Details

sample31.0ms

Algorithm

intervals

Results

10.0ms	236×	body	80	valid
2.0ms	14×	body	640	valid
2.0ms	19×	body	320	valid
2.0ms	8×	body	1280	valid
1.0ms	14×	body	160	valid

simplify16.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 28.8b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
4.0b	(+ x (/ (* (- y x) (- z t)) (- a t)))
21.1b	(/ (* (- y x) (- z t)) (- a t))

rewrite135.0ms

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:

54.0ms	(* (- y x) (- z t))
23.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
52.0ms	(/ (* (- y x) (- z t)) (- a t))

series419.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* (- y x) (- z t))
217.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
153.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify1.3s

Counts

90 → 90

Iterations

Useful iterations: 2 (281.0ms)

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

prune298.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
2.6b	(/ (- y x) (/ (- a t) (- z t)))
4.0b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite252.0ms

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:

44.0ms	(/ (- a t) (- z t))
51.0ms	(/ (- y x) (/ (- a t) (- z t)))
136.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series614.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- a t) (- z t))
287.0ms	(/ (- y x) (/ (- a t) (- z t)))
247.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify1.5s

Counts

283 → 283

Iterations

Useful iterations: 2 (537.0ms)

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

prune755.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.4b	(* (- y x) (/ (- z t) (- a t)))
4.0b	(+ x (* (- y x) (/ (- z t) (- a t))))

rewrite117.0ms

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:

25.0ms	(/ (- z t) (- a t))
69.0ms	(* (- y x) (/ (- z t) (- a t)))
9.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

series463.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- z t) (- a t))
169.0ms	(* (- y x) (/ (- z t) (- a t)))
242.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

simplify1.1s

Counts

128 → 128

Iterations

Useful iterations: 2 (245.0ms)

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

prune465.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.3b	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
2.6b	(/ (/ (- a t) (- z t)) (- y x))
6.5b	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

rewrite703.0ms

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:

48.0ms	(/ (- a t) (- z t))
114.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
57.0ms	(/ (/ (- a t) (- z t)) (- y x))
349.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

series984.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (- a t) (- z t))
477.0ms	(/ 1 (/ (/ (- a t) (- z t)) (- y x)))
207.0ms	(/ (/ (- a t) (- z t)) (- y x))
227.0ms	(+ x (/ 1 (/ (/ (- a t) (- z t)) (- y x))))

simplify2.6s

Counts

958 → 958

Iterations

Useful iterations: done (2.6s)

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

prune2.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.9b

regimes291.0ms

Accuracy

10.5% (6.5b remaining)

Error of 10.8b against oracle of 4.3b and baseline of 11.6b

bsearch116.0ms

Steps

Iters	Range		Point
8	3.3151492280354115e-115	1.2742963028413886e-110	3.5174369309382794e-112
8	-8.95343244323789e-237	-1.779920258003853e-239	-7.490233830340062e-237

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	69
1	39	69
done	39	69

end0.0ms

sample1.4s

Algorithm

intervals

Results

667.0ms	7767×	body	80	valid
135.0ms	493×	body	640	valid
94.0ms	363×	body	320	valid
76.0ms	281×	body	1280	valid
45.0ms	19×	body	2560	valid
32.0ms	273×	body	160	valid