Details

sample311.0ms

Algorithm

intervals

Results

96.0ms	299×	body	80	nan
23.0ms	168×	body	80	valid
16.0ms	24×	body	1280	valid
14.0ms	26×	body	640	valid
12.0ms	15×	body	1280	nan
9.0ms	19×	body	640	nan
8.0ms	20×	body	320	valid
7.0ms	18×	body	320	nan
5.0ms	18×	body	160	valid
2.0ms	8×	body	160	nan

simplify4.7s

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize40.0ms

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)
13.6b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.4b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite239.0ms

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:

106.0ms	(/ (* (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)
59.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
59.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series3.2s

Counts

4 → 12

Calls

4 calls:

680.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
76.0ms	(* (sqrt 2.0) t)
302.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
2.1s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.6s

Counts

102 → 102

Iterations

Useful iterations: done (1.6s)

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

prune573.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.3b

localize26.0ms

Local error

Found 4 expressions with local error:

5.2b	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
6.7b	(/ (pow t 2) x)
6.7b	(/ (pow l 2) x)
29.0b	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

rewrite42.0ms

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:

1.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
22.0ms	(/ (pow t 2) x)
9.0ms	(/ (pow l 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

series582.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))
21.0ms	(/ (pow t 2) x)
29.0ms	(/ (pow l 2) x)
428.0ms	(sqrt (fma 2.0 (fma t t (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))

simplify2.4s

Counts

139 → 139

Iterations

Useful iterations: done (2.4s)

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

prune710.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma t t (* (fabs l) (/ (fabs l) x)))
5.2b	(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
6.7b	(/ (pow t 2) x)
29.0b	(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 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 (* (fabs l) (/ (fabs l) x)))
0.0ms	(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))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(fma t t (* (fabs l) (/ (fabs l) x)))
128.0ms	(fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x)))
35.0ms	(/ (pow t 2) x)
223.0ms	(sqrt (fma 2.0 (fma t t (* (fabs l) (/ (fabs l) x))) (* 4.0 (/ (pow t 2) x))))

simplify2.4s

Counts

98 → 98

Iterations

Useful iterations: done (2.4s)

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

prune575.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize29.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
5.2b	(fma 2.0 (fma t t (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))) (* 4.0 (/ (pow t 2) x)))
6.7b	(/ (pow t 2) x)
29.0b	(sqrt (fma 2.0 (fma t t (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))) (* 4.0 (/ (pow t 2) x))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

16.0ms	(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
0.0ms	(fma 2.0 (fma t t (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))) (* 4.0 (/ (pow t 2) x)))
9.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (fma t t (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))) (* 4.0 (/ (pow t 2) x))))

series808.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
163.0ms	(fma 2.0 (fma t t (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))) (* 4.0 (/ (pow t 2) x)))
23.0ms	(/ (pow t 2) x)
452.0ms	(sqrt (fma 2.0 (fma t t (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))) (* 4.0 (/ (pow t 2) x))))

simplify2.8s

Counts

129 → 129

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	248	2237
1	476	2079
2	1177	1864
3	4085	1578
done	5000	1481

prune686.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

regimes585.0ms

Accuracy

75.7% (5.8b remaining)

Error of 9.6b against oracle of 3.8b and baseline of 27.8b

bsearch730.0ms

Steps

Iters	Range		Point
8	7.407251155982859e+145	4.879894848387411e+149	6.335165898555757e+148
6	-1.4231360660802614e-302	-2.7726430826687857e-303	-1.4020051272573528e-302
8	-2.3731648380204055e-262	-6.820981679032075e-265	-8.549619549454068e-265
5	-1.5004718450719783e+25	-4.978593612221029e+24	-8.54333635658851e+24

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.7s

Algorithm

intervals

Results

1.4s	5159×	body	80	valid
1.3s	10248×	body	80	nan
1.0s	851×	body	1280	valid
825.0ms	635×	body	320	valid
452.0ms	591×	body	640	nan
411.0ms	1001×	body	640	valid
281.0ms	576×	body	1280	nan
90.0ms	334×	body	320	nan
68.0ms	354×	body	160	valid
31.0ms	180×	body	160	nan