Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	258×	body	80	valid
2.0ms	13×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	5×	body	1280	valid
0.0ms	6×	body	160	valid
0.0ms	1×	body	2560	valid

simplify6.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	109	13
4	244	13
5	483	13
6	939	13
7	1537	13
8	2687	13
9	3769	13
10	4241	13
11	4705	13
done	5001	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
1.9b	(+ x (/ (* (- y x) (- z t)) (- a t)))
15.6b	(/ (* (- y x) (- z t)) (- a t))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

21.0ms	(* (- y x) (- z t))
11.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
13.0ms	(/ (* (- y x) (- z t)) (- a t))

series303.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* (- y x) (- z t))
154.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
113.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify703.0ms

Counts

90 → 90

Iterations

Useful iterations: 2 (181.0ms)

Iter	Nodes	Cost
0	162	1284
1	469	1213
2	1885	1111
done	5000	1111

prune254.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.9b	(+ x (* (- y x) (/ (- z t) (- a t))))
2.4b	(* (- y x) (/ (- z t) (- a t)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 119

Calls

3 calls:

11.0ms	(/ (- z t) (- a t))
3.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
33.0ms	(* (- y x) (/ (- z t) (- a t)))

series317.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ (- z t) (- a t))
152.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
115.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify725.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (252.0ms)

Iter	Nodes	Cost
0	183	1813
1	477	1704
2	1694	1606
done	5000	1606

prune299.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
1.9b	(+ x (/ (- y x) (/ (- a t) (- z t))))
2.8b	(/ (- y x) (/ (- a t) (- z t)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

11.0ms	(/ (- a t) (- z t))
67.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
23.0ms	(/ (- y x) (/ (- a t) (- z t)))

series407.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- a t) (- z t))
154.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
202.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify1.3s

Counts

283 → 283

Iterations

Useful iterations: 2 (764.0ms)

Iter	Nodes	Cost
0	354	5984
1	1028	5625
2	3490	5487
done	5000	5487

prune632.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- z t) (/ 1 (- a t)))
2.4b	(* (- y x) (* (- z t) (/ 1 (- a t))))
2.6b	(+ x (* (- y x) (* (- z t) (/ 1 (- a t)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
13×	`prod-exp`
12×	`pow1`
10×	`associate-r/` `associate-l` `associate-l/`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `add-log-exp`
5×	`associate-/r*`
4×	`pow-prod-down` `associate-/r/` `un-div-inv`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 146

Calls

4 calls:

6.0ms	(/ 1 (- a t))
25.0ms	(* (- z t) (/ 1 (- a t)))
37.0ms	(* (- y x) (* (- z t) (/ 1 (- a t))))
3.0ms	(+ x (* (- y x) (* (- z t) (/ 1 (- a t)))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (- a t))
51.0ms	(* (- z t) (/ 1 (- a t)))
111.0ms	(* (- y x) (* (- z t) (/ 1 (- a t))))
156.0ms	(+ x (* (- y x) (* (- z t) (/ 1 (- a t)))))

simplify692.0ms

Counts

158 → 158

Iterations

Useful iterations: 2 (218.0ms)

Iter	Nodes	Cost
0	221	2286
1	587	1896
2	2080	1716
done	5000	1716

prune339.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.6b

regimes221.0ms

Accuracy

17% (6.2b remaining)

Error of 10.4b against oracle of 4.2b and baseline of 11.6b

bsearch122.0ms

Steps

Iters	Range		Point
9	6.409273905094763e-153	1.2309718416917103e-145	2.0695378041879823e-147
11	-7.111888234651541e-127	-4.571959059179775e-147	-4.2852583466209365e-144

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	49
1	37	49
done	37	49

end0.0ms

sample721.0ms

Algorithm

intervals

Results

268.0ms	7821×	body	80	valid
60.0ms	494×	body	640	valid
45.0ms	271×	body	1280	valid
41.0ms	410×	body	320	valid
16.0ms	252×	body	160	valid
3.0ms	16×	body	2560	valid