Details

sample35.0ms

Algorithm

intervals

Results

9.0ms	237×	body	80	valid
3.0ms	18×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	12×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	1×	body	2560	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3465
5	879
4	292
3	111
2	45
1	20
0	11

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
4.4b	(* (/ (- y x) (- a t)) (- z t))
4.5b	(+ x (* (/ (- y x) (- a t)) (- z t)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 127

Calls

3 calls:

33.0ms	(/ (- y x) (- a t))
70.0ms	(* (/ (- y x) (- a t)) (- z t))
12.0ms	(+ x (* (/ (- y x) (- a t)) (- z t)))

series582.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(/ (- y x) (- a t))
265.0ms	(* (/ (- y x) (- a t)) (- z t))
250.0ms	(+ x (* (/ (- y x) (- a t)) (- z t)))

simplify999.0ms

Counts

136 → 136

Iterations

Iter	Nodes
done	5002
2	2186
1	540
0	196

prune811.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.5b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.3b	(* (- y x) (/ (- z t) (- a t)))
3.5b	(+ x (* (- y x) (/ (- z t) (- a t))))

rewrite106.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `associate-l` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`frac-times` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-r/` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

19.0ms	(/ (- z t) (- a t))
76.0ms	(* (- y x) (/ (- z t) (- a t)))
6.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

series482.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- z t) (- a t))
170.0ms	(* (- y x) (/ (- z t) (- a t)))
231.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

simplify1.5s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	2596
1	504
0	183

prune778.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y x))
0.5b	(cbrt (- y x))
1.0b	(* (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (/ (cbrt (- y x)) (/ (- a t) (- z t))))
9.6b	(+ x (* (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (/ (cbrt (- y x)) (/ (- a t) (- z t)))))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

479×	`times-frac`
428×	`add-sqr-sqrt`
390×	`*-un-lft-identity`
253×	`associate-r`
171×	`cbrt-prod`
159×	`add-cube-cbrt`
113×	`distribute-lft-out--` `difference-of-squares`
61×	`add-exp-log`
28×	`add-cbrt-cube`
27×	`div-exp`
21×	`prod-exp`
17×	`associate-/r/`
15×	`cbrt-undiv` `unswap-sqr`
12×	`cbrt-unprod`
10×	`flip3--` `div-inv` `flip--`
7×	`associate-l`
6×	`pow1` `1-exp` `add-log-exp`
4×	`cbrt-div`
2×	`pow1/3`
1×	`frac-times` `+-commutative` `sum-log` `flip3-+` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+`

Counts

4 → 352

Calls

4 calls:

6.0ms	(cbrt (- y x))
6.0ms	(cbrt (- y x))
241.0ms	(* (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (/ (cbrt (- y x)) (/ (- a t) (- z t))))
5.0ms	(+ x (* (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (/ (cbrt (- y x)) (/ (- a t) (- z t)))))

series986.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt (- y x))
213.0ms	(cbrt (- y x))
344.0ms	(* (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (/ (cbrt (- y x)) (/ (- a t) (- z t))))
228.0ms	(+ x (* (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (/ (cbrt (- y x)) (/ (- a t) (- z t)))))

simplify1.3s

Counts

364 → 364

Iterations

Iter	Nodes
done	5000
1	2116
0	553

prune2.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- y x))
0.5b	(/ 1 (/ (- a t) (- y x)))
4.4b	(* (/ 1 (/ (- a t) (- y x))) (- z t))
6.2b	(+ x (* (/ 1 (/ (- a t) (- y x))) (- z t)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
338×	`add-sqr-sqrt`
326×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-l`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*` `add-exp-log`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-r` `unswap-sqr`
4×	`distribute-rgt-in` `rec-exp` `associate-+r+` `sub-neg` `distribute-lft-in` `1-exp`
3×	`cbrt-unprod`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*r/` `associate-/l/`
1×	`+-commutative` `sum-log` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 351

Calls

4 calls:

19.0ms	(/ (- a t) (- y x))
35.0ms	(/ 1 (/ (- a t) (- y x)))
106.0ms	(* (/ 1 (/ (- a t) (- y x))) (- z t))
6.0ms	(+ x (* (/ 1 (/ (- a t) (- y x))) (- z t)))

series1.1s

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- a t) (- y x))
327.0ms	(/ 1 (/ (- a t) (- y x)))
486.0ms	(* (/ 1 (/ (- a t) (- y x))) (- z t))
242.0ms	(+ x (* (/ 1 (/ (- a t) (- y x))) (- z t)))

simplify562.0ms

Counts

363 → 363

Iterations

Iter	Nodes
done	5000
1	1202
0	400

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.4b

regimes726.0ms

Accuracy

18.1% (6.4b remaining)

Error of 10.5b against oracle of 4.1b and baseline of 11.9b

bsearch133.0ms

Steps

Iters	Range		Point
7	4.796121574418588e-114	1.1149325664425158e-112	4.854445287131613e-114
9	-3.3749816605740785e-170	-2.904187976604113e-175	-1.3489359762384461e-173

simplify2.0ms

Iterations

Iter	Nodes
done	31
1	31
0	23

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.1s	7689×	body	80	valid
160.0ms	493×	body	640	valid
117.0ms	403×	body	320	valid
86.0ms	290×	body	1280	valid
31.0ms	282×	body	160	valid
6.0ms	18×	body	2560	valid