Details

sample36.0ms

Algorithm

intervals

Results

10.0ms	242×	body	80	valid
2.0ms	10×	body	1280	valid
1.0ms	9×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	9×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	51	13
3	102	13
4	200	13
5	411	13
6	726	13
7	1105	13
8	1511	13
9	2078	13
10	2934	13
11	4225	13
done	5000	13

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: 14.9b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

2.3b	(- (+ x y) (/ (* (- z t) y) (- a t)))
10.5b	(/ (* (- z t) y) (- a t))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

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

series60.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
19.0ms	(/ (* (- z t) y) (- a t))

simplify399.0ms

Counts

54 → 54

Iterations

Useful iterations: done (397.0ms)

Iter	Nodes	Cost
0	125	825
1	337	775
2	1214	715
done	5001	711

prune113.0ms

Filtered

39 candidates to 54 candidates (-38.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	46	8	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	8	55

Merged error: 3.4b

Counts

55 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
3.0b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.7b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity`
30×	`associate-r`
27×	`cbrt-prod`
25×	`add-exp-log`
23×	`add-cube-cbrt`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
9×	`add-log-exp`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `frac-times` `div-exp`
6×	`pow1` `frac-sub` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
5×	`associate-r/` `associate-l/`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 127

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
36.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
7.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(cbrt (- a t))
36.0ms	(cbrt (- a t))
26.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
42.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify721.0ms

Counts

139 → 139

Iterations

Useful iterations: done (716.0ms)

Iter	Nodes	Cost
0	279	3211
1	794	3049
2	3118	2480
done	5001	2472

prune230.0ms

Filtered

111 candidates to 139 candidates (-25.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	135	12	147

Merged error: 3.4b

Counts

147 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

4.8b	(cbrt (/ y (cbrt (- a t))))
4.8b	(cbrt (/ y (cbrt (- a t))))
4.8b	(cbrt (/ y (cbrt (- a t))))
7.9b	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (/ y (cbrt (- a t))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

135×	`cbrt-prod`
72×	`times-frac`
67×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`cbrt-div`
49×	`add-cube-cbrt`
34×	`frac-times`
30×	`frac-sub`
26×	`associate-*l/`
22×	`associate-*r/`
15×	`flip3-+` `flip-+`
9×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3` `div-inv`
2×	`diff-log`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 161

Calls

4 calls:

7.0ms	(cbrt (/ y (cbrt (- a t))))
7.0ms	(cbrt (/ y (cbrt (- a t))))
7.0ms	(cbrt (/ y (cbrt (- a t))))
14.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (/ y (cbrt (- a t))))))

series237.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(cbrt (/ y (cbrt (- a t))))
63.0ms	(cbrt (/ y (cbrt (- a t))))
60.0ms	(cbrt (/ y (cbrt (- a t))))
55.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (/ y (cbrt (- a t)))) (cbrt (/ y (cbrt (- a t)))))) (cbrt (/ y (cbrt (- a t))))))

simplify672.0ms

Counts

173 → 173

Iterations

Useful iterations: done (664.0ms)

Iter	Nodes	Cost
0	351	5440
1	831	5255
2	2462	4604
done	5001	4601

prune241.0ms

Filtered

125 candidates to 173 candidates (-38.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	173	12	185

Merged error: 3.4b

Counts

185 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))
1.4b	(* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))
1.4b	(* (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))) (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t)))))
7.1b	(- (+ x y) (* (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))) (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

101×	`cbrt-div`
60×	`frac-times`
58×	`cbrt-prod` `add-sqr-sqrt`
43×	`times-frac`
38×	`associate-r/` `associate-l/`
34×	`*-un-lft-identity`
31×	`associate-r`
30×	`add-exp-log` `frac-sub`
24×	`add-cube-cbrt`
21×	`associate-l`
18×	`pow1` `associate-/r/`
15×	`flip3-+` `prod-exp` `add-cbrt-cube` `cbrt-unprod` `flip-+`
14×	`flip3--` `flip--`
9×	`pow-prod-down` `add-log-exp` `unswap-sqr`
5×	`distribute-lft-out--` `difference-of-squares`
3×	`cbrt-undiv` `div-exp` `div-inv`
2×	`diff-log` `*-commutative`
1×	`sub-neg` `pow1/3` `associate--l+` `sum-log`

Counts

4 → 186

Calls

4 calls:

18.0ms	(cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))
26.0ms	(* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))
36.0ms	(* (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))) (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t)))))
11.0ms	(- (+ x y) (* (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))) (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))
375.0ms	(* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))
32.0ms	(* (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))) (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t)))))
42.0ms	(- (+ x y) (* (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))) (* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))))

simplify972.0ms

Counts

198 → 198

Iterations

Useful iterations: done (963.0ms)

Iter	Nodes	Cost
0	466	9276
1	1201	8875
2	3795	7065
done	5000	7064

prune236.0ms

Filtered

139 candidates to 198 candidates (-42.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	195	3	198
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	199	11	210

Merged error: 3.4b

Counts

210 → 11

regimes559.0ms

Accuracy

33.5% (5.2b remaining)

Error of 9.3b against oracle of 4.1b and baseline of 12.0b

bsearch58.0ms

Steps

Iters	Range		Point
8	4.2385532176474676e-160	9.254042445292205e-157	1.0472146471931212e-158
8	-3.50312019056091e-128	-1.947745001128173e-131	-1.4183402044220067e-130

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	69
1	35	69
done	35	69

end0.0ms

sample1.0s

Algorithm

intervals

Results

328.0ms	7315×	body	80	valid
72.0ms	471×	body	640	valid
56.0ms	266×	body	1280	valid
48.0ms	413×	body	320	valid
20.0ms	252×	body	160	valid
3.0ms	13×	body	2560	valid

Details

sample36.0ms

simplify1.4s

prune4.0ms

localize10.0ms

rewrite29.0ms

series60.0ms

simplify399.0ms

prune113.0ms

localize14.0ms

rewrite56.0ms

series137.0ms

simplify721.0ms

prune230.0ms

localize19.0ms

rewrite45.0ms

series237.0ms

simplify672.0ms

prune241.0ms

localize22.0ms

rewrite102.0ms

series566.0ms

simplify972.0ms

prune236.0ms

regimes559.0ms

bsearch58.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling