Details

sample382.0ms

Algorithm

intervals

Results

93.0ms	368×	body	80	nan
55.0ms	17×	body	320	nan
29.0ms	157×	body	80	valid
25.0ms	29×	body	1280	nan
22.0ms	31×	body	640	valid
21.0ms	25×	body	1280	valid
16.0ms	22×	body	640	nan
15.0ms	31×	body	320	valid
4.0ms	12×	body	160	valid
3.0ms	7×	body	160	nan

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4473
5	1119
4	393
3	181
2	93
1	42
0	18

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.7b

localize92.0ms

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)
13.7b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
20.9b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite140.0ms

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:

45.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
16.0ms	(* (sqrt 2) t)
27.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
48.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.2s

Counts

4 → 12

Calls

4 calls:

492.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
52.0ms	(* (sqrt 2) t)
254.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.4s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1525
1	458
0	170

prune743.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.3b

localize73.0ms

Local error

Found 4 expressions with local error:

4.0b	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
5.7b	(/ (* l l) x)
8.8b	(/ (* t t) x)
29.7b	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `div-exp` `associate-l/` `frac-add` `associate-r/` `flip-+` `insert-posit16`
3×	`sqrt-prod`
2×	`associate-+l+` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 78

Calls

4 calls:

26.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
17.0ms	(/ (* l l) x)
23.0ms	(/ (* t t) x)
47.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
34.0ms	(/ (* l l) x)
31.0ms	(/ (* t t) x)
305.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

simplify1.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5004
2	2246
1	536
0	172

prune655.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* t t) (/ l (/ x l)))
4.0b	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
8.8b	(/ (* t t) x)
29.7b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `associate-l/` `frac-add` `associate-r/` `insert-posit16`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+l+` `sum-log` `div-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 68

Calls

4 calls:

11.0ms	(+ (* t t) (/ l (/ x l)))
32.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
18.0ms	(/ (* t t) x)
63.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* t t) (/ l (/ x l)))
81.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
31.0ms	(/ (* t t) x)
356.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

simplify1.6s

Counts

80 → 80

Iterations

Iter	Nodes
done	5003
2	1831
1	462
0	155

prune654.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize96.0ms

Local error

Found 4 expressions with local error:

8.8b	(/ (* t t) x)
29.7b	(sqrt (+ (* 2 (* (sqrt (+ (* t t) (/ l (/ x l)))) (sqrt (+ (* t t) (/ l (/ x l)))))) (* (/ (* t t) x) 4)))
29.7b	(sqrt (+ (* t t) (/ l (/ x l))))
29.7b	(sqrt (+ (* t t) (/ l (/ x l))))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-div`
12×	`add-sqr-sqrt`
10×	`associate-l/` `associate-r/`
9×	`*-un-lft-identity` `flip3-+` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod` `flip-+`
8×	`frac-add`
7×	`pow1`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `associate-/r*` `sqrt-pow1` `times-frac` `pow1/2`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 78

Calls

4 calls:

9.0ms	(/ (* t t) x)
153.0ms	(sqrt (+ (* 2 (* (sqrt (+ (* t t) (/ l (/ x l)))) (sqrt (+ (* t t) (/ l (/ x l)))))) (* (/ (* t t) x) 4)))
25.0ms	(sqrt (+ (* t t) (/ l (/ x l))))
26.0ms	(sqrt (+ (* t t) (/ l (/ x l))))

series618.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (* t t) x)
351.0ms	(sqrt (+ (* 2 (* (sqrt (+ (* t t) (/ l (/ x l)))) (sqrt (+ (* t t) (/ l (/ x l)))))) (* (/ (* t t) x) 4)))
112.0ms	(sqrt (+ (* t t) (/ l (/ x l))))
127.0ms	(sqrt (+ (* t t) (/ l (/ x l))))

simplify1.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1740
1	512
0	196

prune587.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

regimes674.0ms

Accuracy

74.5% (6.1b remaining)

Error of 10.2b against oracle of 4.1b and baseline of 28.0b

bsearch1.6s

Steps

Iters	Range		Point
10	2.2698944026945608e+54	2.1361265904372213e+65	1.9521121079445436e+65
9	-7.865323649264117e-249	-2.5989217204882638e-256	-9.131577791002971e-250
8	-9.554269064230224e-225	-6.56997699479388e-228	-3.1340173156713147e-226
7	-8863632844576612.0	-362820003114431.56	-8781316784794473.0

simplify52.0ms

Iterations

Iter	Nodes
done	60
1	60
0	49

end0.0ms

sample9.2s

Algorithm

intervals

Results

3.2s	10359×	body	80	nan
1.3s	5137×	body	80	valid
938.0ms	848×	body	1280	valid
893.0ms	963×	body	640	valid
639.0ms	633×	body	1280	nan
510.0ms	623×	body	640	nan
468.0ms	672×	body	320	valid
317.0ms	348×	body	320	nan
147.0ms	380×	body	160	valid
70.0ms	183×	body	160	nan