Details

sample447.0ms

Algorithm

intervals

Results

73.0ms	357×	body	80	nan
52.0ms	26×	body	320	valid
33.0ms	161×	body	80	valid
30.0ms	31×	body	1280	nan
28.0ms	28×	body	1280	valid
26.0ms	30×	body	640	valid
19.0ms	23×	body	640	nan
4.0ms	11×	body	160	valid
4.0ms	7×	body	320	nan
1.0ms	2×	body	160	nan

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
7	3812
6	1805
5	729
4	393
3	181
2	93
1	42
0	18

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.4b	(* (sqrt 2) t)
13.3b	(- (* (/ (+ 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)))

rewrite155.0ms

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:

74.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
7.0ms	(* (sqrt 2) t)
28.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
41.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

477.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
59.0ms	(* (sqrt 2) t)
237.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
2.0s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify4.6s

Counts

96 → 96

Iterations

Iter	Nodes
3	8442
2	1582
1	441
0	170

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.1b

localize58.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* t t) (/ (* l l) x))
5.4b	(+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4))
8.1b	(/ (* l l) x)
25.7b	(sqrt (+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

17.0ms	(+ (* t t) (/ (* l l) x))
18.0ms	(+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4))
13.0ms	(/ (* l l) x)
17.0ms	(sqrt (+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (* t t) (/ (* l l) x))
106.0ms	(+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4))
33.0ms	(/ (* l l) x)
378.0ms	(sqrt (+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4)))

simplify3.3s

Counts

78 → 78

Iterations

Iter	Nodes
3	7383
2	1497
1	425
0	151

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
1.0b	(+ (* t t) (* l (/ l x)))
5.4b	(+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4))
25.7b	(sqrt (+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

14.0ms	(* (sqrt 2) t)
15.0ms	(+ (* t t) (* l (/ l x)))
27.0ms	(+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4))
28.0ms	(sqrt (+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sqrt 2) t)
47.0ms	(+ (* t t) (* l (/ l x)))
103.0ms	(+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4))
357.0ms	(sqrt (+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4)))

simplify3.2s

Counts

79 → 79

Iterations

Iter	Nodes
3	6258
2	1360
1	395
0	145

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 4 (/ (/ x t) t))
1.0b	(+ (* t t) (/ l (/ x l)))
5.4b	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (/ 4 (/ (/ x t) t)))
25.7b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (/ 4 (/ (/ x t) t))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 239

Calls

4 calls:

7.0ms	(/ 4 (/ (/ x t) t))
11.0ms	(+ (* t t) (/ l (/ x l)))
38.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (/ 4 (/ (/ x t) t)))
62.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (/ 4 (/ (/ x t) t))))

series500.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 4 (/ (/ x t) t))
54.0ms	(+ (* t t) (/ l (/ x l)))
93.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (/ 4 (/ (/ x t) t)))
307.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (/ 4 (/ (/ x t) t))))

simplify3.4s

Counts

251 → 251

Iterations

Iter	Nodes
2	4539
1	1426
0	537

prune4.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.7b

regimes527.0ms

Accuracy

76.9% (5.4b remaining)

Error of 9.3b against oracle of 3.9b and baseline of 27.2b

bsearch1.8s

Steps

Iters	Range		Point
8	1.6979862654485535e+131	3.234643949939514e+134	1.0420326231034605e+133
10	1.783144167995163e-169	5.475896828624431e-155	1.672688434817364e-158
6	6.116042014021991e-195	5.396120080276413e-194	1.512500005971486e-194
10	-2.791851584579815e-267	-4.0855492648655506e-284	-2.3234922006583374e-268
9	-2.3113061451997505e-162	-2.0386708656630003e-168	-4.157152618984683e-167
8	-3.7906798453089045e+105	-4.0988012647948087e+102	-2.2693742662560688e+103

simplify27.0ms

Iterations

Iter	Nodes
4	70
3	70
2	67
1	64
0	52

end0.0ms

sample8.7s

Algorithm

intervals

Results

2.5s	10045×	body	80	nan
1.6s	5067×	body	80	valid
1.2s	872×	body	1280	valid
936.0ms	1040×	body	640	valid
615.0ms	589×	body	1280	nan
453.0ms	591×	body	640	nan
416.0ms	643×	body	320	valid
192.0ms	328×	body	320	nan
138.0ms	378×	body	160	valid
134.0ms	193×	body	160	nan