Details

sample316.0ms

Algorithm

intervals

Results

85.0ms	355×	body	80	nan
14.0ms	163×	body	80	valid
14.0ms	34×	body	640	valid
10.0ms	26×	body	1280	valid
9.0ms	20×	body	1280	nan
6.0ms	24×	body	640	nan
5.0ms	20×	body	320	valid
3.0ms	13×	body	320	nan
2.0ms	13×	body	160	valid
2.0ms	10×	body	160	nan

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	2276
6	1138
5	616
4	361
3	179
2	90
1	39
0	18

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.8b

localize37.0ms

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))))
0.5b	(* (sqrt 2.0) t)
12.2b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
17.9b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite164.0ms

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`
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 → 80

Calls

4 calls:

75.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
8.0ms	(* (sqrt 2.0) t)
24.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
51.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.7s

Counts

4 → 12

Calls

4 calls:

622.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
52.0ms	(* (sqrt 2.0) t)
307.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.7s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.8s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1572
1	445
0	167

prune687.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.4b

localize49.0ms

Local error

Found 4 expressions with local error:

4.4b	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t))))
5.5b	(/ (* l l) x)
7.6b	(/ (* t t) x)
25.5b	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-*r/`
6×	`associate-/r*` `times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `div-exp` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`associate-+r+` `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 → 74

Calls

4 calls:

27.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t))))
8.0ms	(/ (* l l) x)
8.0ms	(/ (* t t) x)
22.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t)))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t))))
37.0ms	(/ (* l l) x)
25.0ms	(/ (* t t) x)
260.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (/ (* l l) x) (* t t)))))

simplify1.7s

Counts

86 → 86

Iterations

Iter	Nodes
done	5012
2	2531
1	547
0	167

prune663.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* l (/ l x)) (* t t))
4.4b	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t))))
7.6b	(/ (* t t) x)
25.5b	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t)))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `associate-*r/` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+r+` `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 → 64

Calls

4 calls:

18.0ms	(+ (* l (/ l x)) (* t t))
23.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t))))
8.0ms	(/ (* t t) x)
30.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t)))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (* l (/ l x)) (* t t))
101.0ms	(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t))))
21.0ms	(/ (* t t) x)
239.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* l (/ l x)) (* t t)))))

simplify1.8s

Counts

76 → 76

Iterations

Iter	Nodes
done	5004
2	2151
1	475
0	150

prune657.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize54.0ms

Local error

Found 4 expressions with local error:

7.6b	(/ (* t t) x)
25.4b	(sqrt (+ (* l (/ l x)) (* t t)))
25.4b	(sqrt (+ (* l (/ l x)) (* t t)))
25.5b	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (* (sqrt (+ (* l (/ l x)) (* t t))) (sqrt (+ (* l (/ l x)) (* t t)))))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-div`
18×	`associate-*r/`
12×	`add-sqr-sqrt`
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` `add-log-exp`
3×	`rem-sqrt-square` `associate-/r*` `sqrt-pow1` `times-frac` `pow1/2`
2×	`cbrt-undiv` `div-exp` `associate-*l/`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

15.0ms	(/ (* t t) x)
20.0ms	(sqrt (+ (* l (/ l x)) (* t t)))
21.0ms	(sqrt (+ (* l (/ l x)) (* t t)))
61.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (* (sqrt (+ (* l (/ l x)) (* t t))) (sqrt (+ (* l (/ l x)) (* t t)))))))

series730.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* t t) x)
245.0ms	(sqrt (+ (* l (/ l x)) (* t t)))
171.0ms	(sqrt (+ (* l (/ l x)) (* t t)))
280.0ms	(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (* (sqrt (+ (* l (/ l x)) (* t t))) (sqrt (+ (* l (/ l x)) (* t t)))))))

simplify1.7s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	1934
1	499
0	192

prune632.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.4b

regimes963.0ms

Accuracy

76.4% (5.6b remaining)

Error of 9.3b against oracle of 3.7b and baseline of 27.6b

bsearch345.0ms

Steps

Iters	Range		Point
8	4.426853282634998e+56	1.661076069045296e+60	1.6237106520617296e+60
6	-5.111701595882843e+60	-4.544149282436552e+59	-6.172764092322424e+59

simplify24.0ms

Iterations

Iter	Nodes
done	55
1	55
0	43

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.6s	10040×	body	80	nan
740.0ms	5162×	body	80	valid
447.0ms	827×	body	1280	valid
440.0ms	981×	body	640	valid
342.0ms	603×	body	1280	nan
336.0ms	646×	body	640	nan
221.0ms	657×	body	320	valid
147.0ms	373×	body	160	valid
129.0ms	327×	body	320	nan
32.0ms	166×	body	160	nan