Details

sample265.0ms

Algorithm

intervals

Results

79.0ms	289×	body	80	nan
19.0ms	171×	body	80	valid
16.0ms	27×	body	1280	valid
12.0ms	22×	body	640	nan
12.0ms	23×	body	1280	nan
10.0ms	24×	body	640	valid
6.0ms	21×	body	320	valid
4.0ms	12×	body	320	nan
3.0ms	7×	body	160	nan
2.0ms	13×	body	160	valid

simplify5.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	18	27
1	41	26
2	100	26
3	234	26
4	531	26
5	1051	26
6	1929	26
7	4593	26
done	5000	26

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize56.0ms

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)
13.0b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.3b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite268.0ms

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:

103.0ms	(/ (* (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)
71.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
64.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

654.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
73.0ms	(* (sqrt 2.0) t)
329.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.7s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify2.4s

Counts

102 → 102

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	179	2660
1	484	2380
2	2740	2183
done	5001	2176

prune646.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.2b

localize53.0ms

Local error

Found 4 expressions with local error:

2.8b	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
6.0b	(/ (pow l 2) x)
9.5b	(/ (pow t 2) x)
24.6b	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

rewrite36.0ms

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 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
13.0ms	(/ (pow l 2) x)
11.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
33.0ms	(/ (pow l 2) x)
36.0ms	(/ (pow t 2) x)
244.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

simplify978.0ms

Counts

139 → 139

Iterations

Useful iterations: done (969.0ms)

Iter	Nodes	Cost
0	216	1767
1	398	1621
2	1576	1429
done	5000	1426

prune798.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
2.8b	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (fabs l) (/ (fabs l) x)))))
9.5b	(/ (pow t 2) x)
24.6b	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (fabs l) (/ (fabs l) x))))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

12.0ms	(* (sqrt 2.0) t)
0.0ms	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (fabs l) (/ (fabs l) x)))))
16.0ms	(/ (pow t 2) x)
3.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (fabs l) (/ (fabs l) x))))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sqrt 2.0) t)
81.0ms	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (fabs l) (/ (fabs l) x)))))
34.0ms	(/ (pow t 2) x)
216.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (fabs l) (/ (fabs l) x))))))

simplify1.2s

Counts

112 → 112

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	186	1467
1	379	1329
2	1740	1189
done	5002	1186

prune680.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
2.8b	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (fabs l) (/ (fabs l) x)))))
9.5b	(/ (pow t 2) x)
24.6b	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (fabs l) (/ (fabs l) x))))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

72.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
1.0ms	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (fabs l) (/ (fabs l) x)))))
18.0ms	(/ (pow t 2) x)
3.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (fabs l) (/ (fabs l) x))))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
86.0ms	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (fabs l) (/ (fabs l) x)))))
24.0ms	(/ (pow t 2) x)
208.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (* (fabs l) (/ (fabs l) x))))))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	194	1728
1	420	1577
2	1857	1252
done	5000	1178

prune731.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.4b

regimes481.0ms

Accuracy

77.5% (5.3b remaining)

Error of 9.2b against oracle of 4.0b and baseline of 27.4b

bsearch330.0ms

Steps

Iters	Range		Point
7	1.432588733015798e+113	5.43248225308003e+114	3.1662692068386204e+113
8	-3.06497223010665e+106	-6.700067088620505e+103	-1.397305156304466e+105

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	102
1	49	102
done	49	102

end0.0ms

sample6.8s

Algorithm

intervals

Results

1.8s	10001×	body	80	nan
1.2s	5053×	body	80	valid
567.0ms	392×	body	160	valid
559.0ms	844×	body	1280	valid
541.0ms	1076×	body	640	valid
331.0ms	562×	body	1280	nan
278.0ms	608×	body	640	nan
190.0ms	635×	body	320	valid
181.0ms	336×	body	320	nan
104.0ms	176×	body	160	nan