Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	32×	body	2560	valid
7.0ms	194×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	18×	body	1280	valid
1.0ms	5×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify9.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

54.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
28.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
54.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
49.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
73.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify72.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	280	891
1	816	840
2	2500	828
3	5001	827

prune255.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.6b

localize16.0ms

Local error

Found 4 expressions with local error:

5.6b	(cbrt (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
8×	`sqrt-div`
7×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 78

Calls

4 calls:

16.0ms	(cbrt (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
218.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
50.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	238	907
1	664	877
2	2370	866
3	5001	863

prune351.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.6b	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`associate-/r*`
8×	`sqrt-div`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 94

Calls

4 calls:

30.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
50.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify152.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 3 (140.0ms)

Iter	Nodes	Cost
0	342	1276
1	1189	1191
2	4729	1163
3	5001	1145

prune347.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.6b	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`associate-/r*`
8×	`sqrt-div`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 94

Calls

4 calls:

29.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
77.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
51.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify146.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 3 (134.0ms)

Iter	Nodes	Cost
0	342	1276
1	1189	1191
2	4729	1163
3	5001	1145

prune376.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.6b

regimes173.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	26
1	23	26

end0.0ms

sample881.0ms

Algorithm

intervals

Results

212.0ms	6060×	body	80	valid
185.0ms	827×	body	2560	valid
110.0ms	595×	body	1280	valid
101.0ms	8000×	pre	80	true
38.0ms	276×	body	640	valid
20.0ms	151×	body	320	valid
6.0ms	91×	body	160	valid