Details

sample34.0ms

Algorithm

intervals

Results

6.0ms	187×	body	80	valid
6.0ms	28×	body	2560	valid
4.0ms	22×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	10×	body	640	valid
1.0ms	8×	body	320	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

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: 13.9b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
18×	`associate-l`
13×	`distribute-lft-out`
9×	`sqrt-prod`
7×	`add-log-exp`
5×	`add-sqr-sqrt`
4×	`pow1` `add-cube-cbrt`
3×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `sqrt-div` `sum-log`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

3 → 50

Calls

3 calls:

25.0ms	(+ (* (* 4.0 p) p) (* x x))
39.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series429.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* (* 4.0 p) p) (* x x))
329.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify86.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	192	425
1	698	397
2	2405	393
3	5002	386

prune118.0ms

Filtered

59 candidates to 38 candidates (64.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	50	9	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	9	60

Merged error: 13.6b

Counts

60 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
2.5b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
14.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

175×	`*-un-lft-identity`
99×	`associate-l`
72×	`times-frac`
68×	`distribute-lft-out`
37×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
32×	`unpow-prod-down`
18×	`sqrt-prod`
10×	`unpow2` `sqr-pow`
9×	`add-exp-log` `associate-/r*`
8×	`associate-/l*`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
4×	`pow-unpow` `flip3-+` `sqrt-div` `sum-cubes` `flip-+`
3×	`div-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 164

Calls

4 calls:

48.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
30.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
54.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify70.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	391	1541
1	1538	1409
2	5002	1402

prune388.0ms

Filtered

176 candidates to 81 candidates (46.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	176	9	185

Merged error: 13.6b

Counts

185 → 9

localize13.0ms

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)))))
11.0b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite252.0ms

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)))))
127.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (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)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
65.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify70.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (44.0ms)

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

prune272.0ms

Filtered

209 candidates to 73 candidates (34.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	205	4	209
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	209	9	218

Merged error: 13.6b

Counts

218 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

5.2b	(exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b	(- 1.0 (/ x (exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity`
28×	`sqrt-prod`
27×	`associate-l`
22×	`add-sqr-sqrt`
18×	`distribute-lft-out`
14×	`log-prod` `exp-sum`
9×	`add-cube-cbrt`
8×	`pow1`
7×	`add-log-exp`
6×	`exp-prod` `sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
3×	`sqrt-pow1` `flip3-+` `times-frac` `pow1/2` `log-pow` `flip-+`
2×	`rem-sqrt-square` `log-div` `exp-diff` `rem-exp-log`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

29.0ms	(exp (log (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)))
41.0ms	(- 1.0 (/ x (exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))))

series263.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
84.0ms	(- 1.0 (/ x (exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))))

simplify105.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 4 (94.0ms)

Iter	Nodes	Cost
0	211	829
1	458	794
2	1074	774
3	2533	766
4	5001	765

prune359.0ms

Filtered

100 candidates to 67 candidates (67.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 13.6b

Counts

109 → 10

regimes170.0ms

Accuracy

0% (1.2b remaining)

Error of 14.0b against oracle of 12.8b and baseline of 14.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	48
1	45	48

end0.0ms

sample831.0ms

Algorithm

intervals

Results

218.0ms	6042×	body	80	valid
175.0ms	794×	body	2560	valid
111.0ms	609×	body	1280	valid
107.0ms	8000×	pre	80	true
43.0ms	311×	body	640	valid
16.0ms	156×	body	320	valid
6.0ms	88×	body	160	valid