Details

sample242.0ms

Algorithm

intervals

Results

73.0ms	294×	body	80	nan
22.0ms	160×	body	80	valid
19.0ms	32×	body	1280	valid
15.0ms	34×	body	640	valid
10.0ms	17×	body	1280	nan
9.0ms	22×	body	320	valid
7.0ms	17×	body	640	nan
2.0ms	8×	body	320	nan
1.0ms	8×	body	160	valid
1.0ms	7×	body	160	nan

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 1 (17.0ms)

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (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)
12.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.0b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite224.0ms

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:

86.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
12.0ms	(* (sqrt 2.0) t)
49.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
70.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.9s

Counts

4 → 12

Calls

4 calls:

631.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
60.0ms	(* (sqrt 2.0) t)
335.0ms	(- (* (/ (+ 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)))

simplify2.6s

Counts

102 → 102

Iterations

Useful iterations: done (2.6s)

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

prune619.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize52.0ms

Local error

Found 4 expressions with local error:

4.4b	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
5.0b	(/ (pow l 2) x)
10.9b	(/ (pow t 2) x)
28.5b	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

rewrite47.0ms

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

series468.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
29.0ms	(/ (pow l 2) x)
35.0ms	(/ (pow t 2) x)
303.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

simplify966.0ms

Counts

139 → 139

Iterations

Useful iterations: done (960.0ms)

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

prune803.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize42.0ms

Local error

Found 4 expressions with local error:

1.5b	(fma t t (/ (pow l (/ 2 2)) (/ x l)))
4.4b	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l)))))
10.9b	(/ (pow t 2) x)
28.5b	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))))))

rewrite15.0ms

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 (/ (pow l (/ 2 2)) (/ x l)))
0.0ms	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l)))))
10.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(fma t t (/ (pow l (/ 2 2)) (/ x l)))
121.0ms	(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l)))))
36.0ms	(/ (pow t 2) x)
268.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))))))

simplify781.0ms

Counts

98 → 98

Iterations

Useful iterations: done (777.0ms)

Iter	Nodes	Cost
0	159	1532
1	298	1346
2	1157	1124
done	5001	1119

prune585.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize49.0ms

Local error

Found 4 expressions with local error:

10.9b	(/ (pow t 2) x)
28.5b	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))))))
28.7b	(sqrt (fma t t (/ l (/ x l))))
28.7b	(sqrt (fma t t (/ l (/ x l))))

rewrite34.0ms

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

series550.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (pow t 2) x)
239.0ms	(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))))))
148.0ms	(sqrt (fma t t (/ l (/ x l))))
135.0ms	(sqrt (fma t t (/ l (/ x l))))

simplify832.0ms

Counts

108 → 108

Iterations

Useful iterations: done (827.0ms)

Iter	Nodes	Cost
0	155	1536
1	290	1194
2	1007	1088
done	5001	1086

prune586.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.9b

regimes679.0ms

Accuracy

74.2% (6.2b remaining)

Error of 10.1b against oracle of 3.9b and baseline of 27.8b

bsearch286.0ms

Steps

Iters	Range		Point
4	3.6682554499002217e+39	5.731397073736236e+39	4.568115772869942e+39
9	-1.9548292921352193e-18	-3.0117965680222497e-24	-1.9221230409501015e-18

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	120
1	52	120
done	52	120

end0.0ms

sample6.8s

Algorithm

intervals

Results

1.8s	10085×	body	80	nan
935.0ms	868×	body	1280	valid
817.0ms	589×	body	1280	nan
665.0ms	5076×	body	80	valid
548.0ms	1034×	body	640	valid
349.0ms	660×	body	320	valid
343.0ms	695×	body	640	nan
113.0ms	362×	body	160	valid
90.0ms	322×	body	320	nan
89.0ms	196×	body	160	nan