Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	218×	body	80	valid
2.0ms	17×	body	640	valid
2.0ms	22×	body	320	valid
2.0ms	13×	body	1280	valid
0.0ms	5×	body	160	valid

simplify8.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	51	13
3	101	13
4	191	13
5	343	13
6	506	13
7	659	13
8	794	13
9	1026	13
10	1390	13
11	2194	13
12	3236	13
13	4099	13
done	5000	13

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
1.8b	(- (+ x y) (/ (* (- z t) y) (- a t)))
11.4b	(/ (* (- z t) y) (- a t))

rewrite48.0ms

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:

10.0ms	(* (- z t) y)
26.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
10.0ms	(/ (* (- z t) y) (- a t))

series200.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(* (- z t) y)
107.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
61.0ms	(/ (* (- z t) y) (- a t))

simplify604.0ms

Counts

79 → 79

Iterations

Useful iterations: 2 (134.0ms)

Iter	Nodes	Cost
0	150	1010
1	383	951
2	1483	873
done	5001	873

prune203.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.6b	(* (cbrt (- a t)) (cbrt (- a t)))
2.3b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
10.6b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite117.0ms

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:

2.0ms	(cbrt (- a t))
21.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
66.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
19.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (- a t))
115.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
93.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
105.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify1.4s

Counts

180 → 180

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	326	3837
1	884	3584
2	3558	3004
done	5001	2988

prune542.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.9b

localize18.0ms

Local error

Found 4 expressions with local error:

2.7b	(cbrt (/ y (cbrt (- a t))))
2.7b	(cbrt (/ y (cbrt (- a t))))
2.7b	(cbrt (/ y (cbrt (- a t))))
10.6b	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (/ y (cbrt (- a t))))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

135×	`cbrt-prod`
72×	`times-frac`
67×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`cbrt-div`
49×	`add-cube-cbrt`
34×	`frac-times`
30×	`frac-sub`
26×	`associate-*l/`
22×	`associate-*r/`
15×	`flip3-+` `flip-+`
9×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3` `div-inv`
2×	`diff-log`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 161

Calls

4 calls:

4.0ms	(cbrt (/ y (cbrt (- a t))))
4.0ms	(cbrt (/ y (cbrt (- a t))))
4.0ms	(cbrt (/ y (cbrt (- a t))))
32.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (/ y (cbrt (- a t))))))

series787.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt (/ y (cbrt (- a t))))
248.0ms	(cbrt (/ y (cbrt (- a t))))
197.0ms	(cbrt (/ y (cbrt (- a t))))
159.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (/ y (cbrt (- a t))))))

simplify694.0ms

Counts

173 → 173

Iterations

Useful iterations: 2 (235.0ms)

Iter	Nodes	Cost
0	336	5344
1	761	5153
2	2425	4494
done	5000	4494

prune657.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.9b

localize27.0ms

Local error

Found 4 expressions with local error:

2.7b	(cbrt (/ y (cbrt (- a t))))
2.7b	(cbrt (/ y (cbrt (- a t))))
2.7b	(cbrt (/ y (cbrt (- a t))))
10.6b	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (* (cbrt (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (cbrt (/ y (cbrt (- a t))))))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

489×	`cbrt-div`
258×	`frac-times`
142×	`associate-r/` `associate-l/`
135×	`cbrt-prod`
126×	`frac-sub`
72×	`times-frac`
67×	`add-sqr-sqrt` `*-un-lft-identity`
63×	`flip3-+` `flip-+`
49×	`add-cube-cbrt`
9×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3` `div-inv`
2×	`diff-log`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 257

Calls

4 calls:

4.0ms	(cbrt (/ y (cbrt (- a t))))
4.0ms	(cbrt (/ y (cbrt (- a t))))
7.0ms	(cbrt (/ y (cbrt (- a t))))
55.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (* (cbrt (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (cbrt (/ y (cbrt (- a t))))))))

series780.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(cbrt (/ y (cbrt (- a t))))
185.0ms	(cbrt (/ y (cbrt (- a t))))
187.0ms	(cbrt (/ y (cbrt (- a t))))
164.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (* (cbrt (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (cbrt (/ y (cbrt (- a t))))))))

simplify561.0ms

Counts

269 → 269

Iterations

Useful iterations: done (531.0ms)

Iter	Nodes	Cost
0	693	16472
1	1707	16071
done	5000	16062

prune1.2s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.9b

regimes370.0ms

Accuracy

13.2% (6.9b remaining)

Error of 11.0b against oracle of 4.1b and baseline of 12.0b

bsearch108.0ms

Steps

Iters	Range	Point
8	7.716107484148514e+100	2.187027434812202e+103	2.1017965543309036e+103
4	3.921530203054118e-05	6.379368274952145e-05	4.284016413510673e-05
9	-1.0490688862218808e+141	-3.7430369710550457e+133	-6.605766029898568e+137

Iters

Range

Point

7.716107484148514e+100

2.187027434812202e+103

2.1017965543309036e+103

3.921530203054118e-05

6.379368274952145e-05

4.284016413510673e-05

-1.0490688862218808e+141

-3.7430369710550457e+133

-6.605766029898568e+137

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	52
1	32	52
done	32	52

end0.0ms

sample625.0ms

Algorithm

intervals

Results

223.0ms	7307×	body	80	valid
60.0ms	462×	body	640	valid
41.0ms	288×	body	1280	valid
32.0ms	376×	body	320	valid
16.0ms	273×	body	160	valid
3.0ms	16×	body	2560	valid