Details

sample58.0ms

Algorithm

intervals

Results

18.0ms	233×	body	80	valid
4.0ms	15×	body	640	valid
3.0ms	7×	body	1280	valid
2.0ms	11×	body	320	valid
1.0ms	10×	body	160	valid

simplify8.6s

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.8b	(- (+ x y) (/ (* (- z t) y) (- a t)))
12.2b	(/ (* (- z t) y) (- a t))

rewrite108.0ms

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:

23.0ms	(* (- z t) y)
58.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
24.0ms	(/ (* (- z t) y) (- a t))

series252.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* (- z t) y)
138.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
77.0ms	(/ (* (- z t) y) (- a t))

simplify1.1s

Counts

79 → 79

Iterations

Useful iterations: 2 (228.0ms)

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

prune292.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
4.1b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
7.7b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

7.0ms	(cbrt (- a t))
4.0ms	(cbrt (- a t))
138.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
58.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series691.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (- a t))
184.0ms	(cbrt (- a t))
177.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
153.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify1.7s

Counts

139 → 139

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	274	3197
1	764	3031
2	2854	2480
done	5001	2289

prune600.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.6b	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
4.1b	(* (/ (- z t) (* (cbrt (- a t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t))))
7.5b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t)))))

rewrite749.0ms

Algorithm

rewrite-expression-head

Rules

366×	`cbrt-div`
143×	`frac-times`
117×	`flip3--` `flip--`
89×	`associate-l`
82×	`associate-/r/`
55×	`associate-*r/`
49×	`associate-*l/`
40×	`add-sqr-sqrt`
36×	`add-exp-log`
32×	`*-un-lft-identity`
31×	`times-frac`
30×	`associate-r`
24×	`add-cbrt-cube`
22×	`cbrt-prod` `add-cube-cbrt`
14×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
6×	`pow1` `frac-sub`
5×	`distribute-lft-out--` `difference-of-squares`
3×	`flip3-+` `flip-+` `unswap-sqr`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 202

Calls

4 calls:

6.0ms	(cbrt (- a t))
23.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
627.0ms	(* (/ (- z t) (* (cbrt (- a t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t))))
59.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t)))))

series706.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(cbrt (- a t))
183.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
135.0ms	(* (/ (- z t) (* (cbrt (- a t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t))))
183.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t)))))

simplify2.5s

Counts

214 → 214

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	434	7250
1	1238	6832
2	4450	6374
done	5001	6330

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(* (cbrt y) (cbrt y))
0.9b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt y) (cbrt y)))
9.4b	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt y) (cbrt y))) (/ (cbrt y) (cbrt (- a t)))))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-sqr-sqrt`
23×	`associate-l`
19×	`cbrt-prod`
17×	`*-un-lft-identity`
16×	`pow1`
15×	`add-cube-cbrt` `add-cbrt-cube`
12×	`cbrt-div` `prod-exp` `cbrt-unprod`
9×	`associate-*l/` `add-log-exp`
8×	`associate-/r/`
7×	`flip3--` `pow1/3` `associate-r` `flip--`
6×	`frac-times` `times-frac` `swap-sqr` `frac-sub` `unswap-sqr`
5×	`pow-prod-down`
4×	`cbrt-undiv` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`diff-log` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `associate--l+` `sum-log` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

1.0ms	(cbrt y)
12.0ms	(* (cbrt y) (cbrt y))
127.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt y) (cbrt y)))
85.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt y) (cbrt y))) (/ (cbrt y) (cbrt (- a t)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

277.0ms	(cbrt y)
285.0ms	(* (cbrt y) (cbrt y))
272.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt y) (cbrt y)))
246.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt y) (cbrt y))) (/ (cbrt y) (cbrt (- a t)))))

simplify1.4s

Counts

126 → 126

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	262	2621
1	687	2275
2	2625	1907
done	5002	1792

prune462.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 2.7b

regimes365.0ms

Accuracy

27.3% (5.3b remaining)

Error of 9.1b against oracle of 3.8b and baseline of 11.1b

bsearch89.0ms

Steps

Iters	Range		Point
2	4.7419168322748984e-116	5.195215701485888e-116	4.8895291531937833e-116
8	-8.588102644321151e-162	-1.9657628581050384e-165	-1.607251433835726e-162

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	92
1	41	92
done	41	92

end0.0ms

sample1.3s

Algorithm

intervals

Results

605.0ms	7409×	body	80	valid
77.0ms	427×	body	640	valid
57.0ms	243×	body	1280	valid
51.0ms	383×	body	320	valid
51.0ms	257×	body	160	valid
2.0ms	9×	body	2560	valid