Details

sample65.0ms

Algorithm

intervals

Results

20.0ms	244×	body	80	valid
5.0ms	18×	body	640	valid
4.0ms	11×	body	1280	valid
3.0ms	11×	body	160	valid
2.0ms	9×	body	320	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	111	13
4	292	13
5	863	13
6	3383	13
done	5001	13

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
3.3b	(+ x (/ (* (- y z) (- t x)) (- a z)))
20.3b	(/ (* (- y z) (- t x)) (- a z))

rewrite167.0ms

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:

73.0ms	(* (- y z) (- t x))
38.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
51.0ms	(/ (* (- y z) (- t x)) (- a z))

series640.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(* (- y z) (- t x))
298.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
270.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify1.8s

Counts

90 → 90

Iterations

Useful iterations: 2 (461.0ms)

Iter	Nodes	Cost
0	162	1284
1	478	1213
2	2592	1111
done	5000	1111

prune755.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.7b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.7b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite279.0ms

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:

7.0ms	(cbrt (- a z))
7.0ms	(cbrt (- a z))
237.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
13.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

256.0ms	(cbrt (- a z))
256.0ms	(cbrt (- a z))
533.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
313.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify2.8s

Counts

146 → 146

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	255	3364
1	755	3180
2	3441	2663
done	5000	2502

prune1.3s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 4.5b

localize75.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
9.4b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite48.0ms

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:

7.0ms	(cbrt (- t x))
7.0ms	(cbrt (- t x))
7.0ms	(cbrt (- t x))
24.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

280.0ms	(cbrt (- t x))
273.0ms	(cbrt (- t x))
282.0ms	(cbrt (- t x))
322.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify995.0ms

Counts

68 → 68

Iterations

Useful iterations: done (992.0ms)

Iter	Nodes	Cost
0	109	1468
1	264	1408
2	897	988
done	5000	891

prune916.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 3.8b

localize80.0ms

Local error

Found 4 expressions with local error:

1.7b	(cbrt (/ (- t x) (cbrt (- a z))))
1.7b	(cbrt (/ (- t x) (cbrt (- a z))))
1.7b	(cbrt (/ (- t x) (cbrt (- a z))))
9.1b	(+ 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))))))

rewrite121.0ms

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:

24.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
35.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
22.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
16.0ms	(+ 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))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

469.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
431.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
481.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
338.0ms	(+ 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))))))

simplify1.0s

Counts

188 → 188

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	232	4432
1	478	4228
2	1180	3757
done	5000	3710

prune1.7s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 3.8b

regimes1.3s

Accuracy

4.2% (8.9b remaining)

Error of 12.4b against oracle of 3.5b and baseline of 12.7b

bsearch212.0ms

Steps

Iters	Range		Point
9	494987148267.1194	2.4001188468348672e+17	500051093016.9032
8	-1.6829627543292803e-61	-6.2230050197263674e-65	-6.647463183269898e-65

simplify31.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	104
1	48	104
done	48	104

end0.0ms

sample2.2s

Algorithm

intervals

Results

850.0ms	7718×	body	80	valid
193.0ms	499×	body	640	valid
160.0ms	395×	body	320	valid
105.0ms	286×	body	1280	valid
42.0ms	292×	body	160	valid
10.0ms	16×	body	2560	valid