Details

sample393.0ms

Algorithm

intervals

Results

72.0ms	338×	body	80	nan
42.0ms	16×	body	640	nan
36.0ms	161×	body	80	valid
35.0ms	34×	body	1280	valid
23.0ms	29×	body	640	valid
12.0ms	12×	body	1280	nan
11.0ms	20×	body	320	valid
5.0ms	12×	body	160	valid
4.0ms	7×	body	320	nan
2.0ms	5×	body	160	nan

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
7	3164
6	1632
5	695
4	400
3	180
2	91
1	40
0	18

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.4b	(* (sqrt 2) t)
12.7b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
19.3b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`sqrt-div` `insert-posit16`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 84

Calls

4 calls:

71.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
9.0ms	(* (sqrt 2) t)
32.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
68.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

402.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
68.0ms	(* (sqrt 2) t)
239.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.6s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify7.5s

Counts

96 → 96

Iterations

Iter	Nodes
3	7219
2	1568
1	440
0	170

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
3.6b	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
8.9b	(* (/ 4 x) (* t t))
26.0b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-l`
18×	`add-cbrt-cube` `add-exp-log`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow1`
10×	`times-frac`
7×	`prod-exp` `sqrt-prod` `cbrt-unprod`
6×	`add-log-exp`
5×	`associate-*l/`
4×	`flip3-+` `sqrt-div` `associate-r` `pow-prod-down` `frac-add` `associate-*r/` `flip-+` `insert-posit16` `unswap-sqr`
2×	`cbrt-undiv` `associate-+r+` `div-exp` `*-commutative`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 93

Calls

4 calls:

14.0ms	(* (sqrt 2) t)
38.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
23.0ms	(* (/ 4 x) (* t t))
34.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

series649.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sqrt 2) t)
94.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
52.0ms	(* (/ 4 x) (* t t))
461.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

simplify778.0ms

Counts

105 → 105

Iterations

Iter	Nodes
2	2105
1	554
0	192

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
3.6b	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
8.9b	(* (/ 4 x) (* t t))
26.0b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

rewrite451.0ms

Algorithm

rewrite-expression-head

Rules

22×	`associate-l`
21×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
15×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
12×	`sqrt-prod`
10×	`times-frac`
9×	`prod-exp` `cbrt-unprod`
6×	`pow-prod-down` `add-log-exp`
5×	`associate-*l/`
4×	`flip3-+` `sqrt-div` `frac-add` `associate-*r/` `flip-+` `insert-posit16`
2×	`cbrt-undiv` `associate-+r+` `div-exp` `associate-r` `*-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 95

Calls

4 calls:

356.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
24.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
20.0ms	(* (/ 4 x) (* t t))
50.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
106.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
53.0ms	(* (/ 4 x) (* t t))
380.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

simplify622.0ms

Counts

107 → 107

Iterations

Iter	Nodes
2	2213
1	585
0	198

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

localize90.0ms

Local error

Found 4 expressions with local error:

8.9b	(* (/ 4 x) (* t t))
26.0b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
26.0b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
26.0b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-l`
12×	`pow1` `sqrt-div`
10×	`times-frac`
9×	`sqrt-prod`
7×	`associate-*l/`
6×	`flip3-+` `frac-add` `prod-exp` `associate-*r/` `cbrt-unprod` `flip-+`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`cbrt-undiv` `div-exp` `unswap-sqr`
1×	`associate-r` `*-commutative` `div-inv`

Counts

4 → 90

Calls

4 calls:

26.0ms	(* (/ 4 x) (* t t))
28.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
48.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
44.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (/ 4 x) (* t t))
381.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
454.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))
417.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

simplify8.1s

Counts

102 → 102

Iterations

Iter	Nodes
3	9634
2	1744
1	445
0	147

prune2.0s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.0b

regimes809.0ms

Accuracy

78.1% (5.1b remaining)

Error of 8.9b against oracle of 3.9b and baseline of 27.0b

bsearch1.5s

Steps

Iters	Range		Point
8	7.917799159621275e+106	2.002559075649937e+110	1.4994412213892464e+108
10	2.313298500987685e-178	3.946360535693021e-163	3.464075321521421e-166
8	4.923607766514643e-262	1.9892195058960085e-259	8.264925603641206e-260
9	-8.613554016052439e+67	-7.040451668859043e+60	-2.3433794278040432e+67

simplify20.0ms

Iterations

Iter	Nodes
2	65
1	65
0	49

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.5s	10039×	body	80	nan
1.3s	861×	body	1280	valid
1.0s	5077×	body	80	valid
947.0ms	1042×	body	640	valid
559.0ms	620×	body	1280	nan
454.0ms	612×	body	640	nan
384.0ms	665×	body	320	valid
176.0ms	353×	body	320	nan
121.0ms	355×	body	160	valid
61.0ms	186×	body	160	nan