Details

analyze772.0ms

Algorithm

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

sample41.0ms

Algorithm

intervals

Results

13.0ms	195×	body	80	valid
8.0ms	25×	body	2560	valid
4.0ms	256×	pre	80	true
4.0ms	16×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	17
1	38	17

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 13.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.1b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.8b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
14.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
32.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5214	875

prune153.0ms

Filtered

55 candidates to 63 candidates (-14.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	54	9	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	9	64

Merged error: 13.0b

Counts

64 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))) 3))
3.4b	(/ (* x x) (+ (* 4.0 (* p p)) (* x x)))
13.8b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
13.8b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite65.0ms

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:

41.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))) 3))
9.0ms	(/ (* x x) (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
7.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))) 3))
8.0ms	(/ (* x x) (+ (* 4.0 (* p p)) (* x x)))
7.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5047	1187

prune243.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	81	10	91

Merged error: 13.0b

Counts

91 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))
8.9b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
13.8b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
13.8b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite49.0ms

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)))))
10.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))
12.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (sqrt (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)))

simplify40.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5227	1885

prune235.0ms

Filtered

76 candidates to 137 candidates (-80.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	5	3	8
Picked	0	1	1
Done	0	1	1
Total	136	11	147

Merged error: 13.0b

Counts

147 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

8.6b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (sqrt (* (fabs (cbrt (+ (* 4.0 (* p p)) (* x x)))) (sqrt (cbrt (+ (* 4.0 (* p p)) (* x x)))))))))
13.8b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
14.6b	(cbrt (+ (* 4.0 (* p p)) (* x x)))
14.6b	(cbrt (+ (* 4.0 (* p p)) (* x x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

10.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (sqrt (* (fabs (cbrt (+ (* 4.0 (* p p)) (* x x)))) (sqrt (cbrt (+ (* 4.0 (* p p)) (* x x)))))))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))

series128.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (sqrt (* (fabs (cbrt (+ (* 4.0 (* p p)) (* x x)))) (sqrt (cbrt (+ (* 4.0 (* p p)) (* x x)))))))))
11.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
22.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))
22.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5102	1360

prune210.0ms

Filtered

54 candidates to 65 candidates (-20.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	1	7	8
Picked	1	0	1
Done	0	2	2
Total	63	13	76

Merged error: 13.0b

Counts

76 → 13

regimes177.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	52
1	45	52

end0.0ms

sample1.1s

Algorithm

intervals

Results

313.0ms	6009×	body	80	valid
265.0ms	830×	body	2560	valid
153.0ms	604×	body	1280	valid
140.0ms	8000×	pre	80	true
67.0ms	337×	body	640	valid
24.0ms	157×	body	320	valid
6.0ms	63×	body	160	valid

Details

analyze772.0ms

sample41.0ms

simplify3.0ms

prune7.0ms

localize11.0ms

rewrite39.0ms

series58.0ms

simplify42.0ms

prune153.0ms

localize20.0ms

rewrite65.0ms

series37.0ms

simplify44.0ms

prune243.0ms

localize14.0ms

rewrite49.0ms

series35.0ms

simplify40.0ms

prune235.0ms

localize24.0ms

rewrite30.0ms

series128.0ms

simplify62.0ms

prune210.0ms

regimes177.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling