Details

analyze501.0ms

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

sample20.0ms

Algorithm

intervals

Results

12.0ms

256×

body

128

valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

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: 17.2b

Counts

2 → 1

localize18.0ms

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)
4.3b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
16.4b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite50.0ms

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:

6.0ms	(*.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))
17.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

series384.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
74.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
74.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
182.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

simplify86.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4915	1847
1	4915	1847

prune140.0ms

Filtered

74 candidates to 100 candidates (-35.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	6	101

Merged error: 0.0b

Counts

101 → 6

localize15.0ms

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)))
12.9b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite61.0ms

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:

9.0ms	(*.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)))
15.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

series355.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(*.f64 z (+.f64 z 1692356830115869/281474976710656))
80.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
180.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
44.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify96.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4951	2874
1	4951	2874

prune152.0ms

Filtered

88 candidates to 122 candidates (-38.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	122	6	128

Merged error: 0.0b

Counts

128 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

7.6b	(.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))))
12.4b	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
12.4b	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
12.5b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

rewrite94.0ms

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:

40.0ms	(.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))
7.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
18.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(.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))))
31.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
34.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
66.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

simplify99.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5217	6204

prune284.0ms

Filtered

117 candidates to 162 candidates (-38.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	162	6	168

Merged error: 0.0b

Counts

168 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

6.8b	(/.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)))
10.6b	(.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))
12.4b	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
12.4b	(sqrt.f64 (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite82.0ms

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:

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)))
21.0ms	(.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))
7.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
7.0ms	(sqrt.f64 (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

series506.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/.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)))
248.0ms	(.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))
36.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
35.0ms	(sqrt.f64 (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

simplify103.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4958	3970
1	4958	3970

prune208.0ms

Filtered

97 candidates to 128 candidates (-32.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	128	6	134

Merged error: 0.0b

Counts

134 → 6

regimes117.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.3b

bsearch49.0ms

Steps

Iters	Range		Point
9	1362.663684024933	271712907.4169929	532710.2646555883
9	-45546479.909072824	-228.4263982151477	-1249845.8181184959

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	67
1	68	67

end0.0ms

sample583.0ms

Algorithm

intervals

Results

403.0ms

8000×

body

128

valid

Details

analyze501.0ms

sample20.0ms

simplify20.0ms

prune3.0ms

localize18.0ms

rewrite50.0ms

series384.0ms

simplify86.0ms

prune140.0ms

localize15.0ms

rewrite61.0ms

series355.0ms

simplify96.0ms

prune152.0ms

localize19.0ms

rewrite94.0ms

series305.0ms

simplify99.0ms

prune284.0ms

localize19.0ms

rewrite82.0ms

series506.0ms

simplify103.0ms

prune208.0ms

regimes117.0ms

bsearch49.0ms

simplify4.0ms

end0.0ms

sample583.0ms

Profiling