Details

sample373.0ms

Algorithm

intervals

Results

68.0ms	328×	body	80	nan
44.0ms	14×	body	1280	nan
35.0ms	173×	body	80	valid
27.0ms	26×	body	1280	valid
22.0ms	29×	body	640	valid
11.0ms	14×	body	640	nan
10.0ms	19×	body	320	valid
8.0ms	12×	body	320	nan
4.0ms	9×	body	160	valid
4.0ms	9×	body	160	nan

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
7	3164
6	1632
5	695
4	400
3	180
2	91
1	40
0	18

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.4b	(* (sqrt 2) t)
12.8b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.2b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `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` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

40.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
6.0ms	(* (sqrt 2) t)
20.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
28.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

483.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
58.0ms	(* (sqrt 2) t)
229.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
2.0s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify7.7s

Counts

92 → 92

Iterations

Iter	Nodes
3	7610
2	1551
1	435
0	166

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* t t) (/ (* l l) x))
4.6b	(+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (/ (* l l) x))))
6.9b	(/ (* l l) x)
28.4b	(sqrt (+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (/ (* l l) x)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `associate-*r/` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `associate-*l/` `frac-add`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+r+` `sum-log` `div-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 64

Calls

4 calls:

11.0ms	(+ (* t t) (/ (* l l) x))
20.0ms	(+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (/ (* l l) x))))
20.0ms	(/ (* l l) x)
40.0ms	(sqrt (+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (/ (* l l) x)))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (* t t) (/ (* l l) x))
112.0ms	(+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (/ (* l l) x))))
34.0ms	(/ (* l l) x)
232.0ms	(sqrt (+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (/ (* l l) x)))))

simplify5.1s

Counts

76 → 76

Iterations

Iter	Nodes
3	9828
2	1774
1	442
0	149

prune957.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize76.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
0.6b	(+ (* t t) (* l (/ l x)))
4.6b	(+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (* l (/ l x)))))
28.4b	(sqrt (+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (* l (/ l x))))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r/` `add-cube-cbrt` `add-log-exp`
7×	`pow1` `sqrt-prod`
6×	`add-cbrt-cube` `associate-l` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`sqrt-div` `associate-*l/` `frac-add`
3×	`associate-r`
2×	`+-commutative` `associate-+r+` `sum-log` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

12.0ms	(* (sqrt 2) t)
10.0ms	(+ (* t t) (* l (/ l x)))
23.0ms	(+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (* l (/ l x)))))
45.0ms	(sqrt (+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (* l (/ l x))))))

series391.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sqrt 2) t)
54.0ms	(+ (* t t) (* l (/ l x)))
109.0ms	(+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (* l (/ l x)))))
186.0ms	(sqrt (+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (* l (/ l x))))))

simplify7.3s

Counts

77 → 77

Iterations

Iter	Nodes
3	8893
2	1603
1	410
0	143

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize79.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
0.6b	(+ (* t t) (* l (/ l x)))
4.6b	(+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (* l (/ l x)))))
28.4b	(sqrt (+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (* l (/ l x))))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod` `add-log-exp`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `flip3-+` `add-cube-cbrt` `flip-+`
4×	`sqrt-div` `associate-*l/` `frac-add`
3×	`sqrt-prod`
2×	`+-commutative` `associate-+r+` `sum-log`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `*-commutative`

Counts

4 → 65

Calls

4 calls:

29.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
9.0ms	(+ (* t t) (* l (/ l x)))
26.0ms	(+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (* l (/ l x)))))
49.0ms	(sqrt (+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (* l (/ l x))))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
62.0ms	(+ (* t t) (* l (/ l x)))
101.0ms	(+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (* l (/ l x)))))
249.0ms	(sqrt (+ (* 4 (* (/ t x) t)) (* 2 (+ (* t t) (* l (/ l x))))))

simplify4.6s

Counts

77 → 77

Iterations

Iter	Nodes
3	10090
2	1791
1	451
0	148

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

regimes657.0ms

Accuracy

77.7% (5.2b remaining)

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

bsearch311.0ms

Steps

Iters	Range		Point
5	6.427095866430153e+63	2.5010262506421148e+64	2.46097945070799e+64
8	-4.987932973877915e+141	-4.695262149083215e+138	-3.5141814096893173e+140

simplify27.0ms

Iterations

Iter	Nodes
2	60
1	60
0	47

end0.0ms

sample8.8s

Algorithm

intervals

Results

1.9s	10168×	body	80	nan
1.6s	5166×	body	80	valid
1.3s	1047×	body	640	valid
974.0ms	826×	body	1280	valid
744.0ms	644×	body	320	valid
572.0ms	592×	body	1280	nan
501.0ms	609×	body	640	nan
267.0ms	332×	body	320	nan
163.0ms	317×	body	160	valid
148.0ms	195×	body	160	nan