Details

analyze101.0ms

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%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

sample26.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
0.0ms	1×	body	80	nan

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5141	26

prune6.0ms

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: 0.6b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 5 (.f64 v v))
0.3b	(.f64 t (.f64 PI.f64 (-.f64 1 (*.f64 v v))))
0.5b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 t (.f64 PI.f64 (-.f64 1 (.f64 v v))))))
0.5b	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 t (.f64 PI.f64 (-.f64 1 (.f64 v v)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
32×	`associate-*r/_binary64`
23×	`pow1_binary64`
18×	`cbrt-unprod_binary64` `prod-exp_binary64`
16×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
12×	`pow-prod-down_binary64` `sub-neg_binary64` `associate-l_binary64` `sqrt-div_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `associate-*l/_binary64`
3×	`associate-r_binary64` `associate-/l_binary64` `times-frac_binary64` `sqrt-prod_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64`
1×	`associate-/r*_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 119

Calls

4 calls:

6.0ms	(.f64 5 (.f64 v v))
7.0ms	(.f64 t (.f64 PI.f64 (-.f64 1 (*.f64 v v))))
16.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 t (.f64 PI.f64 (-.f64 1 (.f64 v v))))))
13.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 t (.f64 PI.f64 (-.f64 1 (.f64 v v)))))

series99.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(.f64 5 (.f64 v v))
17.0ms	(.f64 t (.f64 PI.f64 (-.f64 1 (*.f64 v v))))
41.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 t (.f64 PI.f64 (-.f64 1 (.f64 v v))))))
34.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 t (.f64 PI.f64 (-.f64 1 (.f64 v v)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5032	2573

prune184.0ms

Filtered

86 candidates to 131 candidates (-52.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	125	6	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	6	132

Merged error: 0.2b

Counts

132 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 v v) 5)
0.3b	(.f64 t (.f64 PI.f64 (-.f64 1 (*.f64 v v))))
0.6b	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 t (.f64 PI.f64 (-.f64 1 (*.f64 v v)))))
1.0b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac_binary64`
48×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
37×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
30×	`sqrt-prod_binary64`
27×	`associate-/l*_binary64`
14×	`pow1_binary64`
12×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`associate-*r/_binary64` `associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`pow-prod-down_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `associate-r_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `div-inv_binary64`
3×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `div-sub_binary64` `flip--_binary64` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`unswap-sqr_binary64`

Counts

4 → 162

Calls

4 calls:

6.0ms	(.f64 (.f64 v v) 5)
8.0ms	(.f64 t (.f64 PI.f64 (-.f64 1 (*.f64 v v))))
17.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 t (.f64 PI.f64 (-.f64 1 (*.f64 v v)))))
9.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (.f64 v v) 5)
17.0ms	(.f64 t (.f64 PI.f64 (-.f64 1 (*.f64 v v))))
44.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 t (.f64 PI.f64 (-.f64 1 (*.f64 v v)))))
15.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4938	4109
1	4938	4109

prune258.0ms

Filtered

115 candidates to 174 candidates (-51.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	175	5	180

Merged error: 0b

Counts

180 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 v v) 5)
0.3b	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) t) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 PI.f64 (-.f64 1 (*.f64 v v)))))
1.0b	(/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
1.0b	(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 PI.f64 (-.f64 1 (.f64 v v))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

248×	`times-frac_binary64`
160×	`sqrt-prod_binary64`
131×	`add-sqr-sqrt_binary64`
122×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
64×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
51×	`associate-r_binary64`
48×	`associate-/l*_binary64`
24×	`cbrt-undiv_binary64` `div-exp_binary64`
23×	`associate-l_binary64`
19×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`associate-/r/_binary64`
11×	`pow1_binary64`
10×	`sqrt-div_binary64`
7×	`associate-/r*_binary64` `div-inv_binary64`
5×	`associate-*r/_binary64`
4×	`pow-prod-down_binary64` `flip3-+_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `flip-+_binary64`
3×	`associate-/l/_binary64` `flip3--_binary64` `flip--_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`sqrt-undiv_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 295

Calls

4 calls:

6.0ms	(.f64 (.f64 v v) 5)
38.0ms	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) t) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 PI.f64 (-.f64 1 (*.f64 v v)))))
12.0ms	(/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
18.0ms	(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 PI.f64 (-.f64 1 (.f64 v v))))

series83.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(.f64 (.f64 v v) 5)
40.0ms	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) t) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 PI.f64 (-.f64 1 (*.f64 v v)))))
12.0ms	(/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
26.0ms	(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 PI.f64 (-.f64 1 (.f64 v v))))

simplify84.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4995	8901
1	4995	8901

prune507.0ms

Filtered

179 candidates to 307 candidates (-71.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	306	1	307
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	308	4	312

Merged error: 0b

Counts

312 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 1 (.f64 (.f64 v v) 5))
0.1b	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))) (.f64 PI.f64 (-.f64 1 (*.f64 v v))))) t)
0.1b	(.f64 v (.f64 v -6))
0.1b	(.f64 (.f64 v v) 5)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

57×	`times-frac_binary64`
32×	`associate-*r/_binary64` `associate-/r/_binary64`
31×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
28×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`sqrt-div_binary64`
16×	`frac-times_binary64`
15×	`associate-/l*_binary64`
14×	`pow1_binary64`
13×	`flip3--_binary64` `flip--_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`associate-*l/_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`pow-prod-down_binary64` `add-log-exp_binary64`
5×	`div-inv_binary64`
4×	`associate-r_binary64` `associate-l_binary64`
3×	`associate-/r*_binary64`
2×	`div-sub_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 131

Calls

4 calls:

4.0ms	(-.f64 1 (.f64 (.f64 v v) 5))
17.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))) (.f64 PI.f64 (-.f64 1 (*.f64 v v))))) t)
5.0ms	(.f64 v (.f64 v -6))
6.0ms	(.f64 (.f64 v v) 5)

series60.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 1 (.f64 (.f64 v v) 5))
40.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))) (.f64 PI.f64 (-.f64 1 (*.f64 v v))))) t)
7.0ms	(.f64 v (.f64 v -6))
4.0ms	(.f64 (.f64 v v) 5)

simplify51.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5084	3422

prune188.0ms

Filtered

109 candidates to 143 candidates (-31.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	143	4	147

Merged error: 0b

Counts

147 → 4

regimes79.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	26
1	61	26

end0.0ms

sample654.0ms

Algorithm

intervals

Results

514.0ms	8000×	body	80	valid
1.0ms	9×	body	80	nan

Details

analyze101.0ms

sample26.0ms

simplify39.0ms

prune6.0ms

localize14.0ms

rewrite47.0ms

series99.0ms

simplify57.0ms

prune184.0ms

localize15.0ms

rewrite46.0ms

series81.0ms

simplify68.0ms

prune258.0ms

localize17.0ms

rewrite88.0ms

series83.0ms

simplify84.0ms

prune507.0ms

localize14.0ms

rewrite38.0ms

series60.0ms

simplify51.0ms

prune188.0ms

regimes79.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample654.0ms

Profiling