Details

sample38.0ms

Algorithm

intervals

Results

11.0ms	249×	body	80	valid
3.0ms	19×	body	640	valid
2.0ms	15×	body	320	valid
2.0ms	10×	body	1280	valid
1.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

simplify13.9s

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: 24.7b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.8b	(+ x (/ (* (- y z) (- t x)) (- a z)))
16.7b	(/ (* (- y z) (- t x)) (- a z))

rewrite122.0ms

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:

46.0ms	(* (- y z) (- t x))
21.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
49.0ms	(/ (* (- y z) (- t x)) (- a z))

series390.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* (- y z) (- t x))
181.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
160.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify1.2s

Counts

90 → 90

Iterations

Useful iterations: 2 (329.0ms)

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

prune416.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
1.4b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.6b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`cbrt-prod`
54×	`associate-r`
52×	`times-frac`
34×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
18×	`add-cbrt-cube`
14×	`flip3--` `flip--`
13×	`pow1`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `pow1/3` `div-exp`
6×	`add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

8.0ms	(cbrt (- a z))
45.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
192.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
15.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

255.0ms	(cbrt (- a z))
180.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
447.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
208.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify2.0s

Counts

187 → 187

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	307	4004
1	821	3733
2	3315	3184
done	5001	3016

prune759.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

localize64.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.6b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
10.8b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-div`
11×	`cbrt-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`flip3--` `flip--`
6×	`add-cube-cbrt` `add-log-exp`
4×	`pow1` `add-exp-log` `frac-times` `add-cbrt-cube`
3×	`pow1/3`
2×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 58

Calls

4 calls:

5.0ms	(cbrt (- t x))
4.0ms	(cbrt (- t x))
23.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
17.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series856.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(cbrt (- t x))
204.0ms	(cbrt (- t x))
208.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
235.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify922.0ms

Counts

70 → 70

Iterations

Useful iterations: done (919.0ms)

Iter	Nodes	Cost
0	179	1659
1	391	1592
2	1038	1462
done	5000	1268

prune613.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.5b	(+ x (* (- y z) (/ (- t x) (- a z))))
4.8b	(* (- y z) (/ (- t x) (- a z)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

21.0ms	(/ (- t x) (- a z))
8.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
74.0ms	(* (- y z) (/ (- t x) (- a z)))

series461.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (- t x) (- a z))
209.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
194.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.3s

Counts

128 → 128

Iterations

Useful iterations: 2 (318.0ms)

Iter	Nodes	Cost
0	183	1813
1	469	1704
2	1736	1606
done	5000	1606

prune403.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 2.4b

regimes371.0ms

Accuracy

26.3% (6.6b remaining)

Error of 10.1b against oracle of 3.5b and baseline of 12.4b

bsearch170.0ms

Steps

Iters	Range		Point
10	2.7753413219507016e+156	1.5853395761105443e+166	4.892583137041057e+158
9	-1.7910089691738227e+194	-1.8921491898552533e+186	-1.0577972736928619e+192

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	31	77
1	39	67
done	39	67

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	7808×	body	80	valid
106.0ms	482×	body	640	valid
100.0ms	414×	body	320	valid
73.0ms	270×	body	1280	valid
31.0ms	283×	body	160	valid
8.0ms	25×	body	2560	valid