Details

sample26.0ms

Algorithm

intervals

Results

9.0ms	257×	body	80	valid
2.0ms	15×	body	640	valid
2.0ms	10×	body	1280	valid
1.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid

simplify6.5s

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	1559	13
8	2514	13
9	3425	13
10	3796	13
11	4264	13
done	5000	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
1.4b	(+ x (/ (* (- y x) (- z t)) (- a t)))
17.2b	(/ (* (- y x) (- z t)) (- a t))

rewrite44.0ms

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:

17.0ms	(* (- y x) (- z t))
11.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
13.0ms	(/ (* (- y x) (- z t)) (- a t))

series298.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* (- y x) (- z t))
150.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
110.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify694.0ms

Counts

90 → 90

Iterations

Useful iterations: 2 (156.0ms)

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

prune240.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
1.4b	(+ x (/ (- y x) (/ (- a t) (- z t))))
2.4b	(/ (- y x) (/ (- a t) (- z t)))

rewrite116.0ms

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))
65.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
23.0ms	(/ (- y x) (/ (- a t) (- z t)))

series392.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (- a t) (- z t))
150.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
198.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify1.0s

Counts

283 → 283

Iterations

Useful iterations: 2 (391.0ms)

Iter	Nodes	Cost
0	354	5984
1	1028	5625
2	3585	5487
done	5000	5487

prune616.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.2b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ x (/ (- y x) (/ (- a t) (- z t))))
2.4b	(/ (- y x) (/ (- a t) (- z t)))
2.4b	(/ (- y x) (/ (- a t) (- z t)))
2.4b	(/ (- y x) (/ (- a t) (- z t)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

915×	`times-frac`
852×	`*-un-lft-identity`
850×	`add-sqr-sqrt`
298×	`add-cube-cbrt`
276×	`distribute-lft-out--` `difference-of-squares`
93×	`associate-/r*`
39×	`associate-/r/`
21×	`flip3--` `flip--` `div-inv`
19×	`add-exp-log` `add-cbrt-cube`
15×	`associate-/l*`
9×	`cbrt-undiv` `div-exp`
6×	`associate-/l/` `add-log-exp`
4×	`pow1` `div-sub`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 640

Calls

4 calls:

67.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
21.0ms	(/ (- y x) (/ (- a t) (- z t)))
20.0ms	(/ (- y x) (/ (- a t) (- z t)))
24.0ms	(/ (- y x) (/ (- a t) (- z t)))

series771.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
205.0ms	(/ (- y x) (/ (- a t) (- z t)))
200.0ms	(/ (- y x) (/ (- a t) (- z t)))
213.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify991.0ms

Counts

652 → 652

Iterations

Useful iterations: 2 (365.0ms)

Iter	Nodes	Cost
0	334	15220
1	969	14250
2	3413	13972
done	5001	13972

prune1.9s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.2b

localize23.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (- y x) (/ (- a t) (- z t)))
2.4b	(/ (- y x) (/ (- a t) (- z t)))
2.4b	(/ (- y x) (/ (- a t) (- z t)))
2.4b	(/ (- y x) (/ (- a t) (- z t)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

1220×	`times-frac`
1132×	`add-sqr-sqrt` `*-un-lft-identity`
396×	`add-cube-cbrt`
368×	`distribute-lft-out--` `difference-of-squares`
124×	`associate-/r*`
52×	`associate-/r/`
28×	`flip3--` `flip--` `div-inv`
24×	`add-exp-log` `add-cbrt-cube`
20×	`associate-/l*`
12×	`cbrt-undiv` `div-exp`
8×	`associate-/l/`
4×	`pow1` `frac-2neg` `div-sub` `clear-num` `add-log-exp`

Counts

4 → 836

Calls

4 calls:

20.0ms	(/ (- y x) (/ (- a t) (- z t)))
26.0ms	(/ (- y x) (/ (- a t) (- z t)))
21.0ms	(/ (- y x) (/ (- a t) (- z t)))
21.0ms	(/ (- y x) (/ (- a t) (- z t)))

series1.0s

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ (- y x) (/ (- a t) (- z t)))
205.0ms	(/ (- y x) (/ (- a t) (- z t)))
195.0ms	(/ (- y x) (/ (- a t) (- z t)))
418.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify979.0ms

Counts

848 → 848

Iterations

Useful iterations: 2 (339.0ms)

Iter	Nodes	Cost
0	313	19888
1	903	18700
2	3238	18276
done	5000	18276

prune2.7s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.2b

regimes270.0ms

Accuracy

-2.3% (7.6b remaining)

Error of 11.6b against oracle of 4.0b and baseline of 11.4b

bsearch89.0ms

Steps

Iters	Range		Point
6	3.7632251814877455e-125	1.6714441882618097e-124	3.803402293530504e-125
10	-1.6489987475949222e-61	-2.525196617024818e-75	-4.009879037502059e-70

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	47
1	32	47
done	32	47

end0.0ms

sample698.0ms

Algorithm

intervals

Results

269.0ms	7839×	body	80	valid
56.0ms	458×	body	640	valid
43.0ms	279×	body	1280	valid
42.0ms	425×	body	320	valid
15.0ms	249×	body	160	valid
3.0ms	14×	body	2560	valid