Details

sample36.0ms

Algorithm

intervals

Results

11.0ms	205×	body	80	valid
6.0ms	27×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	14×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	640	valid
0.0ms	1×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 10.7b

Counts

2 → 1

localize11.0ms

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))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

100×	`*-un-lft-identity`
54×	`associate-l`
45×	`sqrt-prod`
37×	`distribute-lft-out`
36×	`times-frac`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
12×	`associate-/r*`
8×	`add-log-exp`
6×	`add-exp-log` `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`

Counts

4 → 115

Calls

4 calls:

23.0ms	(+ (* (* 4.0 p) p) (* x x))
27.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
36.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* (* 4.0 p) p) (* x x))
58.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify156.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	268	1074
1	965	1025
2	3968	956
3	5001	956

prune211.0ms

Filtered

127 candidates to 67 candidates (47.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	118	9	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	9	128

Merged error: 10.5b

Counts

128 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.8b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

164×	`*-un-lft-identity`
85×	`associate-l`
83×	`sqrt-prod`
76×	`times-frac`
62×	`add-sqr-sqrt`
56×	`distribute-lft-out`
49×	`add-cube-cbrt`
42×	`associate-r`
24×	`associate-/r*`
18×	`associate-*r/`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
7×	`associate-/l*`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+`
3×	`pow-flip` `clear-num` `un-div-inv`
2×	`cbrt-undiv` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `*-commutative` `inv-pow`

Counts

4 → 191

Calls

4 calls:

28.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
43.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
47.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
58.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify132.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	364	1527
1	1612	1320
2	4985	1205
3	5001	1205

prune268.0ms

Filtered

203 candidates to 86 candidates (57.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	199	4	203
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	203	9	212

Merged error: 10.5b

Counts

212 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

300×	`sqrt-prod`
248×	`*-un-lft-identity`
177×	`associate-l`
109×	`distribute-lft-out`
63×	`swap-sqr`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `pow1/2`
15×	`associate-r`
9×	`flip3-+` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 197

Calls

4 calls:

63.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
130.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
80.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
64.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify71.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	279	1800
1	1032	1608
2	5001	1582

prune289.0ms

Filtered

209 candidates to 76 candidates (63.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	205	4	209
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	210	8	218

Merged error: 10.5b

Counts

218 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0b	(+ 1.0 (* (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ (cbrt 1) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
102×	`sqrt-prod`
55×	`associate-l`
45×	`times-frac`
38×	`distribute-lft-out`
36×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
15×	`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 → 132

Calls

4 calls:

29.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
159.0ms	(+ 1.0 (* (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ (cbrt 1) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
84.0ms	(+ 1.0 (* (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ (cbrt 1) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify154.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	332	1633
1	1116	1546
2	4193	1437
3	5002	1437

prune316.0ms

Filtered

144 candidates to 78 candidates (45.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	142	10	152

Merged error: 10.5b

Counts

152 → 10

regimes155.0ms

Accuracy

0% (0.5b remaining)

Error of 13.2b against oracle of 12.8b and baseline of 13.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample855.0ms

Algorithm

intervals

Results

216.0ms	6074×	body	80	valid
185.0ms	768×	body	2560	valid
112.0ms	604×	body	1280	valid
111.0ms	8000×	pre	80	true
46.0ms	298×	body	640	valid
18.0ms	170×	body	320	valid
6.0ms	86×	body	160	valid