Details

sample304.0ms

Algorithm

intervals

Results

53.0ms	21×	body	1280	valid
28.0ms	320×	body	80	nan
14.0ms	156×	body	80	valid
12.0ms	31×	body	320	valid
12.0ms	34×	body	640	valid
9.0ms	22×	body	1280	nan
6.0ms	17×	body	640	nan
4.0ms	16×	body	320	nan
2.0ms	14×	body	160	valid
1.0ms	6×	body	160	nan

simplify5.2s

Counts

1 → 1

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	18	27
1	41	26
2	100	26
3	224	26
4	497	26
5	941	26
6	1555	26
7	3305	26
done	5001	26

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b	(* (sqrt 2.0) t)
14.5b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `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` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

64.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
10.0ms	(* (sqrt 2.0) t)
33.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
53.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series3.2s

Counts

4 → 12

Calls

4 calls:

633.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
60.0ms	(* (sqrt 2.0) t)
328.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
2.2s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.7s

Counts

102 → 102

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	179	2660
1	442	2367
2	1680	2178
done	5001	2125

prune561.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

4.4b	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
8.1b	(/ (pow l 2) x)
10.2b	(/ (pow t 2) x)
26.7b	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
10.0ms	(/ (pow l 2) x)
15.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

series572.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
21.0ms	(/ (pow l 2) x)
21.0ms	(/ (pow t 2) x)
447.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

simplify2.3s

Counts

139 → 139

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	217	1761
1	376	1614
2	912	1411
3	3182	1411
done	5000	1410

prune753.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.0b

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b	(fma t t (* (fabs l) (/ (fabs l) x)))
4.4b	(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
10.2b	(/ (pow t 2) x)
26.7b	(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`fma-udef`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

1.0ms	(fma t t (* (fabs l) (/ (fabs l) x)))
1.0ms	(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
18.0ms	(/ (pow t 2) x)
3.0ms	(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(fma t t (* (fabs l) (/ (fabs l) x)))
104.0ms	(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
35.0ms	(/ (pow t 2) x)
246.0ms	(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

simplify2.5s

Counts

98 → 98

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	169	1458
1	315	1314
2	831	1164
3	3101	1160
done	5001	1159

prune640.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.0b

localize38.0ms

Local error

Found 4 expressions with local error:

2.0b	(fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))
4.4b	(fma 2.0 (fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x)))) (* 4.0 (/ (pow t 2) x)))
10.2b	(/ (pow t 2) x)
26.7b	(sqrt (fma 2.0 (fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x)))) (* 4.0 (/ (pow t 2) x))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`fma-udef`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

0.0ms	(fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))
0.0ms	(fma 2.0 (fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x)))) (* 4.0 (/ (pow t 2) x)))
16.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x)))) (* 4.0 (/ (pow t 2) x))))

series519.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))
157.0ms	(fma 2.0 (fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x)))) (* 4.0 (/ (pow t 2) x)))
32.0ms	(/ (pow t 2) x)
235.0ms	(sqrt (fma 2.0 (fma t t (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x)))) (* 4.0 (/ (pow t 2) x))))

simplify2.3s

Counts

98 → 98

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	170	1759
1	321	1643
2	849	1417
3	3115	1412
done	5000	1267

prune580.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.0b

regimes852.0ms

Accuracy

73.3% (6.4b remaining)

Error of 10.0b against oracle of 3.7b and baseline of 27.6b

bsearch906.0ms

Steps

Iters	Range		Point
7	5.438827393303272e-47	3.255422209678199e-45	3.190616919639676e-45
9	-9.099259929633761e-243	-1.1388205652005344e-250	-4.3039381620799786e-243
8	-4.709429137726002e-147	-1.2135677083227269e-149	-1.2300651500007749e-149
8	-7.002515132037965e+150	-1.149067304892884e+146	-2.3034608226733973e+149

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	45	171
1	50	171
done	50	171

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.1s	10338×	body	80	nan
1.5s	5100×	body	80	valid
661.0ms	1003×	body	640	valid
586.0ms	910×	body	1280	valid
353.0ms	564×	body	1280	nan
256.0ms	655×	body	320	valid
242.0ms	645×	body	640	nan
105.0ms	365×	body	320	nan
69.0ms	332×	body	160	valid
28.0ms	149×	body	160	nan