Details

sample37.0ms

Algorithm

intervals

Results

10.0ms	258×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	7×	body	1280	valid
1.0ms	9×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	2×	body	2560	valid

simplify1.3s

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	250	13
5	525	13
6	1101	13
7	2055	13
8	3462	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: 24.7b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
2.2b	(+ x (/ (* (- y x) (- z t)) (- a t)))
20.0b	(/ (* (- y x) (- z t)) (- a t))

rewrite35.0ms

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:

10.0ms	(* (- y x) (- z t))
8.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
14.0ms	(/ (* (- y x) (- z t)) (- a t))

series112.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(* (- y x) (- z t))
59.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
43.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify537.0ms

Counts

90 → 90

Iterations

Useful iterations: 2 (139.0ms)

Iter	Nodes	Cost
0	162	1284
1	475	1213
2	1941	1111
done	5000	1111

prune140.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	8	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	9	91

Merged error: 3.7b

Counts

91 → 9

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
1.9b	(/ (- y x) (/ (- a t) (- z t)))
2.2b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite92.0ms

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:

9.0ms	(/ (- a t) (- z t))
19.0ms	(/ (- y x) (/ (- a t) (- z t)))
44.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series119.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(/ (- a t) (- z t))
48.0ms	(/ (- y x) (/ (- a t) (- z t)))
61.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify831.0ms

Counts

283 → 283

Iterations

Useful iterations: 2 (312.0ms)

Iter	Nodes	Cost
0	354	5984
1	1030	5625
2	3962	5487
done	5001	5487

prune246.0ms

Filtered

172 candidates to 283 candidates (-64.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	276	7	283
Fresh	3	4	7
Picked	0	1	1
Done	1	0	1
Total	280	12	292

Merged error: 3.6b

Counts

292 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y x))
0.5b	(cbrt (- y x))
0.5b	(cbrt (- y x))
7.1b	(+ x (* (/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt (- z t)) (cbrt (- z t))))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (cbrt (- z t))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

4.0ms	(cbrt (- y x))
4.0ms	(cbrt (- y x))
4.0ms	(cbrt (- y x))
3.0ms	(+ x (* (/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt (- z t)) (cbrt (- z t))))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (cbrt (- z t))))))

series149.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (- y x))
31.0ms	(cbrt (- y x))
29.0ms	(cbrt (- y x))
60.0ms	(+ x (* (/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt (- z t)) (cbrt (- z t))))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (cbrt (- z t))))))

simplify1.7s

Counts

68 → 68

Iterations

Useful iterations: 3 (355.0ms)

Iter	Nodes	Cost
0	114	1453
1	269	1383
2	808	836
3	4873	744
done	5000	744

prune125.0ms

Filtered

52 candidates to 68 candidates (-30.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	68	12	80

Merged error: 3.6b

Counts

80 → 12

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.2b	(+ x (* (- y x) (/ (- z t) (- a t))))
2.3b	(* (- y x) (/ (- z t) (- a t)))

rewrite38.0ms

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:

9.0ms	(/ (- z t) (- a t))
4.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
20.0ms	(* (- y x) (/ (- z t) (- a t)))

series110.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(/ (- z t) (- a t))
58.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
41.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify522.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (140.0ms)

Iter	Nodes	Cost
0	183	1813
1	479	1704
2	1777	1606
done	5001	1606

prune100.0ms

Filtered

86 candidates to 128 candidates (-48.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	8	9
Picked	1	0	1
Done	0	2	2
Total	129	11	140

Merged error: 3.6b

Counts

140 → 11

regimes522.0ms

Accuracy

14.9% (6.4b remaining)

Error of 10.7b against oracle of 4.3b and baseline of 11.8b

bsearch51.0ms

Steps

Iters	Range		Point
6	1.450863666055504e-119	9.656341012194637e-119	3.488515123987334e-119
8	-7.148784622653685e-243	-3.780952941264244e-247	-3.772481445593975e-243

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	23	47
1	30	35
done	30	35

end0.0ms

sample1.1s

Algorithm

intervals

Results

326.0ms	7795×	body	80	valid
86.0ms	512×	body	640	valid
50.0ms	401×	body	320	valid
50.0ms	266×	body	1280	valid
20.0ms	253×	body	160	valid
5.0ms	20×	body	2560	valid

Details

sample37.0ms

simplify1.3s

prune4.0ms

localize9.0ms

rewrite35.0ms

series112.0ms

simplify537.0ms

prune140.0ms

localize9.0ms

rewrite92.0ms

series119.0ms

simplify831.0ms

prune246.0ms

localize22.0ms

rewrite15.0ms

series149.0ms

simplify1.7s

prune125.0ms

localize10.0ms

rewrite38.0ms

series110.0ms

simplify522.0ms

prune100.0ms

regimes522.0ms

bsearch51.0ms

simplify2.0ms

end0.0ms

sample1.1s

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