Details

sample38.0ms

Algorithm

intervals

Results

10.0ms	239×	body	80	valid
3.0ms	18×	body	640	valid
2.0ms	17×	body	320	valid
2.0ms	10×	body	1280	valid
1.0ms	7×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	43	13
3	116	13
4	268	13
5	597	13
6	1102	13
7	2202	13
8	3897	13
done	5001	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: 15.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

3.1b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.5b	(* (- y z) (/ (- t x) (- a z)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
31×	`associate-r`
26×	`times-frac`
14×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`pow1` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 67

Calls

2 calls:

4.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
26.0ms	(* (- y z) (/ (- t x) (- a z)))

series100.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
41.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify474.0ms

Counts

73 → 73

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	147	1105
1	377	1023
2	1502	953
done	5001	953

prune148.0ms

Filtered

51 candidates to 73 candidates (-43.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	61	12	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	13	74

Merged error: 4.1b

Counts

74 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
1.5b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
10.4b	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`*-un-lft-identity` `add-cbrt-cube`
13×	`associate-r`
10×	`cbrt-prod` `flip3--` `flip--`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-/r/`
6×	`pow1` `frac-times` `add-log-exp`
5×	`associate-l`
4×	`cbrt-undiv` `div-exp` `associate-*l/`
3×	`associate-*r/` `distribute-lft-out--` `difference-of-squares`
2×	`times-frac` `pow1/3` `unswap-sqr`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 85

Calls

4 calls:

4.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
27.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
4.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (- t x))
32.0ms	(cbrt (- t x))
135.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
61.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify646.0ms

Counts

97 → 97

Iterations

Useful iterations: done (643.0ms)

Iter	Nodes	Cost
0	257	2532
1	685	2410
2	2503	1766
done	5000	1765

prune182.0ms

Filtered

76 candidates to 97 candidates (-27.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	95	15	110

Merged error: 4.1b

Counts

110 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
3.3b	(* (cbrt (- y z)) (/ (- t x) (- a z)))
3.4b	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
9.2b	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

114×	`cbrt-div`
84×	`frac-times`
58×	`flip3--` `flip--`
52×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`associate-*l/`
32×	`associate-r`
30×	`add-exp-log`
27×	`times-frac` `associate-*r/`
18×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
15×	`prod-exp` `cbrt-unprod`
12×	`cbrt-prod` `distribute-lft-out--` `difference-of-squares`
9×	`associate-l` `pow-prod-down`
6×	`add-log-exp`
4×	`unswap-sqr`
3×	`cbrt-undiv` `div-exp`
2×	`associate-/r/` `*-commutative`
1×	`+-commutative` `flip3-+` `pow1/3` `sum-log` `flip-+` `div-inv`

Counts

4 → 166

Calls

4 calls:

7.0ms	(cbrt (- y z))
21.0ms	(* (cbrt (- y z)) (/ (- t x) (- a z)))
27.0ms	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
4.0ms	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (- y z))
154.0ms	(* (cbrt (- y z)) (/ (- t x) (- a z)))
44.0ms	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
57.0ms	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

simplify723.0ms

Counts

178 → 178

Iterations

Useful iterations: 2 (251.0ms)

Iter	Nodes	Cost
0	317	4813
1	859	4569
2	2677	3966
done	5000	3966

prune438.0ms

Filtered

109 candidates to 178 candidates (-63.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	175	3	178
Fresh	4	8	12
Picked	0	1	1
Done	1	1	2
Total	180	13	193

Merged error: 4.1b

Counts

193 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
0.8b	(pow (cbrt (- y z)) 3)
6.5b	(* (pow (cbrt (- y z)) 3) (/ (- t x) (- a z)))
9.5b	(+ x (* (pow (cbrt (- y z)) 3) (/ (- t x) (- a z))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
31×	`times-frac` `associate-r`
29×	`cbrt-prod`
26×	`add-cube-cbrt`
22×	`associate-l`
20×	`unpow-prod-down` `cube-prod`
18×	`add-exp-log`
15×	`distribute-lft-out--` `difference-of-squares`
12×	`unswap-sqr`
9×	`add-cbrt-cube`
8×	`cbrt-div`
6×	`cube-div` `prod-exp` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`sqr-pow`
3×	`pow-to-exp` `pow-unpow` `div-exp` `pow-exp`
2×	`cube-mult` `frac-times` `pow-pow` `pow1/3` `unpow3` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `sum-log` `-commutative` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 148

Calls

4 calls:

4.0ms	(cbrt (- y z))
6.0ms	(pow (cbrt (- y z)) 3)
27.0ms	(* (pow (cbrt (- y z)) 3) (/ (- t x) (- a z)))
4.0ms	(+ x (* (pow (cbrt (- y z)) 3) (/ (- t x) (- a z))))

series176.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (- y z))
41.0ms	(pow (cbrt (- y z)) 3)
40.0ms	(* (pow (cbrt (- y z)) 3) (/ (- t x) (- a z)))
66.0ms	(+ x (* (pow (cbrt (- y z)) 3) (/ (- t x) (- a z))))

simplify810.0ms

Counts

160 → 160

Iterations

Useful iterations: 2 (208.0ms)

Iter	Nodes	Cost
0	251	2634
1	677	2040
2	2909	1930
done	5000	1930

prune136.0ms

Filtered

93 candidates to 160 candidates (-72.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	1	9	10
Picked	1	0	1
Done	0	2	2
Total	161	12	173

Merged error: 4.1b

Counts

173 → 12

regimes777.0ms

Accuracy

38.8% (6.6b remaining)

Error of 10.9b against oracle of 4.3b and baseline of 15.1b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	23	71
1	31	59
done	31	59

end0.0ms

sample1.1s

Algorithm

intervals

Results

340.0ms	7839×	body	80	valid
74.0ms	462×	body	640	valid
55.0ms	293×	body	1280	valid
48.0ms	420×	body	320	valid
20.0ms	258×	body	160	valid
4.0ms	15×	body	2560	valid

Details

sample38.0ms

simplify1.5s

prune4.0ms

localize9.0ms

rewrite34.0ms

series100.0ms

simplify474.0ms

prune148.0ms

localize18.0ms

rewrite41.0ms

series257.0ms

simplify646.0ms

prune182.0ms

localize14.0ms

rewrite70.0ms

series285.0ms

simplify723.0ms

prune438.0ms

localize13.0ms

rewrite48.0ms

series176.0ms

simplify810.0ms

prune136.0ms

regimes777.0ms

bsearch2.0ms

simplify3.0ms

end0.0ms

sample1.1s

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