Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	197×	body	80	valid
6.0ms	27×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	19×	body	1280	valid
1.0ms	5×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune3.0ms

Filtered

1 candidates to 0 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: 10.9b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.9b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `flip-+`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 79

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* (* 4.0 p) p) (* x x))
59.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
72.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify152.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4246	757
3	5001	757

prune240.0ms

Filtered

91 candidates to 67 candidates (73.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	8	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Merged error: 10.7b

Counts

92 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.6b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
14×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
5×	`unswap-sqr`
4×	`flip3-+` `sqrt-div` `prod-exp` `flip-+`
3×	`associate-l`
2×	`+-commutative` `div-exp` `sum-log` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 86

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
14.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* (* 4.0 p) p) (* x x))
53.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	387	818
1	1925	734
2	5001	700

prune219.0ms

Filtered

98 candidates to 67 candidates (68.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	98	8	106

Merged error: 10.7b

Counts

106 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
7.0b	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

46×	`sqrt-prod`
37×	`add-sqr-sqrt`
27×	`associate-r`
23×	`*-un-lft-identity`
22×	`times-frac`
21×	`add-cube-cbrt`
8×	`pow1`
7×	`sqrt-div`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `flip-+`
3×	`associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`+-commutative` `associate-r/` `pow-prod-down` `prod-exp` `sum-log` `-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 89

Calls

4 calls:

19.0ms	(* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
3.0ms	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
79.0ms	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	376	1085
1	1392	982
2	5001	923

prune329.0ms

Filtered

101 candidates to 75 candidates (74.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	5	101
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	101	8	109

Merged error: 10.7b

Counts

109 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (+ (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1.0) 3))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.6b	(+ (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1.0)
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
24×	`-un-lft-identity` `associate-r*`
22×	`add-cube-cbrt` `times-frac`
14×	`sqrt-prod`
13×	`add-exp-log`
12×	`cbrt-prod`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `sqrt-div` `prod-exp` `flip-+`
3×	`unpow-prod-down` `cube-prod` `associate-l`
2×	`cube-div` `cbrt-div` `div-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `pow1/3` `1-exp` `unpow3` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `rem-cbrt-cube` `div-inv` `sqr-pow`

Counts

4 → 98

Calls

4 calls:

12.0ms	(cbrt (pow (+ (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1.0) 3))
14.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(+ (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1.0)
6.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(cbrt (pow (+ (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1.0) 3))
61.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms	(+ (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 1.0)
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	425	1050
1	1936	996
2	5001	972

prune280.0ms

Filtered

110 candidates to 77 candidates (70.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	107	11	118

Merged error: 10.7b

Counts

118 → 11

regimes161.0ms

Accuracy

0% (0.5b remaining)

Error of 13.3b against oracle of 12.9b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	27	12

end0.0ms

sample828.0ms

Algorithm

intervals

Results

213.0ms	6042×	body	80	valid
179.0ms	796×	body	2560	valid
112.0ms	609×	body	1280	valid
104.0ms	8000×	pre	80	true
42.0ms	309×	body	640	valid
17.0ms	164×	body	320	valid
6.0ms	80×	body	160	valid

Details

sample33.0ms

simplify10.0ms

prune3.0ms

localize15.0ms

rewrite31.0ms

series231.0ms

simplify152.0ms

prune240.0ms

localize13.0ms

rewrite29.0ms

series230.0ms

simplify51.0ms

prune219.0ms

localize15.0ms

rewrite35.0ms

series342.0ms

simplify55.0ms

prune329.0ms

localize15.0ms

rewrite46.0ms

series275.0ms

simplify59.0ms

prune280.0ms

regimes161.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample828.0ms

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