Details

sample117.0ms

Algorithm

intervals

Results

26.0ms	157×	body	80	valid
25.0ms	336×	body	80	nan
12.0ms	34×	body	1280	valid
9.0ms	31×	body	640	valid
4.0ms	13×	body	1280	nan
4.0ms	21×	body	320	valid
4.0ms	16×	body	640	nan
4.0ms	19×	body	320	nan
2.0ms	13×	body	160	valid
1.0ms	5×	body	160	nan

simplify90.0ms

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: 47.0b

Counts

2 → 1

localize19.0ms

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)
18.3b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.1b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite61.0ms

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)
20.0ms	(- (* (/ (+ 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)))

series1.8s

Counts

4 → 12

Calls

4 calls:

425.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
44.0ms	(* (sqrt 2.0) t)
214.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.1s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify63.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (50.0ms)

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

prune287.0ms

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: 6.7b

Counts

93 → 5

localize22.0ms

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))))
9.0b	(/ (pow l 2) x)
10.9b	(/ (pow t 2) x)
30.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite31.0ms

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:

9.0ms	(+ (* 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)
8.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series269.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
18.0ms	(/ (pow l 2) x)
18.0ms	(/ (pow t 2) x)
165.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (53.0ms)

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

prune431.0ms

Filtered

142 candidates to 97 candidates (68.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	136	11	147

Merged error: 3.8b

Counts

147 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (pow t 2) (* l (/ l x)))
5.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
10.9b	(/ (pow t 2) x)
30.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l 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 (/ l x)))
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (pow t 2) (* l (/ l x)))
65.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
18.0ms	(/ (pow t 2) x)
160.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	456	938
1	2000	858
2	5001	855

prune307.0ms

Filtered

104 candidates to 75 candidates (72.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	104	11	115

Merged error: 3.8b

Counts

115 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (pow t 2) (/ l (/ x l)))
5.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
10.9b	(/ (pow t 2) x)
30.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite44.0ms

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:

20.0ms	(+ (pow t 2) (/ l (/ x l)))
9.0ms	(+ (* 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))))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (pow t 2) (/ l (/ x l)))
66.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
18.0ms	(/ (pow t 2) x)
159.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	453	932
1	1835	862
2	5002	859

prune284.0ms

Filtered

105 candidates to 76 candidates (72.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	105	11	116

Merged error: 3.8b

Counts

116 → 11

regimes401.0ms

Accuracy

76.8% (5.4b remaining)

Error of 9.4b against oracle of 3.9b and baseline of 27.4b

bsearch517.0ms

Steps

Iters	Range		Point
10	1.2595621310590059e+82	3.894835433597967e+93	2.258932197835794e+91
6	7.074655084320963e-174	3.1124934180468344e-173	3.030059721002767e-173
11	1.3206601388511477e-263	8.075482312126455e-244	2.85675210770605e-244
7	-5.2688144766041883e+36	-5.369753097786847e+34	-5.1993499904970025e+36

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	92
1	79	92

end0.0ms

sample2.7s

Algorithm

intervals

Results

694.0ms	10056×	body	80	nan
353.0ms	5067×	body	80	valid
304.0ms	882×	body	1280	valid
272.0ms	1034×	body	640	valid
188.0ms	570×	body	1280	nan
164.0ms	613×	body	640	nan
129.0ms	640×	body	320	valid
77.0ms	387×	body	320	nan
50.0ms	377×	body	160	valid
23.0ms	177×	body	160	nan