Details

sample44.0ms

Algorithm

intervals

Results

10.0ms	239×	body	80	valid
7.0ms	10×	body	1280	valid
3.0ms	18×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	7×	body	160	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	1105	13
7	2071	13
8	3497	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: 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))

rewrite43.0ms

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

series111.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(* (- y z) (- t x))
60.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
40.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify541.0ms

Counts

90 → 90

Iterations

Useful iterations: 2 (137.0ms)

Iter	Nodes	Cost
0	162	1284
1	473	1213
2	1935	1111
done	5000	1111

prune148.0ms

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

localize14.0ms

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)))))

rewrite60.0ms

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))
42.0ms	(* (/ (- 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)))))

series185.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (- a z))
32.0ms	(cbrt (- a z))
63.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
61.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify692.0ms

Counts

146 → 146

Iterations

Useful iterations: done (687.0ms)

Iter	Nodes	Cost
0	260	3378
1	753	3206
2	3029	2663
done	5000	2655

prune216.0ms

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

localize21.0ms

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))))))

rewrite97.0ms

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)))
72.0ms	(* (/ (/ (- 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))))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (cbrt (- a z)))
32.0ms	(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)))))
273.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify386.0ms

Counts

201 → 201

Iterations

Useful iterations: done (372.0ms)

Iter	Nodes	Cost
0	373	7254
1	1140	6923
done	5000	5759

prune257.0ms

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

localize22.0ms

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))))))

rewrite44.0ms

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:

10.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
10.0ms	(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))))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
69.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
72.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
63.0ms	(+ 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))))))

simplify1.2s

Counts

188 → 188

Iterations

Useful iterations: 3 (391.0ms)

Iter	Nodes	Cost
0	242	4477
1	498	4324
2	1127	3769
3	4205	3693
done	5000	3693

prune188.0ms

Filtered

129 candidates to 188 candidates (-45.7%)

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

regimes720.0ms

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

sample1.1s

Algorithm

intervals

Results

331.0ms	7840×	body	80	valid
69.0ms	462×	body	640	valid
55.0ms	293×	body	1280	valid
52.0ms	421×	body	320	valid
24.0ms	256×	body	160	valid
3.0ms	15×	body	2560	valid

Details

sample44.0ms

simplify1.3s

prune4.0ms

localize10.0ms

rewrite43.0ms

series111.0ms

simplify541.0ms

prune148.0ms

localize14.0ms

rewrite60.0ms

series185.0ms

simplify692.0ms

prune216.0ms

localize21.0ms

rewrite97.0ms

series400.0ms

simplify386.0ms

prune257.0ms

localize22.0ms

rewrite44.0ms

series277.0ms

simplify1.2s

prune188.0ms

regimes720.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample1.1s

Profiling