Details

sample91.0ms

Algorithm

intervals

Results

18.0ms	340×	body	80	nan
15.0ms	22×	body	1280	nan
8.0ms	42×	body	640	valid
8.0ms	156×	body	80	valid
6.0ms	22×	body	1280	valid
4.0ms	21×	body	640	nan
3.0ms	23×	body	320	valid
1.0ms	13×	body	160	valid
1.0ms	6×	body	320	nan
1.0ms	9×	body	160	nan

simplify85.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.1b

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))))
0.5b	(* (sqrt 2.0) t)
12.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.0b	(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:

24.0ms	(/ (* (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:

424.0ms	(/ (* (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)
213.0ms	(- (* (/ (+ 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)))

simplify60.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (48.0ms)

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

prune297.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.1b

localize17.0ms

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))))
5.9b	(/ (pow l 2) x)
9.9b	(/ (pow t 2) x)
29.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite35.0ms

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:

67.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms	(/ (pow l 2) x)
22.0ms	(/ (pow t 2) x)
161.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (49.0ms)

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

prune447.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (pow t 2) (* l (/ l x)))
4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
9.9b	(/ (pow t 2) x)
29.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite32.0ms

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

series278.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (pow t 2) (* l (/ l x)))
62.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
18.0ms	(/ (pow t 2) x)
161.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (47.0ms)

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

prune333.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize19.0ms

Local error

Found 4 expressions with local error:

9.9b	(/ (pow t 2) x)
29.1b	(sqrt (+ (pow t 2) (* l (/ l x))))
29.1b	(sqrt (+ (pow t 2) (* l (/ l x))))
29.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`sqrt-div`
24×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`associate-*r/`
12×	`unpow-prod-down`
9×	`add-exp-log` `flip3-+` `sqrt-prod` `flip-+`
8×	`frac-add` `associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube`
4×	`frac-times` `unpow2` `add-log-exp` `sqr-pow`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-/r*`
2×	`associate-*l/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 102

Calls

4 calls:

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

series315.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (pow t 2) x)
67.0ms	(sqrt (+ (pow t 2) (* l (/ l x))))
68.0ms	(sqrt (+ (pow t 2) (* l (/ l x))))
162.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	511	1344
1	1766	1286
2	5002	1281

prune383.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.6b

regimes458.0ms

Accuracy

78.4% (5.0b remaining)

Error of 8.7b against oracle of 3.7b and baseline of 26.9b

bsearch378.0ms

Steps

Iters	Range		Point
6	4.78543668174494e+90	3.165910293729609e+91	8.647366978067528e+90
9	-1.2121149253887828e-221	-4.578360144249185e-227	-1.0069231603376872e-226
8	-1.8894950264995623e-157	-6.055389811834972e-162	-1.3093127471214333e-159
6	-8.705958973764969e+134	-8.61730005133688e+133	-6.0190934789368676e+134

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	82
1	66	82
2	66	82

end0.0ms

sample2.1s

Algorithm

intervals

Results

508.0ms	9987×	body	80	nan
266.0ms	5065×	body	80	valid
215.0ms	862×	body	1280	valid
208.0ms	1060×	body	640	valid
154.0ms	616×	body	1280	nan
122.0ms	618×	body	640	nan
99.0ms	668×	body	320	valid
50.0ms	322×	body	320	nan
35.0ms	345×	body	160	valid
18.0ms	188×	body	160	nan