Counts

176 → 5

regimes47.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.9b

bsearch34.0ms

Steps

Iters	Range		Point
9	8.881543230873296e-05	9.909985727051907	0.9557656982210921
8	-2.927024651054935	-0.0017623652220767365	-1.0687018320624295

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms

sample1.9s

Algorithm

intervals

Results

940.0ms	2520×	body	1024	valid
385.0ms	1153×	body	2048	valid
262.0ms	1294×	body	512	valid
109.0ms	2387×	body	128	valid
67.0ms	606×	body	256	valid
19.0ms	40×	body	4096	valid

Details

analyze268.0ms

sample63.0ms

simplify9.0ms

prune2.0ms

localize7.0ms

rewrite24.0ms

series192.0ms

simplify103.0ms

prune71.0ms

localize10.0ms

rewrite27.0ms

series357.0ms

simplify79.0ms

prune76.0ms

localize11.0ms

rewrite78.0ms

series225.0ms

simplify77.0ms

prune90.0ms

localize13.0ms

rewrite111.0ms

series230.0ms

simplify97.0ms

prune176.0ms

regimes47.0ms

bsearch34.0ms

simplify4.0ms

end0.0ms

sample1.9s

Profiling