Details

sample49.0ms

Algorithm

intervals

Results

12.0ms	181×	body	80	valid
9.0ms	28×	body	2560	valid
7.0ms	28×	body	1280	valid
5.0ms	256×	pre	80	true
3.0ms	12×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	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

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: 15.8b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series133.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify113.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	167	267
1	465	248
2	1264	247
3	3249	247
4	5001	247

prune108.0ms

Filtered

33 candidates to 29 candidates (87.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	25	8	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	8	34

Merged error: 15.5b

Counts

34 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
4.0b	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
12.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

37.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
8.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
50.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	296	693
1	1364	633
2	5001	630

prune314.0ms

Filtered

82 candidates to 64 candidates (78.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	82	8	90

Merged error: 15.5b

Counts

90 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

12.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

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)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify89.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	98	500
1	283	484
2	827	484
3	2050	484
4	5001	484

prune467.0ms

Filtered

72 candidates to 64 candidates (88.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	72	8	80

Merged error: 15.5b

Counts

80 → 8

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)))))
9.0b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `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` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

20.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
9.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (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)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
74.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	291	1356
1	1085	1258
2	5002	1216

prune251.0ms

Filtered

137 candidates to 72 candidates (52.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	133	12	145

Merged error: 15.5b

Counts

145 → 12

regimes173.0ms

Accuracy

0% (0.2b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	49
1	40	49

end0.0ms

sample1.2s

Algorithm

intervals

Results

322.0ms	6057×	body	80	valid
244.0ms	766×	body	2560	valid
167.0ms	641×	body	1280	valid
152.0ms	8000×	pre	80	true
66.0ms	313×	body	640	valid
24.0ms	145×	body	320	valid
8.0ms	78×	body	160	valid

Details

sample49.0ms

simplify9.0ms

prune3.0ms

localize11.0ms

rewrite17.0ms

series133.0ms

simplify113.0ms

prune108.0ms

localize19.0ms

rewrite57.0ms

series239.0ms

simplify45.0ms

prune314.0ms

localize33.0ms

rewrite22.0ms

series232.0ms

simplify89.0ms

prune467.0ms

localize13.0ms

rewrite43.0ms

series240.0ms

simplify52.0ms

prune251.0ms

regimes173.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling