Details

analyze498.0ms

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

sample22.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	452	21
1	452	21

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: 18.7b

Counts

2 → 1

localize17.0ms

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)
3.1b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
18.0b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite47.0ms

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)
8.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
12.0ms	(.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))

series57.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
10.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
13.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
29.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

simplify85.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5504	1244

prune110.0ms

Filtered

74 candidates to 100 candidates (-35.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	5	101

Merged error: 0b

Counts

101 → 5

localize14.0ms

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)))
13.9b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite55.0ms

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:

7.0ms	(*.f64 z (+.f64 z 1692356830115869/281474976710656))
8.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
19.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
19.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

series48.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 z (+.f64 z 1692356830115869/281474976710656))
7.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
30.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
6.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify82.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4958	1922
1	4958	1922

prune112.0ms

Filtered

89 candidates to 122 candidates (-37.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	122	5	127

Merged error: 0b

Counts

127 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

7.4b	(/.f64 (.f64 (/.f64 y (sqrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)) (sqrt.f64 (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)))
9.3b	(.f64 (/.f64 y (sqrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
13.3b	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
13.3b	(sqrt.f64 (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
24×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
22×	`sqrt-prod_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64` `sqrt-div_binary64`
6×	`associate-/r*_binary64`
5×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `prod-exp_binary64` `frac-times_binary64`
3×	`associate-r_binary64` `unswap-sqr_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `-commutative_binary64`

Counts

4 → 116

Calls

4 calls:

28.0ms	(/.f64 (.f64 (/.f64 y (sqrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)) (sqrt.f64 (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)))
22.0ms	(.f64 (/.f64 y (sqrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
9.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
7.0ms	(sqrt.f64 (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

series76.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/.f64 (.f64 (/.f64 y (sqrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)) (sqrt.f64 (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)))
36.0ms	(.f64 (/.f64 y (sqrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
4.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
4.0ms	(sqrt.f64 (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

simplify58.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5083	2607

prune157.0ms

Filtered

98 candidates to 128 candidates (-30.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	128	5	133

Merged error: 0b

Counts

133 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)
3.1b	(.f64 y (+.f64 (/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
5.1b	(/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
18.0b	(/.f64 (.f64 y (+.f64 (/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

4.0ms	(*.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)
17.0ms	(.f64 y (+.f64 (/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
13.0ms	(/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
24.0ms	(/.f64 (.f64 y (+.f64 (/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

series94.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(*.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)
30.0ms	(.f64 y (+.f64 (/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
13.0ms	(/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
49.0ms	(/.f64 (.f64 y (+.f64 (/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

simplify58.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5049	1862

prune99.0ms

Filtered

77 candidates to 103 candidates (-33.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	103	5	108

Merged error: 0b

Counts

108 → 5

regimes262.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.5b

bsearch26.0ms

Steps

Iters	Range		Point
7	124.71777197877577	26009.766577771647	25520.883699056
6	-7.928144404603421e+33	-1.2006388770707984e+33	-1.9448004982439977e+33

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	45
1	66	45

end0.0ms

sample605.0ms

Algorithm

intervals

Results

424.0ms

8000×

body

valid

Details

analyze498.0ms

sample22.0ms

simplify15.0ms

prune5.0ms

localize17.0ms

rewrite47.0ms

series57.0ms

simplify85.0ms

prune110.0ms

localize14.0ms

rewrite55.0ms

series48.0ms

simplify82.0ms

prune112.0ms

localize19.0ms

rewrite69.0ms

series76.0ms

simplify58.0ms

prune157.0ms

localize20.0ms

rewrite62.0ms

series94.0ms

simplify58.0ms

prune99.0ms

regimes262.0ms

bsearch26.0ms

simplify3.0ms

end0.0ms

sample605.0ms

Profiling