Details

sample34.0ms

Algorithm

intervals

Results

11.0ms

281×

body

valid

simplify528.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	11
1	20	11
2	33	11
3	53	11
4	85	11
5	115	11
6	143	11
7	161	11
8	186	11
9	220	11
10	286	11
11	375	11
12	421	11
13	499	11
14	521	11
done	521	11

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.8b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* y (/ (- z t) (- a t))))
0.0b	(/ (- z t) (- a t))
2.5b	(* y (/ (- z t) (- a t)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `associate-l` `flip--`
2×	`cbrt-undiv` `div-exp` `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 → 113

Calls

3 calls:

3.0ms	(+ x (* y (/ (- z t) (- a t))))
9.0ms	(/ (- z t) (- a t))
18.0ms	(* y (/ (- z t) (- a t)))

series56.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ x (* y (/ (- z t) (- a t))))
10.0ms	(/ (- z t) (- a t))
17.0ms	(* y (/ (- z t) (- a t)))

simplify1.6s

Counts

122 → 122

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	162	1555
1	422	1454
2	1123	1368
3	3610	1368
done	5000	1366

prune140.0ms

Filtered

85 candidates to 122 candidates (-43.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	6	123

Merged error: 0b

Counts

123 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (* (- z t) (/ 1 (- a t)))))
0.0b	(/ 1 (- a t))
0.2b	(* (- z t) (/ 1 (- a t)))
2.5b	(* y (* (- z t) (/ 1 (- a t))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
8×	`associate-r/` `associate-l*` `distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`flip3--` `div-exp` `flip--` `add-log-exp`
5×	`associate-/r*`
4×	`frac-times` `pow-prod-down` `associate-*l/` `associate-/r/`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`un-div-inv` `*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 130

Calls

4 calls:

4.0ms	(+ x (* y (* (- z t) (/ 1 (- a t)))))
6.0ms	(/ 1 (- a t))
17.0ms	(* (- z t) (/ 1 (- a t)))
13.0ms	(* y (* (- z t) (/ 1 (- a t))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ x (* y (* (- z t) (/ 1 (- a t)))))
5.0ms	(/ 1 (- a t))
10.0ms	(* (- z t) (/ 1 (- a t)))
18.0ms	(* y (* (- z t) (/ 1 (- a t))))

simplify960.0ms

Counts

142 → 142

Iterations

Useful iterations: 2 (164.0ms)

Iter	Nodes	Cost
0	182	1728
1	454	1392
2	1345	1228
done	5001	1228

prune124.0ms

Filtered

85 candidates to 142 candidates (-67.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	142	6	148

Merged error: 0b

Counts

148 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t))))
3.7b	(cbrt (/ (- z t) (- a t)))
3.7b	(cbrt (/ (- z t) (- a t)))
3.7b	(cbrt (/ (- z t) (- a t)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

333×	`*-un-lft-identity`
277×	`cbrt-prod`
273×	`add-sqr-sqrt`
229×	`times-frac`
106×	`distribute-lft-out--`
93×	`add-cube-cbrt`
78×	`difference-of-squares`
58×	`swap-sqr`
34×	`associate-r` `associate-l`
14×	`associate-/r/`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `flip3--` `flip--` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 276

Calls

4 calls:

37.0ms	(* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t))))
8.0ms	(cbrt (/ (- z t) (- a t)))
8.0ms	(cbrt (/ (- z t) (- a t)))
8.0ms	(cbrt (/ (- z t) (- a t)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t))))
66.0ms	(cbrt (/ (- z t) (- a t)))
67.0ms	(cbrt (/ (- z t) (- a t)))
63.0ms	(cbrt (/ (- z t) (- a t)))

simplify2.2s

Counts

288 → 288

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	296	6474
1	549	6067
2	1437	5934
3	3890	5619
done	5000	5617

prune252.0ms

Filtered

176 candidates to 288 candidates (-63.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	288	6	294

Merged error: 0b

Counts

294 → 6

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (pow (* (- z t) (/ y (- a t))) 1))
0.0b	(/ y (- a t))
10.0b	(* (- z t) (/ y (- a t)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 95

Calls

3 calls:

4.0ms	(+ x (pow (* (- z t) (/ y (- a t))) 1))
6.0ms	(/ y (- a t))
14.0ms	(* (- z t) (/ y (- a t)))

series54.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ x (pow (* (- z t) (/ y (- a t))) 1))
7.0ms	(/ y (- a t))
17.0ms	(* (- z t) (/ y (- a t)))

simplify898.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (187.0ms)

Iter	Nodes	Cost
0	157	1262
1	370	1141
2	1336	1063
done	5002	1063

prune108.0ms

Filtered

77 candidates to 104 candidates (-35.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	104	6	110

Merged error: 0b

Counts

110 → 6

regimes460.0ms

Accuracy

43.9% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 1.5b

bsearch18.0ms

Steps

Iters	Range		Point
2	5.691295351696058e-12	6.447125064489246e-12	6.1636889221918e-12
5	-2.0905344850362395e-22	-6.092576105087712e-23	-2.060365571784887e-22

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	45
1	34	43
done	34	43

end0.0ms

sample1.0s

Algorithm

intervals

Results

335.0ms	8728×	body	80	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	320	valid

Details

sample34.0ms

simplify528.0ms

prune4.0ms

localize8.0ms

rewrite35.0ms

series56.0ms

simplify1.6s

prune140.0ms

localize10.0ms

rewrite45.0ms

series62.0ms

simplify960.0ms

prune124.0ms

localize14.0ms

rewrite87.0ms

series283.0ms

simplify2.2s

prune252.0ms

localize13.0ms

rewrite27.0ms

series54.0ms

simplify898.0ms

prune108.0ms

regimes460.0ms

bsearch18.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling