Details

analyze2.3s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

sample97.0ms

Algorithm

intervals

Results

37.0ms	401×	body	80	nan
24.0ms	256×	body	80	valid
3.0ms	36×	body	80	invalid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4939	26
1	4939	26

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 30.2b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

5.4b	(.f64 (/.f64 l Om) (-.f64 U U))
7.0b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
8.7b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
20.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
21×	`add-sqr-sqrt_binary64`
17×	`associate-l_binary64`
16×	`pow-prod-down_binary64` `*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`cbrt-unprod_binary64` `associate-*r/_binary64` `prod-exp_binary64`
10×	`times-frac_binary64`
9×	`associate-r_binary64`
6×	`sub-neg_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `flip--_binary64` `frac-times_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

10.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
11.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

17.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
27.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
163.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
820.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5104	1952

prune170.0ms

Filtered

77 candidates to 121 candidates (-57.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	110	11	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 20.8b

Counts

123 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

4.5b	(*.f64 n (/.f64 l Om))
8.7b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
10.6b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
20.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
21×	`associate-r_binary64` `add-sqr-sqrt_binary64`
16×	`pow-prod-down_binary64` `*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`associate-*r/_binary64` `times-frac_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `sqrt-pow1_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `sqrt-prod_binary64` `associate-*l/_binary64`

Counts

4 → 101

Calls

4 calls:

7.0ms	(*.f64 n (/.f64 l Om))
9.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
10.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

6.0ms	(*.f64 n (/.f64 l Om))
161.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
26.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
816.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4990	1799
1	4990	1799

prune136.0ms

Filtered

70 candidates to 113 candidates (-61.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	114	10	124

Merged error: 20.6b

Counts

124 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

4.2b	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U* U)) (cbrt.f64 n)))
5.4b	(.f64 (/.f64 l Om) (-.f64 U U))
8.7b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U U)) (cbrt.f64 n)))))))
20.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U U)) (cbrt.f64 n))))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log_binary64`
46×	`pow1_binary64`
36×	`add-cbrt-cube_binary64`
30×	`cbrt-unprod_binary64` `prod-exp_binary64`
28×	`pow-prod-down_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`-un-lft-identity_binary64` `associate-l*_binary64`
13×	`associate-*r/_binary64` `add-cube-cbrt_binary64`
10×	`times-frac_binary64`
9×	`associate-r_binary64`
7×	`associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `flip--_binary64` `frac-times_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 117

Calls

4 calls:

19.0ms	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U* U)) (cbrt.f64 n)))
10.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
9.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U U)) (cbrt.f64 n)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U U)) (cbrt.f64 n))))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

33.0ms	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U* U)) (cbrt.f64 n)))
17.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
183.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U U)) (cbrt.f64 n)))))))
820.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U U)) (cbrt.f64 n))))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4981	2043
1	4981	2043

prune133.0ms

Filtered

72 candidates to 129 candidates (-79.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	129	10	139

Merged error: 20.6b

Counts

139 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

8.7b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
8.7b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
20.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
20.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

42×	`pow1_binary64`
24×	`pow-prod-down_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`associate-*r/_binary64` `sqrt-pow1_binary64`
6×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
2×	`pow1/2_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `sqrt-prod_binary64` `*-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
8.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series1.9s

Counts

4 → 12

Calls

4 calls:

160.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
162.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
810.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
803.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

simplify33.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	6274	2450

prune102.0ms

Filtered

58 candidates to 92 candidates (-58.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	91	11	102

Merged error: 20.6b

Counts

102 → 11

regimes735.0ms

Accuracy

14.6% (7.5b remaining)

Error of 29.5b against oracle of 22.0b and baseline of 30.8b

bsearch54.0ms

Steps

Iters	Range		Point
6	1.6541404280564278e-305	1.3341588840302468e-304	1.312713436382444e-304

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	64
1	58	64

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	12807×	body	80	nan
762.0ms	8000×	body	80	valid
118.0ms	1143×	body	80	invalid

Details

analyze2.3s

sample97.0ms

simplify75.0ms

prune15.0ms

localize17.0ms

rewrite44.0ms

series1.0s

simplify49.0ms

prune170.0ms

localize19.0ms

rewrite38.0ms

series1.0s

simplify48.0ms

prune136.0ms

localize20.0ms

rewrite51.0ms

series1.1s

simplify59.0ms

prune133.0ms

localize21.0ms

rewrite37.0ms

series1.9s

simplify33.0ms

prune102.0ms

regimes735.0ms

bsearch54.0ms

simplify2.0ms

end0.0ms

sample2.8s

Profiling