Details

sample255.0ms

Algorithm

intervals

Results

91.0ms	301×	body	80	nan
21.0ms	31×	body	1280	valid
18.0ms	160×	body	80	valid
11.0ms	28×	body	640	valid
10.0ms	18×	body	1280	nan
8.0ms	20×	body	640	nan
8.0ms	26×	body	320	valid
4.0ms	15×	body	320	nan
2.0ms	11×	body	160	valid
2.0ms	10×	body	160	nan

simplify5.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (10.0ms)

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (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)
14.0b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.8b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite265.0ms

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:

99.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
22.0ms	(* (sqrt 2.0) t)
70.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
65.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

658.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
65.0ms	(* (sqrt 2.0) t)
311.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.8s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.8s

Counts

102 → 102

Iterations

Useful iterations: done (1.8s)

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

prune557.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.4b

localize23.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
6.6b	(/ (pow l 2) x)
11.1b	(/ (pow t 2) x)
29.2b	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite52.0ms

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)))
26.0ms	(/ (pow l 2) x)
19.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

series569.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
31.0ms	(/ (pow l 2) x)
21.0ms	(/ (pow t 2) x)
410.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

simplify2.2s

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

prune743.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma t t (/ l (/ x l)))
3.8b	(fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x)))
11.1b	(/ (pow t 2) x)
29.2b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

rewrite24.0ms

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 (/ l (/ x l)))
0.0ms	(fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x)))
17.0ms	(/ (pow t 2) x)
3.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

series642.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(fma t t (/ l (/ x l)))
137.0ms	(fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x)))
36.0ms	(/ (pow t 2) x)
405.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

simplify2.2s

Counts

98 → 98

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	159	1358
1	277	1259
2	659	1108
3	2266	1108
done	5001	1107

prune478.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.8b

localize28.0ms

Local error

Found 4 expressions with local error:

11.1b	(/ (pow t 2) x)
29.2b	(sqrt (fma 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))) (* 4.0 (/ (pow t 2) x))))
29.3b	(sqrt (fma t t (/ l (/ x l))))
29.3b	(sqrt (fma t t (/ l (/ x l))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

19.0ms	(/ (pow t 2) x)
4.0ms	(sqrt (fma 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))) (* 4.0 (/ (pow t 2) x))))
3.0ms	(sqrt (fma t t (/ l (/ x l))))
3.0ms	(sqrt (fma t t (/ l (/ x l))))

series638.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (pow t 2) x)
367.0ms	(sqrt (fma 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))) (* 4.0 (/ (pow t 2) x))))
128.0ms	(sqrt (fma t t (/ l (/ x l))))
117.0ms	(sqrt (fma t t (/ l (/ x l))))

simplify1.6s

Counts

108 → 108

Iterations

Useful iterations: 3 (640.0ms)

Iter	Nodes	Cost
0	154	1527
1	271	1184
2	631	1074
3	1926	1071
done	5001	1071

prune591.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.8b

regimes453.0ms

Accuracy

76.4% (5.7b remaining)

Error of 9.6b against oracle of 3.9b and baseline of 28.1b

bsearch869.0ms

Steps

Iters	Range		Point
7	3.5982350656865885e+59	1.9521708875942868e+61	6.84155195153334e+60
9	-1.6826171280496676e-273	-8.479631811913159e-279	-3.6001123721869805e-276
9	-3.6665974651226154e-165	-3.612130989595206e-170	-7.265062434046063e-166
3	-1.516374921943784e+82	-1.2093633317186018e+82	-1.49718669755471e+82

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	49	178
1	53	178
done	53	178

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.1s	10206×	body	80	nan
1.4s	5116×	body	80	valid
531.0ms	867×	body	1280	valid
496.0ms	1024×	body	640	valid
326.0ms	578×	body	1280	nan
281.0ms	601×	body	640	nan
255.0ms	630×	body	320	valid
181.0ms	363×	body	160	valid
102.0ms	347×	body	320	nan
41.0ms	198×	body	160	nan