Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	188×	body	80	valid
6.0ms	24×	body	2560	valid
5.0ms	26×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	8×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	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: 15.1b

localize11.0ms

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)))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite81.0ms

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:

26.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
29.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
54.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (64.0ms)

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

prune295.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.3b	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

12.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
27.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
273.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
73.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify74.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	290	947
1	783	872
2	2259	860
3	5001	859

prune367.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.7b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

13.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
27.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
101.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	269	900
1	805	835
2	2267	823
3	5002	822

prune358.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.9b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`

Counts

4 → 54

Calls

4 calls:

25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify104.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	167	534
1	465	496
2	1264	494
3	3249	494
4	5001	494

prune396.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.9b

regimes557.0ms

Accuracy

0% (0.6b remaining)

Error of 13.5b against oracle of 12.9b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	12
1	26	12

end0.0ms

sample908.0ms

Algorithm

intervals

Results

235.0ms	6019×	body	80	valid
195.0ms	791×	body	2560	valid
126.0ms	635×	body	1280	valid
114.0ms	8000×	pre	80	true
48.0ms	317×	body	640	valid
17.0ms	153×	body	320	valid
6.0ms	85×	body	160	valid