Details

sample33.0ms

Algorithm

intervals

Results

10.0ms	247×	body	80	valid
4.0ms	25×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	7×	body	1280	valid
1.0ms	10×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	1598
5	656
4	266
3	103
2	43
1	20
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
3.3b	(+ x (/ (* (- y x) (- z t)) (- a t)))
18.3b	(/ (* (- y x) (- z t)) (- a t))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

28.0ms	(* (- y x) (- z t))
23.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
46.0ms	(/ (* (- y x) (- z t)) (- a t))

series463.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* (- y x) (- z t))
252.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
163.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify1.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1904
1	480
0	162

prune629.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.8b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
2.3b	(/ (- y x) (/ (- a t) (- z t)))
3.3b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite203.0ms

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-cbrt-cube` `add-exp-log` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+r-` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

17.0ms	(/ (- a t) (- z t))
52.0ms	(/ (- y x) (/ (- a t) (- z t)))
103.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series617.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (- a t) (- z t))
281.0ms	(/ (- y x) (/ (- a t) (- z t)))
263.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify2.5s

Counts

283 → 283

Iterations

Iter	Nodes
done	5000
2	3727
1	1146
0	354

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.3b	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
2.3b	(/ (/ (- a t) (- z t)) (- y x))
5.0b	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

rewrite574.0ms

Algorithm

rewrite-expression-head

Rules

1933×	`times-frac`
1483×	`*-un-lft-identity`
1480×	`add-sqr-sqrt`
624×	`add-cube-cbrt`
428×	`distribute-lft-out--` `difference-of-squares`
171×	`associate-/r*`
65×	`associate-/r/`
39×	`associate-/l*`
34×	`div-inv`
33×	`flip3--` `flip--`
32×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`div-exp`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `div-sub` `associate-/l/`
2×	`distribute-lft-out`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 946

Calls

4 calls:

22.0ms	(/ (- a t) (- z t))
79.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
53.0ms	(/ (/ (- a t) (- z t)) (- y x))
255.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

series921.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (- a t) (- z t))
380.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
242.0ms	(/ (/ (- a t) (- z t)) (- y x))
238.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

simplify3.3s

Counts

958 → 958

Iterations

Iter	Nodes
done	5002
1	2770
0	928

prune3.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 6.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y x))
0.6b	(cbrt (- y x))
0.6b	(cbrt (- y x))
9.7b	(+ x (/ (/ 1 (* (/ (cbrt (- a t)) (* (cbrt (- y x)) (cbrt (- z t)))) (/ (cbrt (- a t)) (* (cbrt (- y x)) (cbrt (- z t)))))) (/ (/ (cbrt (- a t)) (cbrt (- z t))) (cbrt (- y x)))))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod` `*-un-lft-identity`
13×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 57

Calls

4 calls:

4.0ms	(cbrt (- y x))
5.0ms	(cbrt (- y x))
5.0ms	(cbrt (- y x))
1.8s	(+ x (/ (/ 1 (* (/ (cbrt (- a t)) (* (cbrt (- y x)) (cbrt (- z t)))) (/ (cbrt (- a t)) (* (cbrt (- y x)) (cbrt (- z t)))))) (/ (/ (cbrt (- a t)) (cbrt (- z t))) (cbrt (- y x)))))

series776.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt (- y x))
167.0ms	(cbrt (- y x))
199.0ms	(cbrt (- y x))
229.0ms	(+ x (/ (/ 1 (* (/ (cbrt (- a t)) (* (cbrt (- y x)) (cbrt (- z t)))) (/ (cbrt (- a t)) (* (cbrt (- y x)) (cbrt (- z t)))))) (/ (/ (cbrt (- a t)) (cbrt (- z t))) (cbrt (- y x)))))

simplify3.1s

Counts

69 → 69

Iterations

Iter	Nodes
done	5037
3	3159
2	725
1	254
0	109

prune462.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 6.2b

regimes769.0ms

Accuracy

19.2% (6.3b remaining)

Error of 10.3b against oracle of 4.0b and baseline of 11.8b

bsearch176.0ms

Steps

Iters	Range		Point
10	5.2644298199866365e-157	2.7232975322406408e-140	2.4865790973510872e-154
8	-2.539644303582551e-91	-1.7804719413044463e-94	-1.9039405874823513e-94

simplify11.0ms

Iterations

Iter	Nodes
done	53
1	53
0	42

end0.0ms

sample1.6s

Algorithm

intervals

Results

604.0ms	7837×	body	80	valid
393.0ms	404×	body	320	valid
129.0ms	504×	body	640	valid
72.0ms	266×	body	1280	valid
25.0ms	242×	body	160	valid
3.0ms	11×	body	2560	valid