Details

sample98.0ms

Algorithm

intervals

Results

34.0ms	337×	body	80	nan
10.0ms	39×	body	1280	valid
8.0ms	161×	body	80	valid
6.0ms	29×	body	640	valid
5.0ms	19×	body	1280	nan
4.0ms	21×	body	640	nan
2.0ms	15×	body	320	valid
2.0ms	14×	body	320	nan
1.0ms	12×	body	160	valid
1.0ms	7×	body	160	nan

simplify90.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 46.0b

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)
12.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.6b	(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)
13.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

429.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
41.0ms	(* (sqrt 2.0) t)
218.0ms	(- (* (/ (+ 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)))

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

prune281.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	4	93

Merged error: 8.3b

Counts

93 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.2b	(/ (pow l 2) x)
8.1b	(/ (pow t 2) x)
28.4b	(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:

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

series274.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms	(/ (pow l 2) x)
19.0ms	(/ (pow t 2) x)
168.0ms	(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 (50.0ms)

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

prune418.0ms

Filtered

142 candidates to 97 candidates (68.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	137	9	146

Merged error: 5.8b

Counts

146 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
8.1b	(/ (pow t 2) x)
28.4b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
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))))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sqrt 2.0) t)
65.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
18.0ms	(/ (pow t 2) x)
162.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	477	917
1	2140	851
2	5001	848

prune325.0ms

Filtered

115 candidates to 80 candidates (69.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	114	10	124

Merged error: 5.8b

Counts

124 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
8.1b	(/ (pow t 2) x)
28.4b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

11.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
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))))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
66.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
19.0ms	(/ (pow t 2) x)
163.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	528	1093
1	2319	937
2	5002	895

prune328.0ms

Filtered

115 candidates to 77 candidates (67.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	114	11	125

Merged error: 5.8b

Counts

125 → 11

regimes506.0ms

Accuracy

76.3% (5.6b remaining)

Error of 9.6b against oracle of 4.0b and baseline of 27.7b

bsearch623.0ms

Steps

Iters	Range		Point
9	8.035144973212608e+106	2.245460825297648e+113	4.237815991261577e+112
4	1.2124728414118423e-211	2.2847307266758587e-211	2.2297033326087545e-211
7	1.915898718087215e-234	4.464915074202446e-232	8.22209001535682e-233
8	-1.243875693689644e-199	-2.0983465895690414e-202	-1.2665252057061608e-201
7	-7.309844064450707e-163	-5.607849872840746e-165	-5.9781316899939775e-164
10	-1.1430041385930207e+102	-1.1718803704805511e+85	-2.5865283365572245e+92

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	139
1	95	139

end0.0ms

sample2.1s

Algorithm

intervals

Results

508.0ms	9926×	body	80	nan
272.0ms	5127×	body	80	valid
231.0ms	852×	body	1280	valid
211.0ms	1029×	body	640	valid
141.0ms	549×	body	1280	nan
121.0ms	607×	body	640	nan
96.0ms	637×	body	320	valid
47.0ms	319×	body	320	nan
36.0ms	355×	body	160	valid
19.0ms	175×	body	160	nan