Details

sample414.0ms

Algorithm

intervals

Results

82.0ms	45×	body	640	valid
29.0ms	300×	body	80	nan
19.0ms	156×	body	80	valid
11.0ms	26×	body	1280	valid
9.0ms	13×	body	640	nan
7.0ms	16×	body	1280	nan
6.0ms	17×	body	320	valid
3.0ms	10×	body	320	nan
2.0ms	10×	body	160	nan
2.0ms	12×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3799
6	1449
5	797
4	423
3	199
2	93
1	39
0	18

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt 2.0) (/ (sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))) t))
0.2b	(/ (sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))) t)
14.2b	(- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
19.1b	(sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

rewrite345.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity` `add-cube-cbrt`
147×	`sqrt-prod`
25×	`associate-/r*`
12×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `sqrt-div` `div-exp`
3×	`flip3--` `flip--`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 243

Calls

4 calls:

52.0ms	(/ (sqrt 2.0) (/ (sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))) t))
120.0ms	(/ (sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))) t)
66.0ms	(- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
85.0ms	(sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

series2.0s

Counts

4 → 12

Calls

4 calls:

757.0ms	(/ (sqrt 2.0) (/ (sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))) t))
512.0ms	(/ (sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))) t)
272.0ms	(- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
476.0ms	(sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

simplify1.8s

Counts

255 → 255

Iterations

Iter	Nodes
done	5000
2	4821
1	873
0	336

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize38.0ms

Local error

Found 4 expressions with local error:

4.0b	(+ (/ 4.0 (/ x (* t t))) (+ (/ (* 2.0 (* l l)) x) (* (* t t) 2.0)))
7.4b	(/ (* 2.0 (* l l)) x)
8.1b	(/ x (* t t))
27.7b	(sqrt (+ (/ 4.0 (/ x (* t t))) (+ (/ (* 2.0 (* l l)) x) (* (* t t) 2.0))))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
13×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `add-log-exp`
6×	`times-frac`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`associate-/r` `flip3-+` `sqrt-div` `frac-add` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+` `associate-/l`
3×	`sum-log`
2×	`clear-num` `frac-2neg` `div-inv` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `associate-+r+` `sqrt-pow1` `pow1/2`

Counts

4 → 78

Calls

4 calls:

84.0ms	(+ (/ 4.0 (/ x (* t t))) (+ (/ (* 2.0 (* l l)) x) (* (* t t) 2.0)))
23.0ms	(/ (* 2.0 (* l l)) x)
6.0ms	(/ x (* t t))
143.0ms	(sqrt (+ (/ 4.0 (/ x (* t t))) (+ (/ (* 2.0 (* l l)) x) (* (* t t) 2.0))))

series626.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (/ 4.0 (/ x (* t t))) (+ (/ (* 2.0 (* l l)) x) (* (* t t) 2.0)))
49.0ms	(/ (* 2.0 (* l l)) x)
33.0ms	(/ x (* t t))
446.0ms	(sqrt (+ (/ 4.0 (/ x (* t t))) (+ (/ (* 2.0 (* l l)) x) (* (* t t) 2.0))))

simplify1.8s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	3883
1	559
0	179

prune624.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.4b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t))))) t)
0.8b	(+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l)))
4.0b	(+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t))))
27.7b	(sqrt (+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t)))))

rewrite661.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
11×	`add-log-exp`
8×	`sqrt-div`
7×	`flip3-+` `flip-+`
6×	`add-cbrt-cube` `frac-add` `associate-r/` `add-exp-log` `associate-/l`
5×	`pow1`
4×	`sum-log` `associate-/l/`
3×	`associate-/r*`
2×	`+-commutative`
1×	`cbrt-undiv` `rem-sqrt-square` `associate-+l+` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 86

Calls

4 calls:

248.0ms	(/ (sqrt (+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t))))) t)
27.0ms	(+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l)))
168.0ms	(+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t))))
213.0ms	(sqrt (+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t)))))

series916.0ms

Counts

4 → 12

Calls

4 calls:

353.0ms	(/ (sqrt (+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t))))) t)
76.0ms	(+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l)))
96.0ms	(+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t))))
391.0ms	(sqrt (+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t)))))

simplify935.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1976
1	438
0	174

prune743.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t))))) (/ 1 t))
0.8b	(+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l)))
4.0b	(+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t))))
27.7b	(sqrt (+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t)))))

rewrite657.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`times-frac` `associate-r` `add-exp-log`
12×	`sqrt-div`
11×	`add-log-exp`
9×	`flip3-+` `add-cbrt-cube` `associate-*r/` `sqrt-prod` `flip-+`
8×	`frac-add`
7×	`pow1`
6×	`associate-l` `unswap-sqr`
4×	`frac-times` `sum-log` `associate-*l/` `prod-exp`
2×	`+-commutative` `div-exp` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `associate-+l+` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 93

Calls

4 calls:

342.0ms	(* (sqrt (+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t))))) (/ 1 t))
28.0ms	(+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l)))
118.0ms	(+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t))))
165.0ms	(sqrt (+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t)))))

series959.0ms

Counts

4 → 12

Calls

4 calls:

341.0ms	(* (sqrt (+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t))))) (/ 1 t))
100.0ms	(+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l)))
126.0ms	(+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t))))
391.0ms	(sqrt (+ (+ (* t (* t 2.0)) (/ (* 2.0 l) (/ x l))) (* 4.0 (/ t (/ x t)))))

simplify3.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	3409
1	549
0	196

prune756.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.4b

regimes1.3s

Accuracy

74.5% (6.2b remaining)

Error of 10.1b against oracle of 4.0b and baseline of 28.1b

bsearch815.0ms

Steps

Iters	Range		Point
8	3.2301900138930726e+31	1.1647955323424639e+35	1.9137167633344305e+33
9	6.906315603593477e-164	9.191228058584716e-159	2.813385033315984e-161
5	1.8889114741052636e-285	4.82560000307667e-285	2.8881004934193523e-285
10	-4.431949063779609e+156	-3.328628298892941e+145	-1.653947709277397e+151

simplify18.0ms

Iterations

Iter	Nodes
done	64
2	64
1	61
0	48

end0.0ms

sample6.2s

Algorithm

intervals

Results

1.3s	10078×	body	80	nan
1.3s	5111×	body	80	valid
963.0ms	980×	body	640	valid
626.0ms	902×	body	1280	valid
331.0ms	597×	body	1280	nan
290.0ms	568×	body	640	nan
233.0ms	652×	body	320	valid
91.0ms	334×	body	320	nan
69.0ms	355×	body	160	valid
39.0ms	184×	body	160	nan