Details

sample543.0ms

Algorithm

intervals

Results

107.0ms	355×	body	80	nan
82.0ms	28×	body	1280	valid
38.0ms	168×	body	80	valid
29.0ms	33×	body	640	valid
23.0ms	5×	body	160	nan
22.0ms	19×	body	1280	nan
19.0ms	21×	body	640	nan
14.0ms	21×	body	320	valid
10.0ms	15×	body	320	nan
3.0ms	6×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize42.0ms

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))))
0.5b	(* (sqrt 2) t)
12.4b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
19.2b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite200.0ms

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:

63.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
14.0ms	(* (sqrt 2) t)
56.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
63.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.5s

Counts

4 → 12

Calls

4 calls:

467.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
59.0ms	(* (sqrt 2) t)
243.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.8s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify7.5s

Counts

96 → 96

Iterations

Iter	Nodes
3	7219
2	1568
1	440
0	170

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.2b

localize65.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ l (/ x l)) (* t t))
4.6b	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
9.5b	(* (/ 4 x) (* t t))
26.9b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

rewrite159.0ms

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:

29.0ms	(+ (/ l (/ x l)) (* t t))
51.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
23.0ms	(* (/ 4 x) (* t t))
53.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

series650.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (/ l (/ x l)) (* t t))
127.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t))))
36.0ms	(* (/ 4 x) (* t t))
420.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (/ l (/ x l)) (* t t)))))

simplify633.0ms

Counts

94 → 94

Iterations

Iter	Nodes
2	2070
1	527
0	176

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* (/ l x) l) (* t t))
4.6b	(+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t))))
9.5b	(* (/ 4 x) (* t t))
26.9b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t)))))

rewrite122.0ms

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:

10.0ms	(+ (* (/ l x) l) (* t t))
33.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t))))
37.0ms	(* (/ 4 x) (* t t))
40.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t)))))

series579.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (* (/ l x) l) (* t t))
97.0ms	(+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t))))
38.0ms	(* (/ 4 x) (* t t))
378.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (+ (* (/ l x) l) (* t t)))))

simplify651.0ms

Counts

94 → 94

Iterations

Iter	Nodes
2	2106
1	529
0	176

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.1b

localize46.0ms

Local error

Found 4 expressions with local error:

26.9b	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (* (* (cbrt (+ (/ l (/ x l)) (* t t))) (cbrt (+ (/ l (/ x l)) (* t t)))) (cbrt (+ (/ l (/ x l)) (* t t)))))))
27.7b	(cbrt (+ (/ l (/ x l)) (* t t)))
27.7b	(cbrt (+ (/ l (/ x l)) (* t t)))
27.7b	(cbrt (+ (/ l (/ x l)) (* t t)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
40×	`associate-*l/`
34×	`associate-*r/`
31×	`flip3-+` `flip-+`
28×	`frac-times` `sqrt-div`
26×	`frac-add`
9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 84

Calls

4 calls:

80.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (* (* (cbrt (+ (/ l (/ x l)) (* t t))) (cbrt (+ (/ l (/ x l)) (* t t)))) (cbrt (+ (/ l (/ x l)) (* t t)))))))
8.0ms	(cbrt (+ (/ l (/ x l)) (* t t)))
13.0ms	(cbrt (+ (/ l (/ x l)) (* t t)))
8.0ms	(cbrt (+ (/ l (/ x l)) (* t t)))

series801.0ms

Counts

4 → 12

Calls

4 calls:

422.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* 2 (* (* (cbrt (+ (/ l (/ x l)) (* t t))) (cbrt (+ (/ l (/ x l)) (* t t)))) (cbrt (+ (/ l (/ x l)) (* t t)))))))
108.0ms	(cbrt (+ (/ l (/ x l)) (* t t)))
130.0ms	(cbrt (+ (/ l (/ x l)) (* t t)))
141.0ms	(cbrt (+ (/ l (/ x l)) (* t t)))

simplify2.5s

Counts

96 → 96

Iterations

Iter	Nodes
3	4623
2	1649
1	677
0	300

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.1b

regimes627.0ms

Accuracy

75.5% (5.7b remaining)

Error of 9.6b against oracle of 3.9b and baseline of 27.2b

bsearch1.4s

Steps

Iters	Range		Point
10	5.9175479702302504e+66	1.8619779487277368e+77	4.169836755076731e+68
9	2.180155274432473e-229	2.2769420534463193e-220	1.5173692864293495e-227
7	9.479799914111636e-251	2.4756009306801646e-249	1.0624147501299982e-249
9	-4.546275778593449e-29	-6.195157292696725e-35	-4.4981693604397794e-29

simplify19.0ms

Iterations

Iter	Nodes
4	64
3	64
2	61
1	58
0	46

end0.0ms

sample9.3s

Algorithm

intervals

Results

2.3s	9936×	body	80	nan
1.7s	5080×	body	80	valid
934.0ms	826×	body	1280	valid
893.0ms	1022×	body	640	valid
747.0ms	644×	body	1280	nan
695.0ms	351×	body	320	nan
536.0ms	583×	body	640	nan
516.0ms	671×	body	320	valid
209.0ms	401×	body	160	valid
103.0ms	198×	body	160	nan