Details

sample395.0ms

Algorithm

intervals

Results

112.0ms	328×	body	80	nan
41.0ms	173×	body	80	valid
29.0ms	26×	body	1280	valid
22.0ms	29×	body	640	valid
15.0ms	14×	body	1280	nan
12.0ms	19×	body	320	valid
12.0ms	14×	body	640	nan
7.0ms	12×	body	320	nan
4.0ms	9×	body	160	valid
4.0ms	9×	body	160	nan

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
6	2403
5	990
4	463
3	210
2	99
1	42
0	18

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.1b

localize85.0ms

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)
12.8b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.2b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite109.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

38.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
6.0ms	(* (sqrt 2) t)
26.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
35.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.2s

Counts

4 → 12

Calls

4 calls:

472.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
72.0ms	(* (sqrt 2) t)
235.0ms	(- (* (/ (+ 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)))

simplify10.6s

Counts

102 → 102

Iterations

Iter	Nodes
3	7564
2	1675
1	463
0	177

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma t t (/ (* l l) x))
4.6b	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 t) (/ x t)))
6.9b	(/ (* l l) x)
28.4b	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 t) (/ x t))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `div-exp` `fma-udef`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 58

Calls

4 calls:

0.0ms	(fma t t (/ (* l l) x))
0.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 t) (/ x t)))
9.0ms	(/ (* l l) x)
1.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 t) (/ x t))))

series556.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma t t (/ (* l l) x))
115.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 t) (/ x t)))
26.0ms	(/ (* l l) x)
337.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 t) (/ x t))))

simplify657.0ms

Counts

70 → 70

Iterations

Iter	Nodes
3	2059
2	641
1	228
0	111

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.9b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
0.8b	(fma t t (* l (/ l x)))
4.6b	(fma 2 (fma t t (* l (/ l x))) (/ (* 4 t) (/ x t)))
28.4b	(sqrt (fma 2 (fma t t (* l (/ l x))) (/ (* 4 t) (/ x t))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`add-cbrt-cube` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`fma-udef` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 59

Calls

4 calls:

12.0ms	(* (sqrt 2) t)
0.0ms	(fma t t (* l (/ l x)))
0.0ms	(fma 2 (fma t t (* l (/ l x))) (/ (* 4 t) (/ x t)))
2.0ms	(sqrt (fma 2 (fma t t (* l (/ l x))) (/ (* 4 t) (/ x t))))

series572.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sqrt 2) t)
72.0ms	(fma t t (* l (/ l x)))
94.0ms	(fma 2 (fma t t (* l (/ l x))) (/ (* 4 t) (/ x t)))
350.0ms	(sqrt (fma 2 (fma t t (* l (/ l x))) (/ (* 4 t) (/ x t))))

simplify3.8s

Counts

71 → 71

Iterations

Iter	Nodes
4	5717
3	1501
2	526
1	201
0	103

prune1.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (/ l x) (* 2 l) (* (* t t) (+ 2 (/ 4 x))))
0.1b	(/ (* (sqrt 2) t) (sqrt (fma (/ l x) (* 2 l) (* (* t t) (+ 2 (/ 4 x))))))
0.4b	(* (sqrt 2) t)
28.4b	(sqrt (fma (/ l x) (* 2 l) (* (* t t) (+ 2 (/ 4 x)))))

rewrite22.0ms

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*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `fma-udef` `div-inv` `associate-/l`

Counts

4 → 78

Calls

4 calls:

0.0ms	(fma (/ l x) (* 2 l) (* (* t t) (+ 2 (/ 4 x))))
9.0ms	(/ (* (sqrt 2) t) (sqrt (fma (/ l x) (* 2 l) (* (* t t) (+ 2 (/ 4 x))))))
9.0ms	(* (sqrt 2) t)
2.0ms	(sqrt (fma (/ l x) (* 2 l) (* (* t t) (+ 2 (/ 4 x)))))

series793.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(fma (/ l x) (* 2 l) (* (* t t) (+ 2 (/ 4 x))))
194.0ms	(/ (* (sqrt 2) t) (sqrt (fma (/ l x) (* 2 l) (* (* t t) (+ 2 (/ 4 x))))))
46.0ms	(* (sqrt 2) t)
478.0ms	(sqrt (fma (/ l x) (* 2 l) (* (* t t) (+ 2 (/ 4 x)))))

simplify1.4s

Counts

90 → 90

Iterations

Iter	Nodes
3	3274
2	854
1	286
0	128

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

regimes743.0ms

Accuracy

77.7% (5.2b remaining)

Error of 9.1b against oracle of 3.9b and baseline of 27.2b

bsearch344.0ms

Steps

Iters	Range		Point
5	6.427095866430153e+63	2.5010262506421148e+64	2.2206986511032415e+64
10	-6.07299216690422e+154	-4.987932973877915e+141	-3.8166792423498327e+149

simplify22.0ms

Iterations

Iter	Nodes
2	44
1	44
0	37

end0.0ms

sample8.7s

Algorithm

intervals

Results

2.6s	10168×	body	80	nan
1.3s	826×	body	1280	valid
1.2s	5166×	body	80	valid
989.0ms	1047×	body	640	valid
651.0ms	592×	body	1280	nan
514.0ms	609×	body	640	nan
414.0ms	644×	body	320	valid
182.0ms	332×	body	320	nan
119.0ms	317×	body	160	valid
95.0ms	195×	body	160	nan