Details

sample738.0ms

Algorithm

intervals

Results

187.0ms	39×	body	1280	valid
97.0ms	277×	body	80	nan
63.0ms	140×	body	80	valid
49.0ms	28×	body	320	valid
37.0ms	11×	body	320	nan
35.0ms	37×	body	640	valid
19.0ms	14×	body	1280	nan
15.0ms	14×	body	640	nan
5.0ms	12×	body	160	valid
3.0ms	5×	body	160	nan

simplify2.4s

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: 45.0b

localize44.0ms

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)
16.7b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
17.8b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite160.0ms

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:

45.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
8.0ms	(* (sqrt 2) t)
60.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
43.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

532.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
56.0ms	(* (sqrt 2) t)
243.0ms	(- (* (/ (+ 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)))

simplify5.0s

Counts

96 → 96

Iterations

Iter	Nodes
3	8442
2	1582
1	441
0	170

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* t t) (/ (* l l) x))
3.6b	(+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4))
9.2b	(/ (* l l) x)
26.6b	(sqrt (+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4)))

rewrite70.0ms

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))
16.0ms	(+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4))
9.0ms	(/ (* l l) x)
27.0ms	(sqrt (+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4)))

series593.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (* t t) (/ (* l l) x))
115.0ms	(+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4))
22.0ms	(/ (* l l) x)
405.0ms	(sqrt (+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4)))

simplify3.4s

Counts

78 → 78

Iterations

Iter	Nodes
3	7383
2	1497
1	425
0	151

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
0.8b	(+ (* t t) (* l (/ l x)))
3.6b	(+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4))
26.6b	(sqrt (+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4)))

rewrite73.0ms

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:

9.0ms	(* (sqrt 2) t)
10.0ms	(+ (* t t) (* l (/ l x)))
27.0ms	(+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4))
25.0ms	(sqrt (+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4)))

series570.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sqrt 2) t)
58.0ms	(+ (* t t) (* l (/ l x)))
101.0ms	(+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4))
347.0ms	(sqrt (+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4)))

simplify3.4s

Counts

79 → 79

Iterations

Iter	Nodes
3	6258
2	1360
1	395
0	145

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2)) t)
0.8b	(+ (* t t) (* l (/ l x)))
3.6b	(+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4))
26.6b	(sqrt (+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

19.0ms	(* (sqrt (sqrt 2)) t)
16.0ms	(+ (* t t) (* l (/ l x)))
27.0ms	(+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4))
34.0ms	(sqrt (+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4)))

series549.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (sqrt (sqrt 2)) t)
46.0ms	(+ (* t t) (* l (/ l x)))
104.0ms	(+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4))
286.0ms	(sqrt (+ (* (+ (* t t) (* l (/ l x))) 2) (* (/ t (/ x t)) 4)))

simplify2.9s

Counts

83 → 83

Iterations

Iter	Nodes
3	6336
2	1374
1	406
0	151

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.0b

regimes801.0ms

Accuracy

78.2% (5.2b remaining)

Error of 9.2b against oracle of 4.0b and baseline of 27.6b

bsearch1.5s

Steps

Iters	Range		Point
9	1.3356406669163853e+121	2.4586850594315566e+126	3.7543841451851774e+122
9	5.484666736935185e-166	2.0396808824752205e-160	5.72877141657189e-164
10	1.1525372111554329e-223	4.636776026529116e-210	3.622605389449186e-213
6	-6.778571632960239e+103	-9.951417039093262e+102	-1.9501808158464715e+103

simplify24.0ms

Iterations

Iter	Nodes
4	71
3	71
2	68
1	65
0	49

end0.0ms

sample8.9s

Algorithm

intervals

Results

2.2s	10002×	body	80	nan
1.6s	5128×	body	80	valid
945.0ms	608×	body	640	nan
930.0ms	1009×	body	640	valid
890.0ms	863×	body	1280	valid
646.0ms	549×	body	1280	nan
580.0ms	641×	body	320	valid
242.0ms	351×	body	320	nan
134.0ms	359×	body	160	valid
70.0ms	182×	body	160	nan