Details

sample29.0ms

Algorithm

intervals

Results

7.0ms	259×	body	80	valid
2.0ms	21×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid

simplify9.1s

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	288	13
5	631	13
6	1195	13
7	2059	13
8	2903	13
9	3426	13
10	3861	13
11	4158	13
done	5000	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.8b	(+ x (/ (* (- y z) (- t x)) (- a z)))
17.7b	(/ (* (- y z) (- t x)) (- a z))

rewrite95.0ms

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:

37.0ms	(* (- y z) (- t x))
20.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
35.0ms	(/ (* (- y z) (- t x)) (- a z))

series356.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* (- y z) (- t x))
174.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
143.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify914.0ms

Counts

90 → 90

Iterations

Useful iterations: 2 (230.0ms)

Iter	Nodes	Cost
0	162	1284
1	466	1213
2	1986	1111
done	5000	1111

prune230.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.0b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.4b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite152.0ms

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:

4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
127.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series790.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- a z))
153.0ms	(cbrt (- a z))
313.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
175.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify1.3s

Counts

146 → 146

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	255	3364
1	722	3180
2	2785	2663
done	5000	2496

prune427.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
4.5b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite24.0ms

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:

4.0ms	(cbrt (- y z))
4.0ms	(cbrt (- y z))
6.0ms	(cbrt (- y z))
9.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series611.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (- y z))
143.0ms	(cbrt (- y z))
147.0ms	(cbrt (- y z))
171.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify1.7s

Counts

68 → 68

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	108	1234
1	263	1187
2	783	1093
3	3518	892
done	5000	853

prune270.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
0.6b	(cbrt (cbrt (- y z)))
6.0b	(+ x (* (/ (* (* (cbrt (* (cbrt (- y z)) (cbrt (- y z)))) (cbrt (cbrt (- y z)))) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cbrt-prod`
14×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `cbrt-div`
6×	`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 → 59

Calls

4 calls:

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

series621.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- y z))
152.0ms	(cbrt (- y z))
146.0ms	(cbrt (cbrt (- y z)))
175.0ms	(+ x (* (/ (* (* (cbrt (* (cbrt (- y z)) (cbrt (- y z)))) (cbrt (cbrt (- y z)))) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify2.6s

Counts

71 → 71

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	150	1511
1	348	1449
2	976	1329
3	4771	1292
done	5000	1258

prune310.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.5b

regimes289.0ms

Accuracy

17.1% (7.3b remaining)

Error of 10.6b against oracle of 3.4b and baseline of 12.1b

bsearch112.0ms

Steps

Iters	Range		Point
9	2.8440206351852415e-253	4.247425426467879e-244	4.1604463818278907e-244
11	-2.413717548537463e-66	-3.452617791225645e-93	-9.705632488691707e-90

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	89
1	36	55
done	36	55

end0.0ms

sample765.0ms

Algorithm

intervals

Results

237.0ms	7805×	body	80	valid
51.0ms	497×	body	640	valid
41.0ms	268×	body	1280	valid
30.0ms	376×	body	320	valid
15.0ms	276×	body	160	valid
3.0ms	16×	body	2560	valid