Details

analyze111.0ms

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

sample24.0ms

Algorithm

intervals

Results

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

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5141	26

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: 0.6b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 v v))
0.2b	(*.f64 PI.f64 t)
0.4b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
0.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

6.0ms	(.f64 3 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)
13.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
18.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(.f64 3 (.f64 v v))
3.0ms	(*.f64 PI.f64 t)
24.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
39.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))

simplify41.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5564	1795

prune111.0ms

Filtered

75 candidates to 106 candidates (-41.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	99	7	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	8	107

Merged error: 0.3b

Counts

107 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 v v) 3)
0.3b	(.f64 PI.f64 (.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3))))) (+.f64 (*.f64 v v) -1)))
0.4b	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))
0.4b	(/.f64 (+.f64 (.f64 5 (.f64 v v)) -1) (.f64 PI.f64 (.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3))))) (+.f64 (*.f64 v v) -1))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

48×	`associate-*r/_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`pow1_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
14×	`sqrt-div_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`pow-prod-down_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-r_binary64` `associate-/r/_binary64` `frac-times_binary64`
7×	`flip3-+_binary64` `flip3--_binary64` `associate-l_binary64` `flip--_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-exp_binary64` `associate-*l/_binary64`
3×	`associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `unswap-sqr_binary64`
1×	`associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 108

Calls

4 calls:

6.0ms	(.f64 (.f64 v v) 3)
16.0ms	(.f64 PI.f64 (.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3))))) (+.f64 (*.f64 v v) -1)))
9.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))
25.0ms	(/.f64 (+.f64 (.f64 5 (.f64 v v)) -1) (.f64 PI.f64 (.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3))))) (+.f64 (*.f64 v v) -1))))

series105.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(.f64 (.f64 v v) 3)
40.0ms	(.f64 PI.f64 (.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3))))) (+.f64 (*.f64 v v) -1)))
24.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))
38.0ms	(/.f64 (+.f64 (.f64 5 (.f64 v v)) -1) (.f64 PI.f64 (.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3))))) (+.f64 (*.f64 v v) -1))))

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4997	2485
1	4997	2485

prune122.0ms

Filtered

85 candidates to 120 candidates (-41.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	121	7	128

Merged error: 0.0b

Counts

128 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.2b	(.f64 (.f64 v v) 3)
0.4b	(/.f64 (/.f64 (+.f64 (.f64 5 (.f64 v v)) -1) PI.f64) (.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3))))) (+.f64 (.f64 v v) -1)))
0.4b	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
31×	`times-frac_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`associate-*r/_binary64`
16×	`pow1_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`associate-r_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
7×	`pow-prod-down_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `frac-times_binary64`
3×	`flip3-+_binary64` `unswap-sqr_binary64` `div-inv_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`associate-*l/_binary64`
1×	`associate-/l/_binary64` `associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-prod_binary64`

Counts

4 → 117

Calls

4 calls:

6.0ms	(.f64 5 (.f64 v v))
6.0ms	(.f64 (.f64 v v) 3)
25.0ms	(/.f64 (/.f64 (+.f64 (.f64 5 (.f64 v v)) -1) PI.f64) (.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3))))) (+.f64 (.f64 v v) -1)))
9.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(.f64 5 (.f64 v v))
3.0ms	(.f64 (.f64 v v) 3)
38.0ms	(/.f64 (/.f64 (+.f64 (.f64 5 (.f64 v v)) -1) PI.f64) (.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3))))) (+.f64 (.f64 v v) -1)))
21.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5196	2510

prune121.0ms

Filtered

91 candidates to 129 candidates (-41.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	129	7	136

Merged error: 0.0b

Counts

136 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 v v) 3)
0.3b	(/.f64 (+.f64 (.f64 5 (.f64 v v)) -1) (.f64 (+.f64 (.f64 v v) -1) (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))))
0.4b	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))
0.4b	(.f64 (/.f64 1 PI.f64) (/.f64 (+.f64 (.f64 5 (.f64 v v)) -1) (.f64 (+.f64 (.f64 v v) -1) (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (*.f64 v v) 3))))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-exp-log_binary64`
52×	`add-cbrt-cube_binary64`
35×	`prod-exp_binary64`
33×	`associate-*r/_binary64`
28×	`add-sqr-sqrt_binary64`
23×	`div-exp_binary64`
22×	`associate-r_binary64`
21×	`cbrt-unprod_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
17×	`associate-l_binary64` `times-frac_binary64`
16×	`associate-/r/_binary64`
14×	`sqrt-div_binary64`
13×	`pow1_binary64` `cbrt-undiv_binary64`
9×	`frac-times_binary64`
7×	`flip3-+_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64`
5×	`pow-prod-down_binary64` `unswap-sqr_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `1-exp_binary64` `rec-exp_binary64`
3×	`associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64`
1×	`associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-prod_binary64`

Counts

4 → 140

Calls

4 calls:

6.0ms	(.f64 (.f64 v v) 3)
22.0ms	(/.f64 (+.f64 (.f64 5 (.f64 v v)) -1) (.f64 (+.f64 (.f64 v v) -1) (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))))
8.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))
30.0ms	(.f64 (/.f64 1 PI.f64) (/.f64 (+.f64 (.f64 5 (.f64 v v)) -1) (.f64 (+.f64 (.f64 v v) -1) (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (*.f64 v v) 3))))))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(.f64 (.f64 v v) 3)
32.0ms	(/.f64 (+.f64 (.f64 5 (.f64 v v)) -1) (.f64 (+.f64 (.f64 v v) -1) (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))))
21.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (.f64 v v) 3)))))
41.0ms	(.f64 (/.f64 1 PI.f64) (/.f64 (+.f64 (.f64 5 (.f64 v v)) -1) (.f64 (+.f64 (.f64 v v) -1) (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 (*.f64 v v) 3))))))))

simplify79.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4944	3566
1	4944	3566

prune148.0ms

Filtered

103 candidates to 152 candidates (-47.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	153	6	159

Merged error: 0b

Counts

159 → 6

regimes127.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	28
1	60	28

end0.0ms

sample666.0ms

Algorithm

intervals

Results

523.0ms	8000×	body	80	valid
0.0ms	6×	body	80	nan

Details

analyze111.0ms

sample24.0ms

simplify42.0ms

prune5.0ms

localize15.0ms

rewrite45.0ms

series69.0ms

simplify41.0ms

prune111.0ms

localize15.0ms

rewrite61.0ms

series105.0ms

simplify58.0ms

prune122.0ms

localize15.0ms

rewrite51.0ms

series65.0ms

simplify45.0ms

prune121.0ms

localize19.0ms

rewrite73.0ms

series98.0ms

simplify79.0ms

prune148.0ms

regimes127.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample666.0ms

Profiling