Details

sample400.0ms

Algorithm

intervals

Results

145.0ms	322×	body	80	nan
45.0ms	20×	body	1280	valid
19.0ms	167×	body	80	valid
14.0ms	35×	body	640	valid
5.0ms	19×	body	320	valid
5.0ms	14×	body	640	nan
5.0ms	13×	body	1280	nan
3.0ms	15×	body	160	valid
3.0ms	14×	body	320	nan
1.0ms	8×	body	160	nan

simplify4.7s

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
0.4b	(* (sqrt 2.0) t)
12.7b	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
24.0b	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite202.0ms

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-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 88

Calls

4 calls:

61.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
12.0ms	(* (sqrt 2.0) t)
50.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
68.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series1.6s

Counts

4 → 12

Calls

4 calls:

693.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
78.0ms	(* (sqrt 2.0) t)
291.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
510.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify3.9s

Counts

100 → 100

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	155	2445
1	345	2250
2	1195	2062
3	4993	2025
done	5000	2025

prune592.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 33.6b

localize46.0ms

Local error

Found 4 expressions with local error:

5.5b	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
5.5b	(/ (pow l 2) x)
10.0b	(/ (pow t 2) x)
29.5b	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite33.0ms

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)))
9.0ms	(/ (pow l 2) x)
16.0ms	(/ (pow t 2) x)
4.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
34.0ms	(/ (pow l 2) x)
29.0ms	(/ (pow t 2) x)
398.0ms	(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 (2.3s)

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

prune791.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma t t (/ l (/ x l)))
5.5b	(fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x)))
10.0b	(/ (pow t 2) x)
29.5b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

rewrite19.0ms

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 (/ l (/ x l)))
1.0ms	(fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x)))
10.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

53.0ms	(fma t t (/ l (/ x l)))
127.0ms	(fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x)))
29.0ms	(/ (pow t 2) x)
829.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: done (1.6s)

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

prune467.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.0b

localize43.0ms

Local error

Found 4 expressions with local error:

10.0b	(/ (pow t 2) x)
10.0b	(/ (pow t 2) x)
29.5b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))
29.5b	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
42×	`add-sqr-sqrt`
40×	`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×	`pow1` `div-exp` `associate-/r*` `sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 132

Calls

4 calls:

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

series857.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (pow t 2) x)
36.0ms	(/ (pow t 2) x)
347.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))
441.0ms	(sqrt (fma 2.0 (fma t t (/ l (/ x l))) (* 4.0 (/ (pow t 2) x))))

simplify1.5s

Counts

144 → 144

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	133	1862
1	233	1676
2	559	1492
3	1789	1492
done	5000	1490

prune960.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.0b

regimes461.0ms

Accuracy

77.9% (5.2b remaining)

Error of 9.1b against oracle of 3.9b and baseline of 27.5b

bsearch264.0ms

Steps

Iters	Range		Point
4	2.8615303770675884e+117	4.371962998755528e+117	3.380741590772817e+117
8	-2.123549231421323e+124	-2.3823582692630786e+120	-3.696744411039917e+122

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	66
1	34	66
done	34	66

end0.0ms

sample6.3s

Algorithm

intervals

Results

1.2s	10131×	body	80	nan
1.1s	1035×	body	640	valid
945.0ms	5121×	body	80	valid
811.0ms	608×	body	1280	nan
549.0ms	881×	body	1280	valid
260.0ms	611×	body	320	valid
240.0ms	613×	body	640	nan
157.0ms	362×	body	320	nan
70.0ms	352×	body	160	valid
29.0ms	156×	body	160	nan