Details

sample142.0ms

Algorithm

intervals

Results

45.0ms	333×	body	80	nan
18.0ms	168×	body	80	valid
16.0ms	32×	body	1280	valid
10.0ms	27×	body	640	valid
9.0ms	20×	body	1280	nan
9.0ms	23×	body	640	nan
7.0ms	24×	body	320	valid
2.0ms	7×	body	320	nan
1.0ms	5×	body	160	valid
1.0ms	5×	body	160	nan

simplify85.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize25.0ms

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)
14.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite63.0ms

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:

23.0ms	(/ (* (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)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

405.0ms	(/ (* (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)
204.0ms	(- (* (/ (+ 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 (48.0ms)

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

prune283.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 7.4b

localize17.0ms

Local error

Found 4 expressions with local error:

5.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.7b	(/ (pow l 2) x)
9.2b	(/ (pow t 2) x)
29.2b	(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:

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

series258.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
18.0ms	(/ (pow l 2) x)
20.0ms	(/ (pow t 2) x)
155.0ms	(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	1067
1	2113	984
2	5001	978

prune434.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (pow t 2) (/ l (/ x l)))
5.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
9.2b	(/ (pow t 2) x)
29.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite47.0ms

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:

24.0ms	(+ (pow t 2) (/ l (/ x l)))
7.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
4.0ms	(/ (pow t 2) x)
9.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (pow t 2) (/ l (/ x l)))
62.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
18.0ms	(/ (pow t 2) x)
154.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	453	945
1	1899	862
2	5003	859

prune335.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize19.0ms

Local error

Found 4 expressions with local error:

9.2b	(/ (pow t 2) x)
29.2b	(sqrt (+ (pow t 2) (/ l (/ x l))))
29.2b	(sqrt (+ (pow t 2) (/ l (/ x l))))
29.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ l (/ x l)))) (sqrt (+ (pow t 2) (/ l (/ x l))))))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`sqrt-div`
24×	`add-cube-cbrt` `times-frac`
18×	`associate-*r/`
12×	`unpow-prod-down`
11×	`sqrt-prod`
9×	`add-exp-log` `flip3-+` `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/` `distribute-lft-out`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 104

Calls

4 calls:

4.0ms	(/ (pow t 2) x)
46.0ms	(sqrt (+ (pow t 2) (/ l (/ x l))))
46.0ms	(sqrt (+ (pow t 2) (/ l (/ x l))))
13.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ l (/ x l)))) (sqrt (+ (pow t 2) (/ l (/ x l))))))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (pow t 2) x)
63.0ms	(sqrt (+ (pow t 2) (/ l (/ x l))))
66.0ms	(sqrt (+ (pow t 2) (/ l (/ x l))))
157.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ l (/ x l)))) (sqrt (+ (pow t 2) (/ l (/ x l))))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	508	1356
1	1734	1296
2	5001	1291

prune371.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

regimes245.0ms

Accuracy

77.8% (5.3b remaining)

Error of 9.3b against oracle of 4.0b and baseline of 27.8b

bsearch315.0ms

Steps

Iters	Range		Point
11	2.3978422144747918e+88	1.8292938033907602e+110	2.0467080239710555e+93
10	-2.9582771485052574e+72	-2.98384958962079e+60	-2.9422530870118713e+66

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	57
1	59	57

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.1s	10037×	body	80	nan
568.0ms	5133×	body	80	valid
416.0ms	850×	body	1280	valid
390.0ms	1016×	body	640	valid
262.0ms	558×	body	1280	nan
233.0ms	620×	body	640	nan
181.0ms	628×	body	320	valid
93.0ms	328×	body	320	nan
73.0ms	373×	body	160	valid
36.0ms	182×	body	160	nan