Details

sample42.0ms

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

simplify9.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	43	13
3	115	13
4	263	13
5	568	13
6	1005	13
7	1711	13
8	3060	13
9	3801	13
10	4007	13
11	4459	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: 15.8b

Counts

2 → 1

localize15.0ms

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)))

rewrite25.0ms

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

series95.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
38.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify944.0ms

Counts

73 → 73

Iterations

Useful iterations: done (941.0ms)

Iter	Nodes	Cost
0	147	1105
1	375	1023
2	1459	953
done	5000	949

prune142.0ms

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: 3.8b

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)))))

rewrite40.0ms

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))
26.0ms	(* (- 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)))))

series246.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (- t x))
31.0ms	(cbrt (- t x))
129.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
58.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify813.0ms

Counts

97 → 97

Iterations

Useful iterations: done (805.0ms)

Iter	Nodes	Cost
0	257	2532
1	681	2410
2	2434	1766
done	5001	1765

prune180.0ms

Filtered

77 candidates to 97 candidates (-26.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	96	14	110

Merged error: 3.1b

Counts

110 → 14

localize13.0ms

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)))))

rewrite68.0ms

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:

4.0ms	(cbrt (- y z))
20.0ms	(* (cbrt (- y z)) (/ (- t x) (- a z)))
29.0ms	(* (* (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)))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (- y z))
149.0ms	(* (cbrt (- y z)) (/ (- t x) (- a z)))
38.0ms	(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
60.0ms	(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

simplify1.0s

Counts

178 → 178

Iterations

Useful iterations: 2 (464.0ms)

Iter	Nodes	Cost
0	317	4813
1	851	4569
2	2586	3966
done	5001	3966

prune222.0ms

Filtered

109 candidates to 178 candidates (-63.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	2	10	12
Picked	0	1	1
Done	0	1	1
Total	178	14	192

Merged error: 3.1b

Counts

192 → 14

localize12.0ms

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))))

rewrite49.0ms

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:

3.0ms	(cbrt (- y z))
6.0ms	(pow (cbrt (- y z)) 3)
27.0ms	(* (pow (cbrt (- y z)) 3) (/ (- t x) (- a z)))
3.0ms	(+ x (* (pow (cbrt (- y z)) 3) (/ (- t x) (- a z))))

series160.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (- y z))
37.0ms	(pow (cbrt (- y z)) 3)
41.0ms	(* (pow (cbrt (- y z)) 3) (/ (- t x) (- a z)))
54.0ms	(+ x (* (pow (cbrt (- y z)) 3) (/ (- t x) (- a z))))

simplify1.3s

Counts

160 → 160

Iterations

Useful iterations: 2 (378.0ms)

Iter	Nodes	Cost
0	251	2634
1	667	2040
2	2752	1930
done	5000	1930

prune130.0ms

Filtered

91 candidates to 160 candidates (-75.8%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	1	10	11
Picked	0	1	1
Done	0	2	2
Total	160	14	174

Merged error: 3.1b

Counts

174 → 14

regimes827.0ms

Accuracy

40.6% (6.9b remaining)

Error of 10.4b against oracle of 3.5b and baseline of 15.1b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	22	69
1	29	57
done	29	57

end0.0ms

sample1.1s

Algorithm

intervals

Results

314.0ms	7839×	body	80	valid
79.0ms	462×	body	640	valid
54.0ms	420×	body	320	valid
54.0ms	293×	body	1280	valid
20.0ms	258×	body	160	valid
3.0ms	15×	body	2560	valid

Details

sample42.0ms

simplify9.1s

prune4.0ms

localize15.0ms

rewrite25.0ms

series95.0ms

simplify944.0ms

prune142.0ms

localize18.0ms

rewrite40.0ms

series246.0ms

simplify813.0ms

prune180.0ms

localize13.0ms

rewrite68.0ms

series276.0ms

simplify1.0s

prune222.0ms

localize12.0ms

rewrite49.0ms

series160.0ms

simplify1.3s

prune130.0ms

regimes827.0ms

bsearch2.0ms

simplify3.0ms

end0.0ms

sample1.1s

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