Details

analyze506.0ms

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

sample25.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	452	21
1	452	21

prune10.0ms

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: 13.9b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (+ z 6.012459259764103))
0.1b	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
0.1b	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
13.4b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
22×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
5×	`flip3-+` `associate-*r/` `flip-+`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `div-inv` `associate-/l/`
1×	`frac-2neg` `clear-num` `distribute-lft-out`

Counts

4 → 110

Calls

4 calls:

8.0ms	(* z (+ z 6.012459259764103))
16.0ms	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
14.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series39.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* z (+ z 6.012459259764103))
24.0ms	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
6.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify70.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4982	1944
1	4982	1944

prune208.0ms

Filtered

89 candidates to 122 candidates (-37.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	119	5	124

Merged error: 0b

Counts

124 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) y)
0.3b	(* (* (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) y) (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
13.4b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
13.4b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
37×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
32×	`sqrt-prod`
21×	`associate-r`
19×	`associate-l`
15×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-/r/`
6×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
5×	`sqrt-div`
4×	`pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
3×	`unswap-sqr`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `*-commutative`
1×	`frac-times` `associate-*r/`

Counts

4 → 134

Calls

4 calls:

19.0ms	(* (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) y)
29.0ms	(* (* (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) y) (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
14.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
14.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series49.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) y)
13.0ms	(* (* (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) y) (sqrt (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
6.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
5.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify45.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5034	3589

prune384.0ms

Filtered

113 candidates to 146 candidates (-29.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	146	5	151

Merged error: 0b

Counts

151 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b	(cbrt (+ (* z 0.0692910599291889) 0.4917317610505968))
0.9b	(cbrt (+ (* z 0.0692910599291889) 0.4917317610505968))
0.9b	(cbrt (+ (* z 0.0692910599291889) 0.4917317610505968))
13.4b	(/ (+ (* (* z (* (cbrt (+ (* z 0.0692910599291889) 0.4917317610505968)) (cbrt (+ (* z 0.0692910599291889) 0.4917317610505968)))) (cbrt (+ (* z 0.0692910599291889) 0.4917317610505968))) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `cbrt-div` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 70

Calls

4 calls:

4.0ms	(cbrt (+ (* z 0.0692910599291889) 0.4917317610505968))
4.0ms	(cbrt (+ (* z 0.0692910599291889) 0.4917317610505968))
4.0ms	(cbrt (+ (* z 0.0692910599291889) 0.4917317610505968))
29.0ms	(/ (+ (* (* z (* (cbrt (+ (* z 0.0692910599291889) 0.4917317610505968)) (cbrt (+ (* z 0.0692910599291889) 0.4917317610505968)))) (cbrt (+ (* z 0.0692910599291889) 0.4917317610505968))) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series27.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(cbrt (+ (* z 0.0692910599291889) 0.4917317610505968))
7.0ms	(cbrt (+ (* z 0.0692910599291889) 0.4917317610505968))
7.0ms	(cbrt (+ (* z 0.0692910599291889) 0.4917317610505968))
6.0ms	(/ (+ (* (* z (* (cbrt (+ (* z 0.0692910599291889) 0.4917317610505968)) (cbrt (+ (* z 0.0692910599291889) 0.4917317610505968)))) (cbrt (+ (* z 0.0692910599291889) 0.4917317610505968))) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4962	1558
1	4962	1558

prune226.0ms

Filtered

75 candidates to 82 candidates (-9.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	82	5	87

Merged error: 0b

Counts

87 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

7.0b	(* (/ y (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
12.7b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
12.9b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
12.9b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 150

Calls

4 calls:

36.0ms	(* (/ y (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
15.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series38.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (/ y (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
7.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
3.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
4.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify47.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5363	4141

prune340.0ms

Filtered

117 candidates to 162 candidates (-38.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	162	5	167

Merged error: 0b

Counts

167 → 5

regimes318.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.6b

bsearch41.0ms

Steps

Iters	Range		Point
9	5.855895722313977	5022909.458131179	458236.22514243907
9	-9.343068239039799e+26	-3.49027869528185e+21	-1.120362690310111e+22

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	60
1	70	60

end0.0ms

sample602.0ms

Algorithm

intervals

Results

428.0ms

8000×

body

valid

Details

analyze506.0ms

sample25.0ms

simplify11.0ms

prune10.0ms

localize14.0ms

rewrite47.0ms

series39.0ms

simplify70.0ms

prune208.0ms

localize17.0ms

rewrite80.0ms

series49.0ms

simplify45.0ms

prune384.0ms

localize21.0ms

rewrite42.0ms

series27.0ms

simplify44.0ms

prune226.0ms

localize17.0ms

rewrite69.0ms

series38.0ms

simplify47.0ms

prune340.0ms

regimes318.0ms

bsearch41.0ms

simplify2.0ms

end0.0ms

sample602.0ms

Profiling