Details

sample550.0ms

Algorithm

intervals

Results

174.0ms	176×	body	80	valid
85.0ms	330×	body	80	nan
34.0ms	6×	body	160	nan
31.0ms	27×	body	1280	valid
26.0ms	25×	body	640	valid
20.0ms	20×	body	640	nan
19.0ms	18×	body	1280	nan
12.0ms	17×	body	320	nan
12.0ms	17×	body	320	valid
5.0ms	11×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.5b

localize84.0ms

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)
11.6b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.1b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite152.0ms

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:

64.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
7.0ms	(* (sqrt 2) t)
43.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
36.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.2s

Counts

4 → 12

Calls

4 calls:

494.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
58.0ms	(* (sqrt 2) t)
230.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.5s	(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

prune572.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.7b

localize45.0ms

Local error

Found 4 expressions with local error:

4.0b	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
5.5b	(/ (* l l) x)
9.5b	(/ (* t t) x)
25.8b	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

rewrite124.0ms

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:

33.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
17.0ms	(/ (* l l) x)
17.0ms	(/ (* t t) x)
55.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
38.0ms	(/ (* l l) x)
33.0ms	(/ (* t t) x)
363.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

simplify1.6s

Counts

90 → 90

Iterations

Iter	Nodes
done	5004
2	2246
1	536
0	172

prune567.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.5b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* t t) (/ l (/ x l)))
4.0b	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
9.5b	(/ (* t t) x)
25.8b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

rewrite118.0ms

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:

20.0ms	(+ (* t t) (/ l (/ x l)))
36.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
8.0ms	(/ (* t t) x)
51.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

series570.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (* t t) (/ l (/ x l)))
91.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
36.0ms	(/ (* t t) x)
376.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

simplify1.4s

Counts

80 → 80

Iterations

Iter	Nodes
done	5003
2	1831
1	462
0	155

prune495.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.5b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* t t) (* l (/ l x)))
4.0b	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
9.5b	(/ (* t t) x)
25.8b	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

rewrite69.0ms

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:

15.0ms	(+ (* t t) (* l (/ l x)))
18.0ms	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
8.0ms	(/ (* t t) x)
27.0ms	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (* t t) (* l (/ l x)))
87.0ms	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
30.0ms	(/ (* t t) x)
354.0ms	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

simplify1.8s

Counts

80 → 80

Iterations

Iter	Nodes
done	5005
2	1889
1	465
0	155

prune528.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.5b

regimes1.1s

Accuracy

77.7% (5.2b remaining)

Error of 9.0b against oracle of 3.8b and baseline of 27.3b

bsearch534.0ms

Steps

Iters	Range		Point
8	1.1851330097179606e+57	4.62892497053394e+59	4.561118037024944e+59
7	-1.2036851434557175e+108	-1.4050859331810362e+106	-6.081620194545127e+107

simplify19.0ms

Iterations

Iter	Nodes
done	50
1	50
0	39

end0.0ms

sample9.2s

Algorithm

intervals

Results

2.7s	10190×	body	80	nan
1.5s	981×	body	640	valid
1.2s	878×	body	1280	valid
1.2s	5134×	body	80	valid
599.0ms	574×	body	1280	nan
455.0ms	562×	body	640	nan
443.0ms	665×	body	320	valid
320.0ms	363×	body	320	nan
128.0ms	342×	body	160	valid
73.0ms	194×	body	160	nan