Details

sample72.0ms

Algorithm

intervals

Results

34.0ms	236×	body	80	valid
6.0ms	19×	body	640	valid
5.0ms	11×	body	1280	valid
2.0ms	8×	body	320	valid
0.0ms	1×	body	160	valid

simplify9.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	52	13
3	107	13
4	186	13
5	380	13
6	529	13
7	668	13
8	820	13
9	969	13
10	1222	13
11	1531	13
12	2279	13
13	3564	13
done	5000	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
0.8b	(- (+ x y) (/ (* (- z t) y) (- a t)))
12.6b	(/ (* (- z t) y) (- a t))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-l` `associate-/r*` `distribute-lft-out--`
4×	`flip3--` `associate-*l/` `flip--` `difference-of-squares`
3×	`associate-r`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `associate-/r/` `frac-sub` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 70

Calls

3 calls:

22.0ms	(* (- z t) y)
53.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
32.0ms	(/ (* (- z t) y) (- a t))

series329.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* (- z t) y)
165.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
114.0ms	(/ (* (- z t) y) (- a t))

simplify1.0s

Counts

79 → 79

Iterations

Useful iterations: 2 (232.0ms)

Iter	Nodes	Cost
0	150	1010
1	382	951
2	1543	873
done	5000	873

prune205.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.4b

localize12.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (+ x y) (/ (- z t) (/ (- a t) y)))
9.0b	(/ (- z t) (/ (- a t) y))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

188×	`times-frac`
161×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
76×	`add-cube-cbrt`
41×	`difference-of-squares`
40×	`distribute-lft-out--`
19×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `div-inv` `add-log-exp`
5×	`associate-/l*`
3×	`cbrt-undiv` `div-exp`
2×	`pow1` `flip3--` `diff-log` `div-sub` `frac-sub` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `associate--l+` `clear-num` `sum-log` `associate-/r/` `flip-+` `distribute-lft-out` `associate--r-`

Counts

2 → 159

Calls

2 calls:

90.0ms	(- (+ x y) (/ (- z t) (/ (- a t) y)))
27.0ms	(/ (- z t) (/ (- a t) y))

series282.0ms

Counts

2 → 6

Calls

2 calls:

168.0ms	(- (+ x y) (/ (- z t) (/ (- a t) y)))
114.0ms	(/ (- z t) (/ (- a t) y))

simplify1.5s

Counts

165 → 165

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	284	3252
1	790	3044
2	2573	2956
done	5000	2954

prune455.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.6b	(* (cbrt (- a t)) (cbrt (- a t)))
2.7b	(/ (- z t) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y))))
7.6b	(- (+ x y) (/ (/ (- z t) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (cbrt (- a t)) (cbrt y))))

rewrite902.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
73×	`times-frac`
56×	`*-un-lft-identity`
43×	`cbrt-prod`
26×	`difference-of-squares`
25×	`add-cube-cbrt`
24×	`add-exp-log`
14×	`add-cbrt-cube` `distribute-lft-out--`
12×	`cbrt-div`
11×	`pow1`
10×	`swap-sqr`
9×	`cbrt-undiv` `div-exp` `add-log-exp`
8×	`flip3--` `associate-r` `associate-l` `flip--`
7×	`pow1/3` `div-inv`
5×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l`
4×	`frac-times` `unswap-sqr`
3×	`div-sub`
2×	`diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `frac-sub` `associate-/l/`
1×	`pow2` `sub-neg` `frac-2neg` `flip3-+` `pow-plus` `associate--l+` `clear-num` `sum-log` `associate-/r/` `*-commutative` `flip-+` `distribute-lft-out` `associate--r-`

Counts

4 → 161

Calls

4 calls:

2.0ms	(cbrt y)
66.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
57.0ms	(/ (- z t) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y))))
761.0ms	(- (+ x y) (/ (/ (- z t) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (cbrt (- a t)) (cbrt y))))

series911.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(cbrt y)
162.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
262.0ms	(/ (- z t) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y))))
224.0ms	(- (+ x y) (/ (/ (- z t) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (cbrt (- a t)) (cbrt y))))

simplify1.6s

Counts

173 → 173

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	380	4733
1	958	4524
2	3266	3597
done	5001	3468

prune744.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ z (/ (- a t) y)) (/ t (/ (- a t) y)))
2.2b	(- (+ x y) (- (/ z (/ (- a t) y)) (/ t (/ (- a t) y))))
5.1b	(/ z (/ (- a t) y))
8.4b	(/ t (/ (- a t) y))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

344×	`times-frac`
280×	`*-un-lft-identity`
236×	`add-sqr-sqrt`
138×	`add-cube-cbrt`
68×	`distribute-lft-out--`
40×	`difference-of-squares`
38×	`associate-/r*`
18×	`add-log-exp`
14×	`add-exp-log` `add-cbrt-cube` `div-inv`
11×	`frac-sub`
7×	`diff-log`
6×	`cbrt-undiv` `div-exp` `associate-/l*`
4×	`pow1` `flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+`
3×	`sub-neg` `sub-div`
2×	`distribute-rgt-out--` `frac-2neg` `clear-num` `sum-log` `distribute-lft-out` `associate--r+`
1×	`associate--l+` `associate--r-`

Counts

4 → 271

Calls

4 calls:

319.0ms	(- (/ z (/ (- a t) y)) (/ t (/ (- a t) y)))
790.0ms	(- (+ x y) (- (/ z (/ (- a t) y)) (/ t (/ (- a t) y))))
24.0ms	(/ z (/ (- a t) y))
24.0ms	(/ t (/ (- a t) y))

series521.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(- (/ z (/ (- a t) y)) (/ t (/ (- a t) y)))
119.0ms	(- (+ x y) (- (/ z (/ (- a t) y)) (/ t (/ (- a t) y))))
111.0ms	(/ z (/ (- a t) y))
127.0ms	(/ t (/ (- a t) y))

simplify2.4s

Counts

283 → 283

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	424	5438
1	1043	5069
2	3583	4761
done	5000	4757

prune914.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

regimes277.0ms

Accuracy

21.4% (5.4b remaining)

Error of 9.1b against oracle of 3.8b and baseline of 10.6b

bsearch167.0ms

Steps

Iters	Range		Point
9	2.427738159071072e-235	1.7163587562235555e-229	5.913406836150694e-231
10	-1.2606852365757149e-221	-8.95343244323789e-237	-1.3141380891097557e-225

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	26	77
1	32	47
done	32	47

end0.0ms

sample1.3s

Algorithm

intervals

Results

626.0ms	7343×	body	80	valid
107.0ms	231×	body	1280	valid
96.0ms	454×	body	640	valid
92.0ms	405×	body	320	valid
26.0ms	244×	body	160	valid
5.0ms	16×	body	2560	valid