Details

sample296.0ms

Algorithm

intervals

Results

78.0ms	347×	body	80	nan
22.0ms	161×	body	80	valid
20.0ms	31×	body	1280	valid
19.0ms	38×	body	640	valid
12.0ms	18×	body	1280	nan
11.0ms	22×	body	640	nan
6.0ms	17×	body	320	valid
4.0ms	9×	body	160	valid
4.0ms	10×	body	320	nan
2.0ms	5×	body	160	nan

simplify2.2s

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.7b

localize73.0ms

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)
15.2b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
19.8b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* 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` `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:

44.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
11.0ms	(* (sqrt 2) t)
56.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
49.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

504.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
81.0ms	(* (sqrt 2) t)
295.0ms	(- (* (/ (+ 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)))

simplify7.4s

Counts

96 → 96

Iterations

Iter	Nodes
3	7219
2	1568
1	440
0	170

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.7b

localize71.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ l (/ x l)) (* t t))
5.2b	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
8.3b	(* (/ 4 x) (* t t))
25.2b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

18.0ms	(+ (/ l (/ x l)) (* t t))
26.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
24.0ms	(* (/ 4 x) (* t t))
56.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

series601.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (/ l (/ x l)) (* t t))
97.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
32.0ms	(* (/ 4 x) (* t t))
428.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

simplify691.0ms

Counts

94 → 94

Iterations

Iter	Nodes
2	2070
1	527
0	176

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.6b

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* (/ l x) l) (* t t))
5.2b	(+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t))))
8.3b	(* (/ 4 x) (* t t))
25.2b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t)))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

21.0ms	(+ (* (/ l x) l) (* t t))
45.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t))))
21.0ms	(* (/ 4 x) (* t t))
27.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t)))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (* (/ l x) l) (* t t))
90.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t))))
32.0ms	(* (/ 4 x) (* t t))
396.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t)))))

simplify911.0ms

Counts

94 → 94

Iterations

Iter	Nodes
2	2106
1	529
0	176

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.6b

localize92.0ms

Local error

Found 4 expressions with local error:

8.3b	(* (/ 4 x) (* t t))
25.2b	(sqrt (+ (* (/ l x) l) (* t t)))
25.2b	(sqrt (+ (* (/ l x) l) (* t t)))
25.2b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (* (sqrt (+ (* (/ l x) l) (* t t))) (sqrt (+ (* (/ l x) l) (* t t)))))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-div`
20×	`add-sqr-sqrt`
16×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-l`
12×	`pow1`
11×	`associate-*l/`
10×	`times-frac` `associate-*r/`
9×	`flip3-+` `sqrt-prod` `flip-+`
8×	`frac-add`
6×	`prod-exp` `cbrt-unprod`
4×	`frac-times` `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 → 92

Calls

4 calls:

29.0ms	(* (/ 4 x) (* t t))
11.0ms	(sqrt (+ (* (/ l x) l) (* t t)))
16.0ms	(sqrt (+ (* (/ l x) l) (* t t)))
69.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (* (sqrt (+ (* (/ l x) l) (* t t))) (sqrt (+ (* (/ l x) l) (* t t)))))))

series922.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (/ 4 x) (* t t))
210.0ms	(sqrt (+ (* (/ l x) l) (* t t)))
205.0ms	(sqrt (+ (* (/ l x) l) (* t t)))
459.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (* (sqrt (+ (* (/ l x) l) (* t t))) (sqrt (+ (* (/ l x) l) (* t t)))))))

simplify7.7s

Counts

104 → 104

Iterations

Iter	Nodes
3	8310
2	1879
1	569
0	219

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 1.6b

regimes895.0ms

Accuracy

78.3% (5.2b remaining)

Error of 9.1b against oracle of 3.9b and baseline of 27.7b

bsearch339.0ms

Steps

Iters	Range		Point
6	1.1534490798277808e+139	5.896067947804245e+139	4.088323180304518e+139
8	-2.771602622336687e+93	-5.381658407530287e+90	-2.661507795721962e+93

simplify17.0ms

Iterations

Iter	Nodes
2	51
1	51
0	39

end0.0ms

sample9.2s

Algorithm

intervals

Results

2.2s	10466×	body	80	nan
1.7s	5143×	body	80	valid
1.0s	606×	body	1280	nan
872.0ms	865×	body	1280	valid
860.0ms	1004×	body	640	valid
557.0ms	624×	body	640	nan
554.0ms	348×	body	160	valid
447.0ms	640×	body	320	valid
226.0ms	338×	body	320	nan
100.0ms	197×	body	160	nan