Details

sample70.0ms

Algorithm

intervals

Results

31.0ms	246×	body	80	valid
5.0ms	12×	body	1280	valid
5.0ms	15×	body	640	valid
2.0ms	10×	body	320	valid
2.0ms	10×	body	160	valid

simplify15.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	111	13
4	288	13
5	633	13
6	1189	13
7	2048	13
8	2872	13
9	3396	13
10	3629	13
11	3899	13
12	4189	13
done	5001	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
2.2b	(+ x (/ (* (- y x) (- z t)) (- a t)))
18.0b	(/ (* (- y x) (- z t)) (- a t))

rewrite169.0ms

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:

55.0ms	(* (- y x) (- z t))
47.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
62.0ms	(/ (* (- y x) (- z t)) (- a t))

series492.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* (- y x) (- z t))
262.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
174.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify1.2s

Counts

90 → 90

Iterations

Useful iterations: 2 (369.0ms)

Iter	Nodes	Cost
0	162	1284
1	468	1213
2	1991	1111
done	5000	1111

prune327.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.6b	(* (- y x) (/ (- z t) (- a t)))
2.2b	(+ x (* (- y x) (/ (- z t) (- a t))))

rewrite156.0ms

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:

40.0ms	(/ (- z t) (- a t))
98.0ms	(* (- y x) (/ (- z t) (- a t)))
12.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

series405.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (- z t) (- a t))
131.0ms	(* (- y x) (/ (- z t) (- a t)))
219.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

simplify788.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (225.0ms)

Iter	Nodes	Cost
0	183	1813
1	472	1704
2	1748	1606
done	5001	1606

prune361.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
1.6b	(/ (- y x) (/ (- a t) (- z t)))
2.2b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite199.0ms

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:

25.0ms	(/ (- a t) (- z t))
37.0ms	(/ (- y x) (/ (- a t) (- z t)))
120.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series585.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (- a t) (- z t))
295.0ms	(/ (- y x) (/ (- a t) (- z t)))
218.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify1.9s

Counts

283 → 283

Iterations

Useful iterations: 2 (1.0s)

Iter	Nodes	Cost
0	354	5984
1	1010	5625
2	3649	5487
done	5001	5487

prune674.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 4.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.4b	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
1.6b	(/ (/ (- a t) (- z t)) (- y x))
3.1b	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

rewrite556.0ms

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` `frac-2neg` `1-exp` `div-sub` `clear-num` `associate-/l/`
2×	`distribute-lft-out`
1×	`+-commutative` `pow-flip` `flip3-+` `sum-log` `flip-+` `inv-pow`

Counts

4 → 946

Calls

4 calls:

46.0ms	(/ (- a t) (- z t))
92.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
53.0ms	(/ (/ (- a t) (- z t)) (- y x))
225.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

series915.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (- a t) (- z t))
397.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
184.0ms	(/ (/ (- a t) (- z t)) (- y x))
264.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

simplify2.0s

Counts

958 → 958

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	928	25047
1	2271	22294
done	5000	20384

prune1.8s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 4.0b

regimes471.0ms

Accuracy

13.8% (6.7b remaining)

Error of 10.9b against oracle of 4.1b and baseline of 11.9b

bsearch92.0ms

Steps

Iters	Range		Point
8	1.3793369693960326e-72	5.420309125457467e-70	1.4749780862081662e-72
3	-1.350252423850461e-228	-1.1088529455719019e-228	-1.2641226895694537e-228

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample1.4s

Algorithm

intervals

Results

610.0ms	7755×	body	80	valid
122.0ms	423×	body	320	valid
107.0ms	288×	body	1280	valid
100.0ms	477×	body	640	valid
29.0ms	272×	body	160	valid
4.0ms	13×	body	2560	valid