Details

sample103.0ms

Algorithm

intervals

Results

30.0ms	339×	body	80	nan
11.0ms	163×	body	80	valid
10.0ms	28×	body	1280	valid
8.0ms	32×	body	640	valid
5.0ms	15×	body	1280	nan
5.0ms	24×	body	320	valid
4.0ms	14×	body	640	nan
3.0ms	14×	body	320	nan
1.0ms	9×	body	160	valid
1.0ms	9×	body	160	nan

simplify89.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

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: 44.9b

Counts

2 → 1

localize18.0ms

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))))
0.4b	(* (sqrt 2.0) t)
11.8b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.4b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite53.0ms

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:

17.0ms	(/ (* (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)
13.0ms	(- (* (/ (+ 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)))

series1.9s

Counts

4 → 12

Calls

4 calls:

418.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
43.0ms	(* (sqrt 2.0) t)
210.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify65.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (49.0ms)

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

prune284.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 6.4b

Counts

93 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (pow l 2) x)
5.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
10.0b	(/ (pow t 2) x)
30.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite33.0ms

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:

5.0ms	(/ (pow l 2) x)
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0ms	(/ (pow t 2) x)
9.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series269.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (pow l 2) x)
66.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms	(/ (pow t 2) x)
166.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	526	1093
1	2235	984
2	5001	978

prune403.0ms

Filtered

142 candidates to 97 candidates (68.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	138	9	147

Merged error: 4.6b

Counts

147 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
5.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
10.0b	(/ (pow t 2) x)
30.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite29.0ms

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:

5.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
9.0ms	(+ (* 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)))))))

series335.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
82.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
18.0ms	(/ (pow t 2) x)
179.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (51.0ms)

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

prune336.0ms

Filtered

104 candidates to 75 candidates (72.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	103	10	113

Merged error: 4.6b

Counts

113 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

30.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (* (cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))) (cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))))
30.8b	(cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))
30.8b	(cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))
30.8b	(cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div` `associate-*r/`
31×	`flip3-+` `flip-+`
28×	`frac-times` `sqrt-div`
26×	`frac-add`
14×	`associate-*l/`
9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 80

Calls

4 calls:

14.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (* (cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))) (cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))))
4.0ms	(cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))
4.0ms	(cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))
4.0ms	(cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (* (cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))) (cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))) (cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))))
107.0ms	(cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))
104.0ms	(cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))
109.0ms	(cbrt (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))

simplify84.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	711	5254
1	1790	5154
2	5001	5147

prune376.0ms

Filtered

92 candidates to 70 candidates (76.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	92	10	102

Merged error: 4.6b

Counts

102 → 10

regimes424.0ms

Accuracy

75.8% (5.8b remaining)

Error of 9.5b against oracle of 3.7b and baseline of 27.8b

bsearch510.0ms

Steps

Iters	Range		Point
9	1.3146782014653472e+94	2.2549696368179095e+99	2.771748845321087e+98
5	1.4318730439593602e-216	4.0711342710850435e-216	2.5468123883314033e-216
9	-2.974695126671388e-299	-2.4643609579596305e-304	-2.4944316805165755e-304
8	-1.132161819823307e+80	-4.2334860278696157e+77	-1.0479409207087712e+80

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	102
1	75	102
2	78	102
3	78	102

end0.0ms

sample2.6s

Algorithm

intervals

Results

679.0ms	9971×	body	80	nan
363.0ms	5224×	body	80	valid
265.0ms	799×	body	1280	valid
255.0ms	985×	body	640	valid
186.0ms	573×	body	1280	nan
153.0ms	578×	body	640	nan
127.0ms	637×	body	320	valid
68.0ms	347×	body	320	nan
48.0ms	355×	body	160	valid
28.0ms	190×	body	160	nan