Details

analyze529.0ms

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%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
21.8%	78%	0.1%	9
49.1%	50.7%	0.1%	10
52.7%	47.2%	0.1%	11
52.7%	47.2%	0.1%	12
71.7%	28.2%	0.1%	13
74.1%	25.8%	0.1%	14

sample24.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	453	31
1	453	31

prune3.0ms

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: 21.4b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
0.1b	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
5.5b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
20.7b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64` `associate-l_binary64`
9×	`associate-r_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64` `associate-l/_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `unswap-sqr_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64`
1×	`distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 88

Calls

4 calls:

7.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
7.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
11.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
18.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

series202.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
37.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
41.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
91.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

simplify133.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4905	1847
1	4905	1847

prune123.0ms

Filtered

74 candidates to 100 candidates (-35.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	4	101

Merged error: 0b

Counts

101 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 z (+.f64 z 1692356830115869/281474976710656))
0.1b	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
0.1b	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
17.3b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`
19×	`times-frac_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`associate-l_binary64`
5×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`distribute-lft-out_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 110

Calls

4 calls:

6.0ms	(*.f64 z (+.f64 z 1692356830115869/281474976710656))
7.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
18.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
16.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

series185.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(*.f64 z (+.f64 z 1692356830115869/281474976710656))
37.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
98.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
22.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify121.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4953	2874
1	4953	2874

prune139.0ms

Filtered

88 candidates to 122 candidates (-38.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	122	4	126

Merged error: 0b

Counts

126 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

8.7b	(.f64 (/.f64 y (sqrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
16.6b	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
16.6b	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
16.7b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt_binary64`
66×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
42×	`sqrt-prod_binary64`
24×	`associate-r_binary64` `associate-l_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`sqrt-div_binary64`
9×	`unswap-sqr_binary64`
8×	`pow1_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `associate-/r/_binary64` `flip-+_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`associate-/l*_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 150

Calls

4 calls:

38.0ms	(.f64 (/.f64 y (sqrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
7.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
9.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
17.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(.f64 (/.f64 y (sqrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
17.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
19.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
36.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

simplify106.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5220	6199

prune471.0ms

Filtered

117 candidates to 162 candidates (-38.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	162	4	166

Merged error: 0b

Counts

166 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
0.5b	(/.f64 1 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
5.5b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
20.2b	(.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (/.f64 1 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`add-cbrt-cube_binary64`
21×	`associate-r_binary64`
18×	`times-frac_binary64`
14×	`pow1_binary64` `prod-exp_binary64`
8×	`cbrt-unprod_binary64`
7×	`associate-r/_binary64` `associate-l*_binary64`
6×	`flip3-+_binary64` `div-exp_binary64` `flip-+_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `associate-*l/_binary64`
3×	`associate-/r_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64` `div-inv_binary64` `frac-times_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64`

Counts

4 → 119

Calls

4 calls:

8.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
9.0ms	(/.f64 1 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
11.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
26.0ms	(.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (/.f64 1 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

series197.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
15.0ms	(/.f64 1 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
44.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
100.0ms	(.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (/.f64 1 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

simplify120.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4979	2877
1	4979	2877

prune130.0ms

Filtered

86 candidates to 131 candidates (-52.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	131	4	135

Merged error: 0b

Counts

135 → 4

regimes128.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.8b

bsearch51.0ms

Steps

Iters	Range		Point
10	1.3315706460943291e-11	35205389.054761395	608410.2706810925
9	-7490444.585746592	-0.003962694951595999	-1102359.9607622703

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	68	67
1	68	67

end0.0ms

sample611.0ms

Algorithm

intervals

Results

433.0ms

8000×

body

valid

Details

analyze529.0ms

sample24.0ms

simplify27.0ms

prune3.0ms

localize14.0ms

rewrite48.0ms

series202.0ms

simplify133.0ms

prune123.0ms

localize16.0ms

rewrite51.0ms

series185.0ms

simplify121.0ms

prune139.0ms

localize17.0ms

rewrite76.0ms

series169.0ms

simplify106.0ms

prune471.0ms

localize15.0ms

rewrite57.0ms

series197.0ms

simplify120.0ms

prune130.0ms

regimes128.0ms

bsearch51.0ms

simplify5.0ms

end0.0ms

sample611.0ms

Profiling