Details

sample356.0ms

Algorithm

intervals

Results

90.0ms	292×	body	80	nan
28.0ms	168×	body	80	valid
25.0ms	27×	body	1280	valid
21.0ms	25×	body	1280	nan
18.0ms	29×	body	640	valid
13.0ms	22×	body	640	nan
12.0ms	22×	body	320	valid
6.0ms	12×	body	320	nan
3.0ms	10×	body	160	valid
2.0ms	6×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.4b

localize78.0ms

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)))

rewrite229.0ms

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:

84.0ms	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
15.0ms	(* (sqrt 2) t)
56.0ms	(- (* (/ (+ 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)))

series2.0s

Counts

4 → 12

Calls

4 calls:

194.0ms	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
49.0ms	(* (sqrt 2) t)
235.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
2	3371
1	761
0	236

prune810.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.0b

localize62.0ms

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)))

rewrite73.0ms

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:

20.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
9.0ms	(/ (* l l) x)
9.0ms	(/ (* t t) x)
32.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
35.0ms	(/ (* l l) x)
29.0ms	(/ (* t t) x)
394.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

simplify4.4s

Counts

90 → 90

Iterations

Iter	Nodes
3	7426
2	1719
1	480
0	172

prune601.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize74.0ms

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)))

rewrite104.0ms

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:

15.0ms	(* (sqrt 2) t)
32.0ms	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
18.0ms	(/ (* t t) x)
36.0ms	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

series555.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sqrt 2) t)
82.0ms	(+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4))
40.0ms	(/ (* t t) x)
375.0ms	(sqrt (+ (* 2 (+ (* t t) (* l (/ l x)))) (* (/ (* t t) x) 4)))

simplify3.5s

Counts

91 → 91

Iterations

Iter	Nodes
3	5955
2	1527
1	459
0	171

prune597.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize69.0ms

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)))

rewrite54.0ms

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)
22.0ms	(+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4))
9.0ms	(/ (* t t) x)
20.0ms	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))

series832.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(cbrt x)
138.0ms	(+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4))
21.0ms	(/ (* t t) x)
371.0ms	(sqrt (+ (* 2 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt x)) (/ l (cbrt x))))) (* (/ (* t t) x) 4)))

simplify3.7s

Counts

80 → 80

Iterations

Iter	Nodes
3	7599
2	1672
1	459
0	163

prune482.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.5b

regimes772.0ms

Accuracy

78.3% (5.0b remaining)

Error of 9.1b against oracle of 4.1b and baseline of 27.3b

bsearch380.0ms

Steps

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

simplify15.0ms

Iterations

Iter	Nodes
2	46
1	46
0	36

end0.0ms

sample9.2s

Algorithm

intervals

Results

2.3s	9884×	body	80	nan
1.9s	5062×	body	80	valid
1.3s	1015×	body	640	valid
1.0s	868×	body	1280	valid
623.0ms	613×	body	1280	nan
554.0ms	609×	body	640	nan
416.0ms	686×	body	320	valid
238.0ms	344×	body	320	nan
179.0ms	369×	body	160	valid
69.0ms	192×	body	160	nan