Details

sample350.0ms

Algorithm

intervals

Results

56.0ms	292×	body	80	nan
54.0ms	29×	body	640	valid
33.0ms	168×	body	80	valid
31.0ms	27×	body	1280	valid
25.0ms	25×	body	1280	nan
17.0ms	22×	body	640	nan
11.0ms	22×	body	320	valid
7.0ms	12×	body	320	nan
4.0ms	10×	body	160	valid
3.0ms	6×	body	160	nan

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
6	2002
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: 44.4b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
0.4b	(* (sqrt 2) t)
13.5b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
22.3b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`associate-l`
29×	`times-frac`
21×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
8×	`difference-of-squares`
7×	`sqrt-prod` `distribute-lft-out`
6×	`associate-r` `add-log-exp`
4×	`difference-of-sqr-1` `insert-posit16` `distribute-lft-out--` `unswap-sqr`
3×	`flip3--` `prod-exp` `cbrt-unprod` `flip--`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3-+` `sqrt-div` `pow-prod-down` `associate--l+` `associate-r/` `associate-/r/` `-commutative` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `associate-*l/` `div-inv`

Counts

4 → 114

Calls

4 calls:

52.0ms	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
14.0ms	(* (sqrt 2) t)
31.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
69.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
53.0ms	(* (sqrt 2) t)
248.0ms	(- (* (/ (+ 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)))

simplify1.1s

Counts

126 → 126

Iterations

Iter	Nodes
done	2003
2	2003
1	781
0	236

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.0b

localize38.0ms

Local error

Found 4 expressions with local error:

3.8b	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
7.6b	(/ (* l l) x)
11.9b	(/ (* t t) x)
27.8b	(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:

28.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
19.0ms	(/ (* l l) x)
18.0ms	(/ (* t t) x)
55.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
21.0ms	(/ (* l l) x)
32.0ms	(/ (* t t) x)
348.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

simplify1.0s

Counts

90 → 90

Iterations

Iter	Nodes
done	2000
2	2000
1	536
0	172

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize69.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
3.8b	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
11.9b	(/ (* t t) x)
27.8b	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

7.0ms	(* (sqrt 2) t)
17.0ms	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
19.0ms	(/ (* t t) x)
36.0ms	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sqrt 2) t)
99.0ms	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
35.0ms	(/ (* t t) x)
358.0ms	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

simplify911.0ms

Counts

91 → 91

Iterations

Iter	Nodes
done	2003
2	2003
1	499
0	171

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize83.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
3.8b	(+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4))
11.9b	(/ (* t t) x)
27.8b	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt x)
32.0ms	(+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4))
18.0ms	(/ (* t t) x)
38.0ms	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))

series765.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(cbrt x)
87.0ms	(+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4))
20.0ms	(/ (* t t) x)
360.0ms	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
done	2000
3	2000
2	1914
1	476
0	163

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

regimes679.0ms

Accuracy

77.9% (5.1b remaining)

Error of 9.1b against oracle of 3.9b and baseline of 27.3b

bsearch379.0ms

Steps

Iters	Range		Point
6	4.7332403373153464e+123	3.3768436627244136e+124	3.3304656260583313e+124
10	-1.5304224262738304e+84	-6.960410891925428e+71	-6.377624199137871e+80

simplify22.0ms

Iterations

Iter	Nodes
done	65
3	65
2	64
1	50
0	37

end0.0ms

sample9.4s

Algorithm

intervals

Results

2.4s	9884×	body	80	nan
1.9s	868×	body	1280	valid
1.2s	1015×	body	640	valid
1.1s	5062×	body	80	valid
673.0ms	613×	body	1280	nan
567.0ms	609×	body	640	nan
477.0ms	686×	body	320	valid
224.0ms	344×	body	320	nan
208.0ms	369×	body	160	valid
70.0ms	192×	body	160	nan