Details

sample46.0ms

Algorithm

intervals

Results

11.0ms	202×	body	80	valid
6.0ms	8×	body	640	valid
5.0ms	16×	body	2560	valid
5.0ms	19×	body	1280	valid
5.0ms	256×	pre	80	true
1.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify8.0ms

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 (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: 11.9b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.9b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 38

Calls

3 calls:

5.0ms	(+ (* (* 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)))

series28.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
14.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	203	365
1	753	336
2	2672	332
3	5002	332

prune124.0ms

Filtered

47 candidates to 39 candidates (17.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	37	10	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	10	48

Merged error: 11.6b

Counts

48 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
5.8b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
16.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
16×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`pow1` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out`
4×	`flip3-+` `sqrt-div` `cube-prod` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*`
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` `sum-cubes` `div-inv`

Counts

4 → 98

Calls

4 calls:

38.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
10.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
8.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	352	1056
1	1610	965
2	5001	964

prune361.0ms

Filtered

110 candidates to 81 candidates (26.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	110	10	120

Merged error: 11.6b

Counts

120 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.9b	(log (exp (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
5.8b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
16.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`log-pow`
9×	`add-exp-log` `exp-prod`
8×	`associate-/l*`
7×	`pow1`
6×	`sqrt-prod` `add-cbrt-cube`
5×	`distribute-lft-out`
4×	`log-prod` `sqrt-div` `cube-prod` `unpow2` `add-log-exp` `sqr-pow`
3×	`flip3-+` `div-exp` `associate-/r*` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `rem-log-exp` `exp-sum` `pow-exp` `clear-num` `sum-cubes` `div-inv`

Counts

4 → 103

Calls

4 calls:

40.0ms	(log (exp (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
10.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(log (exp (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
9.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	338	1056
1	1380	962
2	5001	961

prune432.0ms

Filtered

115 candidates to 82 candidates (28.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	109	6	115
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	111	14	125

Merged error: 11.6b

Counts

125 → 14

localize31.0ms

Local error

Found 4 expressions with local error:

5.8b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
16.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
12×	`unpow-prod-down`
9×	`add-exp-log` `sqrt-prod`
8×	`associate-/l*`
7×	`pow1`
6×	`sqrt-div` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `unpow2` `add-log-exp` `sqr-pow`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-/r*`
2×	`associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 96

Calls

4 calls:

8.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(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)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	256	941
1	1094	877
2	5002	876

prune547.0ms

Filtered

108 candidates to 81 candidates (25.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	8	5	13
Picked	0	1	1
Done	0	0	0
Total	110	12	122

Merged error: 11.6b

Counts

122 → 12

regimes333.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	43
1	35	43

end0.0ms

sample1.3s

Algorithm

intervals

Results

320.0ms	6013×	body	80	valid
251.0ms	762×	body	2560	valid
180.0ms	678×	body	1280	valid
142.0ms	8000×	pre	80	true
66.0ms	320×	body	640	valid
23.0ms	151×	body	320	valid
8.0ms	76×	body	160	valid

Details

sample46.0ms

simplify8.0ms

prune3.0ms

localize11.0ms

rewrite24.0ms

series28.0ms

simplify79.0ms

prune124.0ms

localize21.0ms

rewrite61.0ms

series40.0ms

simplify52.0ms

prune361.0ms

localize25.0ms

rewrite63.0ms

series41.0ms

simplify49.0ms

prune432.0ms

localize31.0ms

rewrite26.0ms

series31.0ms

simplify44.0ms

prune547.0ms

regimes333.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling