Details

sample166.0ms

Algorithm

intervals

Results

54.0ms	348×	body	80	nan
35.0ms	21×	body	1280	nan
12.0ms	164×	body	80	valid
12.0ms	33×	body	1280	valid
7.0ms	27×	body	640	valid
6.0ms	22×	body	640	nan
5.0ms	25×	body	320	valid
2.0ms	11×	body	320	nan
1.0ms	7×	body	160	valid
1.0ms	7×	body	160	nan

simplify76.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize23.0ms

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)
11.6b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.8b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite452.0ms

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×	`sqrt-div`
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` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

63.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
11.0ms	(* (sqrt 2.0) t)
31.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
344.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.0s

Counts

4 → 12

Calls

4 calls:

460.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
47.0ms	(* (sqrt 2.0) t)
235.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.3s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify57.0ms

Counts: 92 → 92

prune325.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.9b

localize21.0ms

Local error

Found 4 expressions with local error:

3.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.2b	(/ (pow l 2) x)
10.2b	(/ (pow t 2) x)
26.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite66.0ms

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×	`associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `associate-+r+` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 130

Calls

4 calls:

20.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
9.0ms	(/ (pow l 2) x)
9.0ms	(/ (pow t 2) x)
24.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
24.0ms	(/ (pow l 2) x)
20.0ms	(/ (pow t 2) x)
176.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify62.0ms

Counts: 142 → 142

prune491.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (pow t 2) (* l (/ l x)))
3.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
10.2b	(/ (pow t 2) x)
26.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite68.0ms

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-r/` `associate-/l` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`+-commutative` `associate-+r+` `sum-log`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 92

Calls

4 calls:

13.0ms	(+ (pow t 2) (* l (/ l x)))
19.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
9.0ms	(/ (pow t 2) x)
24.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (pow t 2) (* l (/ l x)))
78.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
21.0ms	(/ (pow t 2) x)
177.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify58.0ms

Counts: 104 → 104

prune372.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize32.0ms

Local error

Found 4 expressions with local error:

10.2b	(/ (pow t 2) x)
26.0b	(sqrt (+ (pow t 2) (* l (/ l x))))
26.0b	(sqrt (+ (pow t 2) (* l (/ l x))))
26.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`sqrt-div`
24×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`associate-*r/`
12×	`unpow-prod-down`
9×	`add-exp-log` `flip3-+` `sqrt-prod` `flip-+`
8×	`frac-add` `associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube`
4×	`frac-times` `unpow2` `add-log-exp` `sqr-pow`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-/r*`
2×	`associate-*l/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 102

Calls

4 calls:

9.0ms	(/ (pow t 2) x)
16.0ms	(sqrt (+ (pow t 2) (* l (/ l x))))
13.0ms	(sqrt (+ (pow t 2) (* l (/ l x))))
30.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (pow t 2) x)
75.0ms	(sqrt (+ (pow t 2) (* l (/ l x))))
72.0ms	(sqrt (+ (pow t 2) (* l (/ l x))))
180.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))

simplify62.0ms

Counts: 114 → 114

prune431.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

regimes474.0ms

Accuracy

77.5% (5.4b remaining)

Error of 9.3b against oracle of 3.8b and baseline of 27.9b

bsearch214.0ms

Steps

Iters	Range		Point
7	7.357052851829637e+72	5.384774946468905e+74	3.052533510544754e+74
8	-4.414808484807544e+93	-2.2690465926685535e+89	-1.2993792963240973e+93

simplify2.0ms

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.3s	10167×	body	80	nan
577.0ms	879×	body	1280	valid
444.0ms	5098×	body	80	valid
427.0ms	347×	body	320	nan
334.0ms	989×	body	640	valid
237.0ms	631×	body	1280	nan
224.0ms	627×	body	640	nan
214.0ms	657×	body	320	valid
53.0ms	164×	body	160	nan
52.0ms	377×	body	160	valid