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

simplify7.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	109	13
4	244	13
5	485	13
6	944	13
7	1551	13
8	2732	13
9	3945	13
10	4555	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: 27.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.7b	(+ x (/ (* (- y z) (- t x)) (- a z)))
20.2b	(/ (* (- y z) (- t x)) (- a z))

rewrite39.0ms

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 z) (- t x))
8.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
18.0ms	(/ (* (- y z) (- t x)) (- a z))

series106.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(* (- y z) (- t x))
58.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
38.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify964.0ms

Counts

90 → 90

Iterations

Useful iterations: 2 (205.0ms)

Iter	Nodes	Cost
0	162	1284
1	467	1213
2	1880	1111
done	5000	1111

prune147.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	81	9	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Merged error: 4.1b

Counts

91 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
2.2b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.0b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
43.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
4.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (- a z))
31.0ms	(cbrt (- a z))
60.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
59.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify1.0s

Counts

146 → 146

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	260	3378
1	750	3186
2	2885	2663
done	5000	2655

prune212.0ms

Filtered

108 candidates to 146 candidates (-35.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	143	12	155

Merged error: 4.1b

Counts

155 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (- a z)))
0.6b	(cbrt (cbrt (- a z)))
2.2b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
9.7b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
100×	`cbrt-prod`
98×	`times-frac`
76×	`*-un-lft-identity`
69×	`add-exp-log`
61×	`associate-r`
48×	`cbrt-div`
42×	`add-cbrt-cube`
38×	`add-cube-cbrt`
29×	`associate-l`
27×	`cbrt-undiv` `div-exp`
24×	`prod-exp` `cbrt-unprod`
19×	`distribute-lft-out--` `difference-of-squares`
18×	`associate-/r/`
15×	`flip3--` `flip--`
12×	`unswap-sqr`
9×	`frac-times`
6×	`pow1` `add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`div-inv`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 189

Calls

4 calls:

4.0ms	(cbrt (cbrt (- a z)))
4.0ms	(cbrt (cbrt (- a z)))
70.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
4.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series180.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (cbrt (- a z)))
28.0ms	(cbrt (cbrt (- a z)))
64.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
59.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify1.5s

Counts

201 → 201

Iterations

Useful iterations: 2 (747.0ms)

Iter	Nodes	Cost
0	373	7254
1	1134	6879
2	4644	5759
done	5000	5759

prune253.0ms

Filtered

143 candidates to 201 candidates (-40.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	202	11	213

Merged error: 4.1b

Counts

213 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

1.8b	(cbrt (/ (- t x) (cbrt (- a z))))
1.8b	(cbrt (/ (- t x) (cbrt (- a z))))
1.8b	(cbrt (/ (- t x) (cbrt (- a z))))
9.2b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

213×	`cbrt-prod`
139×	`add-sqr-sqrt` `*-un-lft-identity`
120×	`times-frac`
61×	`add-cube-cbrt`
39×	`distribute-lft-out--` `difference-of-squares`
9×	`cbrt-div`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 176

Calls

4 calls:

9.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
9.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
10.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
4.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
69.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
69.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
56.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

simplify1.5s

Counts

188 → 188

Iterations

Useful iterations: 3 (591.0ms)

Iter	Nodes	Cost
0	242	4477
1	497	4288
2	1084	3805
3	3959	3729
done	5001	3729

prune192.0ms

Filtered

132 candidates to 188 candidates (-42.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	187	12	199

Merged error: 3.1b

Counts

199 → 12

regimes696.0ms

Accuracy

37.5% (5.9b remaining)

Error of 9.4b against oracle of 3.5b and baseline of 12.9b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	131
1	54	131
done	54	131

end0.0ms

sample1.3s

Algorithm

intervals

Results

328.0ms	7840×	body	80	valid
71.0ms	462×	body	640	valid
56.0ms	293×	body	1280	valid
49.0ms	421×	body	320	valid
20.0ms	256×	body	160	valid
4.0ms	15×	body	2560	valid

Details

sample42.0ms

simplify7.9s

prune4.0ms

localize10.0ms

rewrite39.0ms

series106.0ms

simplify964.0ms

prune147.0ms

localize13.0ms

rewrite61.0ms

series179.0ms

simplify1.0s

prune212.0ms

localize18.0ms

rewrite95.0ms

series180.0ms

simplify1.5s

prune253.0ms

localize18.0ms

rewrite47.0ms

series261.0ms

simplify1.5s

prune192.0ms

regimes696.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample1.3s

Profiling