Details

sample43.0ms

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

simplify1.8s

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	400	13
6	688	13
7	910	13
8	1120	13
9	1483	13
10	2214	13
11	4319	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

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

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:

10.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
21.0ms	(/ (* (- z t) y) (- a t))

series56.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
17.0ms	(/ (* (- z t) y) (- a t))

simplify417.0ms

Counts

54 → 54

Iterations

Useful iterations: done (415.0ms)

Iter	Nodes	Cost
0	125	825
1	337	778
2	1261	717
done	5000	711

prune102.0ms

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

localize21.0ms

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)))))

rewrite49.0ms

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))
30.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series136.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(cbrt (- a t))
28.0ms	(cbrt (- a t))
25.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
47.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify1.0s

Counts

139 → 139

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	279	3211
1	794	3053
2	3152	2532
done	5000	2472

prune224.0ms

Filtered

110 candidates to 139 candidates (-26.4%)

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

localize18.0ms

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))))))

rewrite40.0ms

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))))
11.0ms	(- (+ 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))))))

series220.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(cbrt (/ y (cbrt (- a t))))
59.0ms	(cbrt (/ y (cbrt (- a t))))
53.0ms	(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))))))

simplify684.0ms

Counts

173 → 173

Iterations

Useful iterations: done (659.0ms)

Iter	Nodes	Cost
0	351	5440
1	831	5256
2	2493	4604
done	5000	4601

prune227.0ms

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

localize19.0ms

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))))))

rewrite101.0ms

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:

14.0ms	(cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))
26.0ms	(* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))
41.0ms	(* (* (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)))))
10.0ms	(- (+ 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))))))

series530.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))))
346.0ms	(* (cbrt (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (- a t))))
26.0ms	(* (* (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)))))
50.0ms	(- (+ 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))))))

simplify967.0ms

Counts

198 → 198

Iterations

Useful iterations: done (958.0ms)

Iter	Nodes	Cost
0	466	9276
1	1201	8934
2	3923	7124
done	5001	7064

prune231.0ms

Filtered

142 candidates to 198 candidates (-39.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	194	4	198
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	199	11	210

Merged error: 3.4b

Counts

210 → 11

regimes533.0ms

Accuracy

33.5% (5.2b remaining)

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

bsearch59.0ms

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

312.0ms	7315×	body	80	valid
78.0ms	471×	body	640	valid
57.0ms	266×	body	1280	valid
46.0ms	413×	body	320	valid
19.0ms	252×	body	160	valid
3.0ms	13×	body	2560	valid

Details

sample43.0ms

simplify1.8s

prune4.0ms

localize9.0ms

rewrite32.0ms

series56.0ms

simplify417.0ms

prune102.0ms

localize21.0ms

rewrite49.0ms

series136.0ms

simplify1.0s

prune224.0ms

localize18.0ms

rewrite40.0ms

series220.0ms

simplify684.0ms

prune227.0ms

localize19.0ms

rewrite101.0ms

series530.0ms

simplify967.0ms

prune231.0ms

regimes533.0ms

bsearch59.0ms

simplify3.0ms

end0.0ms

sample1.0s

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