Details

sample372.0ms

Algorithm

intervals

Results

77.0ms	20×	body	320	nan
43.0ms	338×	body	80	nan
24.0ms	40×	body	640	valid
22.0ms	156×	body	80	valid
16.0ms	24×	body	1280	valid
13.0ms	19×	body	1280	nan
11.0ms	14×	body	640	nan
9.0ms	24×	body	320	valid
3.0ms	12×	body	160	valid
1.0ms	5×	body	160	nan

simplify5.1s

Counts

1 → 1

Iterations

Useful iterations: 1 (17.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
0.5b	(* (sqrt 2.0) t)
13.9b	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
21.6b	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite190.0ms

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:

80.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
11.0ms	(* (sqrt 2.0) t)
31.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
57.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series1.7s

Counts

4 → 12

Calls

4 calls:

772.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
59.0ms	(* (sqrt 2.0) t)
305.0ms	(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
547.0ms	(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify4.1s

Counts

100 → 100

Iterations

Useful iterations: 3 (2.1s)

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

prune664.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 30.8b

localize45.0ms

Local error

Found 4 expressions with local error:

5.3b	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
6.9b	(/ (pow l 2) x)
9.5b	(/ (pow t 2) x)
28.2b	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite29.0ms

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)
11.0ms	(/ (pow t 2) x)
3.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
22.0ms	(/ (pow l 2) x)
35.0ms	(/ (pow t 2) x)
443.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

simplify2.1s

Counts

139 → 139

Iterations

Useful iterations: done (2.1s)

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

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma t t (* (fabs l) (/ (fabs l) x)))
5.3b	(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
9.5b	(/ (pow t 2) x)
28.2b	(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

rewrite17.0ms

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

series474.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(fma t t (* (fabs l) (/ (fabs l) x)))
126.0ms	(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
32.0ms	(/ (pow t 2) x)
262.0ms	(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

simplify2.2s

Counts

98 → 98

Iterations

Useful iterations: done (2.2s)

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

prune550.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
5.3b	(fma 2.0 (fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))) (* 4.0 (/ (pow t 2) x)))
9.5b	(/ (pow t 2) x)
28.2b	(sqrt (fma 2.0 (fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))) (* 4.0 (/ (pow t 2) x))))

rewrite26.0ms

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

series674.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
129.0ms	(fma 2.0 (fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))) (* 4.0 (/ (pow t 2) x)))
21.0ms	(/ (pow t 2) x)
428.0ms	(sqrt (fma 2.0 (fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))) (* 4.0 (/ (pow t 2) x))))

simplify1.9s

Counts

98 → 98

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	163	1745
1	287	1587
2	694	1327
3	2390	1216
done	5000	1107

prune625.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.3b

regimes499.0ms

Accuracy

76.5% (5.6b remaining)

Error of 9.6b against oracle of 4.0b and baseline of 27.9b

bsearch295.0ms

Steps

Iters	Range		Point
9	9.324172023423285e+142	1.1012045087961449e+149	1.6421833813677545e+146
10	-1.1979006433782284e+85	-5.09199279650327e+67	-2.8442338941596414e+80

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	79
1	45	79
done	45	79

end0.0ms

sample6.4s

Algorithm

intervals

Results

1.3s	10110×	body	80	nan
1.2s	5091×	body	80	valid
1.0s	1030×	body	640	valid
697.0ms	847×	body	1280	valid
334.0ms	601×	body	1280	nan
273.0ms	656×	body	320	valid
257.0ms	584×	body	640	nan
168.0ms	381×	body	320	nan
75.0ms	376×	body	160	valid
38.0ms	183×	body	160	nan