Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	228×	body	80	valid
1.0ms	14×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	14×	body	320	valid
0.0ms	9×	body	160	valid
0.0ms	2×	body	2560	valid

simplify6.1s

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
2.5b	(- (+ x y) (/ (* (- z t) y) (- a t)))
12.2b	(/ (* (- z t) y) (- a t))

rewrite96.0ms

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:

20.0ms	(* (- z t) y)
50.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
23.0ms	(/ (* (- z t) y) (- a t))

series217.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(* (- z t) y)
120.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
64.0ms	(/ (* (- z t) y) (- a t))

simplify795.0ms

Counts

79 → 79

Iterations

Useful iterations: 2 (178.0ms)

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

prune174.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(* (cbrt (- a t)) (cbrt (- a t)))
2.5b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
8.6b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
50×	`cbrt-prod`
38×	`associate-r`
36×	`times-frac`
30×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
18×	`add-cbrt-cube`
15×	`flip3--` `flip--`
13×	`pow1`
11×	`frac-times` `distribute-lft-out--`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`prod-exp` `cbrt-unprod` `add-log-exp` `difference-of-squares`
7×	`cbrt-undiv` `pow1/3` `associate-r/` `div-exp` `associate-l/`
6×	`frac-sub`
3×	`flip3-+` `pow-prod-down` `flip-+`
2×	`diff-log` `pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`pow2` `sub-neg` `pow-plus` `associate--l+` `sum-log`

Counts

4 → 168

Calls

4 calls:

4.0ms	(cbrt (- a t))
36.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
106.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
37.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- a t))
122.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
100.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
123.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify1.3s

Counts

180 → 180

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	326	3837
1	864	3584
2	3445	3004
done	5000	2813

prune504.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.8b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
32×	`cbrt-div`
22×	`add-sqr-sqrt` `add-cbrt-cube`
19×	`frac-times`
17×	`associate-l`
16×	`times-frac` `associate-r` `associate-/r/`
15×	`associate-*l/` `prod-exp` `cbrt-unprod`
14×	`frac-sub`
13×	`flip3--` `flip--`
12×	`cbrt-undiv` `*-un-lft-identity` `div-exp`
11×	`associate-*r/`
10×	`add-cube-cbrt`
9×	`cbrt-prod` `add-log-exp`
7×	`flip3-+` `flip-+`
6×	`pow1` `unswap-sqr`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 119

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
321.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))))
38.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

series815.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt y)
185.0ms	(cbrt y)
292.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))))
167.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

simplify1.6s

Counts

131 → 131

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	338	4899
1	964	4760
2	3909	4003
done	5001	3866

prune584.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
0.6b	(cbrt (cbrt (- a t)))
2.5b	(* (/ (- z t) (* (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t))))
8.4b	(- (+ x y) (* (/ (- z t) (* (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t)))))

rewrite444.0ms

Algorithm

rewrite-expression-head

Rules

368×	`cbrt-div`
143×	`frac-times`
117×	`flip3--` `flip--`
89×	`associate-l`
82×	`associate-/r/`
55×	`associate-*l/`
49×	`associate-*r/`
41×	`add-sqr-sqrt`
36×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`times-frac`
30×	`cbrt-prod` `associate-r`
24×	`add-cbrt-cube`
23×	`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 → 205

Calls

4 calls:

13.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
4.0ms	(cbrt (cbrt (- a t)))
370.0ms	(* (/ (- z t) (* (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t))))
34.0ms	(- (+ x y) (* (/ (- z t) (* (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t)))))

series508.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
152.0ms	(cbrt (cbrt (- a t)))
103.0ms	(* (/ (- z t) (* (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t))))
124.0ms	(- (+ x y) (* (/ (- z t) (* (* (cbrt (- a t)) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t)))))

simplify1.7s

Counts

217 → 217

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	447	7252
1	1261	6831
2	4435	6381
done	5002	6217

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

regimes328.0ms

Accuracy

9.9% (6.2b remaining)

Error of 10.2b against oracle of 4.0b and baseline of 10.9b

bsearch100.0ms

Steps

Iters	Range		Point
10	3.5203588644576918e-146	5.218300859785189e-131	9.681339001705814e-139
7	-7.445094056825134	-0.1692380679741423	-0.17192721297922683

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	153
1	46	153
done	46	153

end0.0ms

sample695.0ms

Algorithm

intervals

Results

225.0ms	7352×	body	80	valid
46.0ms	447×	body	640	valid
33.0ms	246×	body	1280	valid
30.0ms	376×	body	320	valid
14.0ms	266×	body	160	valid
3.0ms	17×	body	2560	valid