Details

sample82.0ms

Algorithm

intervals

Results

24.0ms	295×	body	80	nan
8.0ms	169×	body	80	valid
7.0ms	29×	body	1280	valid
5.0ms	20×	body	1280	nan
4.0ms	21×	body	640	valid
4.0ms	19×	body	640	nan
3.0ms	18×	body	320	valid
2.0ms	19×	body	160	valid
1.0ms	10×	body	320	nan
1.0ms	6×	body	160	nan

simplify100.0ms

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: 40.4b

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)
12.3b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.6b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite71.0ms

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))))
5.0ms	(* (sqrt 2.0) t)
18.0ms	(- (* (/ (+ 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)))

series1.9s

Counts

4 → 12

Calls

4 calls:

426.0ms	(/ (* (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)))

simplify70.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (58.0ms)

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

prune315.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

localize20.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (pow l 2) x)
5.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.9b	(/ (pow t 2) x)
25.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite30.0ms

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:

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

series274.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify71.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	526	1067
1	2113	984
2	5001	978

prune469.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
5.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
7.9b	(/ (pow t 2) x)
25.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-r/` `associate-/l`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `unpow2` `sqr-pow`
3×	`cbrt-prod` `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` `pow1/3` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

0.0ms	(cbrt x)
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
4.0ms	(/ (pow t 2) x)
11.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt x)
66.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
18.0ms	(/ (pow t 2) x)
159.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	502	1312
1	2198	1195
2	5003	1187

prune424.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.8b

localize25.0ms

Local error

Found 4 expressions with local error:

7.9b	(/ (pow t 2) x)
7.9b	(/ (pow t 2) x)
25.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))
25.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
42×	`add-sqr-sqrt`
40×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`sqrt-div` `associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`pow1` `div-exp` `associate-/r*` `sqrt-prod`
4×	`flip3-+` `frac-add` `flip-+` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 132

Calls

4 calls:

4.0ms	(/ (pow t 2) x)
4.0ms	(/ (pow t 2) x)
11.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))
9.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (pow t 2) x)
21.0ms	(/ (pow t 2) x)
153.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))
158.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	428	1612
1	1792	1510
2	5001	1504

prune641.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 4.8b

regimes562.0ms

Accuracy

77.2% (5.4b remaining)

Error of 9.4b against oracle of 4.1b and baseline of 27.7b

bsearch373.0ms

Steps

Iters	Range		Point
2	4.258838753023189e+61	4.8864700944733366e+61	4.808016176792068e+61
7	-1.4478719089695824e-243	-3.729343639150035e-245	-9.1577416971198e-244
7	-5.388105193354488e-210	-3.2415088457474183e-211	-7.0895915203531395e-211
9	-2.884473285972568e+119	-1.203303521956221e+113	-3.093140357296897e+118

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	101
1	67	101
2	67	101

end0.0ms

sample2.0s

Algorithm

intervals

Results

472.0ms	10064×	body	80	nan
256.0ms	5025×	body	80	valid
224.0ms	905×	body	1280	valid
198.0ms	1028×	body	640	valid
140.0ms	601×	body	1280	nan
112.0ms	622×	body	640	nan
95.0ms	654×	body	320	valid
49.0ms	364×	body	320	nan
37.0ms	388×	body	160	valid
19.0ms	185×	body	160	nan