Details

analyze767.0ms

Algorithm: search

sample210.0ms

Algorithm

intervals

Results

150.0ms	21×	body	640	nan
12.0ms	170×	body	80	valid
9.0ms	28×	body	1280	valid
9.0ms	33×	body	640	valid
5.0ms	17×	body	1280	nan
4.0ms	18×	body	320	valid
3.0ms	51×	body	80	nan
3.0ms	17×	body	320	nan
1.0ms	7×	body	160	valid
0.0ms	3×	body	160	nan

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	14
1	93	14
2	193	14
3	414	14
4	718	14
5	1192	14
6	2816	14
7	5001	14

prune4.0ms

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: 42.0b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
11.2b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.6b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

16.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
15.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms	(* (sqrt 2.0) t)
57.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
185.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify59.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	417	1207
1	2051	1099
2	5002	1094

prune195.0ms

Filtered

65 candidates to 92 candidates (-41.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	4	93

Merged error: 5.3b

Counts

93 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

5.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.4b	(/ (pow l 2) x)
9.7b	(/ (pow t 2) x)
27.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `associate-+r+` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 130

Calls

4 calls:

11.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0ms	(/ (pow l 2) x)
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
3.0ms	(/ (pow l 2) x)
3.0ms	(/ (pow t 2) x)
24.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	526	1067
1	2113	984
2	5001	978

prune344.0ms

Filtered

97 candidates to 142 candidates (-46.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	138	8	146

Merged error: 3.1b

Counts

146 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (pow t 2) (/ l (/ x l)))
5.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
9.7b	(/ (pow t 2) x)
27.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

19.0ms	(+ (pow t 2) (/ l (/ x l)))
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (pow t 2) (/ l (/ x l)))
17.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
3.0ms	(/ (pow t 2) x)
25.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	453	932
1	1835	862
2	5001	859

prune232.0ms

Filtered

75 candidates to 105 candidates (-40.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Merged error: 3.1b

Counts

113 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
5.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
9.7b	(/ (pow t 2) x)
27.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

4.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
11.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
17.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
3.0ms	(/ (pow t 2) x)
28.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	463	1308
1	1965	1213
2	5001	1210

prune195.0ms

Filtered

74 candidates to 104 candidates (-40.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	104	8	112

Merged error: 3.1b

Counts

112 → 8

regimes514.0ms

Accuracy

74.1% (6.1b remaining)

Error of 9.9b against oracle of 3.8b and baseline of 27.2b

bsearch2.0s

Steps

Iters	Range		Point
6	3.1237386677247707e-17	1.57618174907215e-16	1.5562822777343958e-16
8	6.858805240157086e-209	5.362988684288142e-205	1.263558129808245e-206
12	9.560095028034299e-271	1.515518315749916e-226	2.8567070245163782e-257
5	-3.398472748085882e+70	-1.16461144655804e+70	-1.3816745027479693e+70

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	87
1	71	87
2	74	87
3	74	87

end0.0ms

analyze781.0ms

Algorithm: search

sample1.9s

Algorithm

intervals

Results

366.0ms	5105×	body	80	valid
288.0ms	1071×	body	640	valid
281.0ms	838×	body	1280	valid
201.0ms	607×	body	1280	nan
142.0ms	536×	body	640	nan
126.0ms	635×	body	320	valid
90.0ms	1343×	body	80	nan
62.0ms	322×	body	320	nan
47.0ms	351×	body	160	valid
19.0ms	152×	body	160	nan

Details

analyze767.0ms

sample210.0ms

simplify78.0ms

prune4.0ms

localize15.0ms

rewrite49.0ms

series334.0ms

simplify59.0ms

prune195.0ms

localize17.0ms

rewrite32.0ms

series78.0ms

simplify63.0ms

prune344.0ms

localize19.0ms

rewrite42.0ms

series53.0ms

simplify56.0ms

prune232.0ms

localize21.0ms

rewrite30.0ms

series60.0ms

simplify63.0ms

prune195.0ms

regimes514.0ms

bsearch2.0s

simplify3.0ms

end0.0ms

analyze781.0ms

sample1.9s

Profiling