Details

sample86.0ms

Algorithm

intervals

Results

17.0ms	156×	body	80	valid
16.0ms	316×	body	80	nan
9.0ms	43×	body	640	valid
8.0ms	29×	body	1280	valid
4.0ms	16×	body	1280	nan
4.0ms	23×	body	320	valid
3.0ms	17×	body	640	nan
2.0ms	12×	body	320	nan
1.0ms	5×	body	160	nan
1.0ms	5×	body	160	valid

simplify87.0ms

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: 45.4b

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)
11.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.4b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite72.0ms

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:

30.0ms	(/ (* (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)
12.0ms	(- (* (/ (+ 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:

432.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
45.0ms	(* (sqrt 2.0) t)
216.0ms	(- (* (/ (+ 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 (51.0ms)

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

prune311.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.0b

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))))
5.2b	(/ (pow l 2) x)
9.0b	(/ (pow t 2) x)
28.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite34.0ms

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

series271.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms	(/ (pow l 2) x)
18.0ms	(/ (pow t 2) x)
167.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (50.0ms)

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

prune466.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
9.0b	(/ (pow t 2) x)
28.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

rewrite30.0ms

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:

6.0ms	(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
4.0ms	(/ (pow t 2) x)
9.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

series247.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
55.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
19.0ms	(/ (pow t 2) x)
148.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	493	1086
1	2067	999
2	5002	996

prune380.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

localize27.0ms

Local error

Found 4 expressions with local error:

28.2b	(sqrt (* (* (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))) (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))) (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))))
29.1b	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))
29.1b	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))
29.1b	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

336×	`associate-*r/`
312×	`cbrt-div`
176×	`frac-times`
156×	`flip3-+` `frac-add` `flip-+`
124×	`sqrt-div`
44×	`associate-*l/`
24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 193

Calls

4 calls:

74.0ms	(sqrt (* (* (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))) (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))) (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))))
5.0ms	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))
5.0ms	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))
5.0ms	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

series802.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(sqrt (* (* (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))) (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))) (cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))))
215.0ms	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))
215.0ms	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))
224.0ms	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

simplify182.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	1050	16390
1	2318	16272
2	5002	16239

prune719.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

regimes490.0ms

Accuracy

72.5% (6.5b remaining)

Error of 10.3b against oracle of 3.8b and baseline of 27.4b

bsearch654.0ms

Steps

Iters	Range		Point
6	1.772474996099602e+22	9.816334120698393e+22	9.67333495452905e+22
7	1.511609718335987e-222	1.5314766828107433e-220	8.296676812285223e-221
8	9.830296204345552e-280	4.771728286328876e-277	4.692908969753362e-277
8	-5.5469828895486275e-251	-5.367476004269873e-254	-4.917024371515258e-252
5	-5.1248532454389843e-166	-1.4680611298719264e-166	-5.0482585651684744e-166
10	-5.429880568053305e+57	-4.398563231493774e+43	-2.3830943467781888e+52

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	144
1	88	144

end0.0ms

sample2.2s

Algorithm

intervals

Results

513.0ms	10166×	body	80	nan
267.0ms	5061×	body	80	valid
235.0ms	866×	body	1280	valid
216.0ms	1048×	body	640	valid
163.0ms	622×	body	1280	nan
115.0ms	591×	body	640	nan
105.0ms	662×	body	320	valid
46.0ms	322×	body	320	nan
37.0ms	363×	body	160	valid
17.0ms	181×	body	160	nan