Details

sample48.0ms

Algorithm

intervals

Results

16.0ms	258×	body	80	valid
2.0ms	17×	body	320	valid
2.0ms	6×	body	1280	valid
1.0ms	7×	body	640	valid
1.0ms	7×	body	160	valid

simplify18.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	44	13
3	122	13
4	327	13
5	732	13
6	1485	13
7	2361	13
8	3197	13
9	3665	13
10	3837	13
11	4148	13
12	4410	13
done	5000	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.8b	(+ x (* (- y z) (/ (- t x) (- a z))))
7.4b	(* (- y z) (/ (- t x) (- a z)))

rewrite114.0ms

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:

30.0ms	(/ (- t x) (- a z))
8.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
70.0ms	(* (- y z) (/ (- t x) (- a z)))

series554.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(/ (- t x) (- a z))
250.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
214.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.2s

Counts

128 → 128

Iterations

Useful iterations: 2 (273.0ms)

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

prune468.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.7b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.7b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite251.0ms

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:

5.0ms	(cbrt (- a z))
7.0ms	(cbrt (- a z))
220.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
12.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

190.0ms	(cbrt (- a z))
192.0ms	(cbrt (- a z))
478.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
229.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify1.7s

Counts

146 → 146

Iterations

Useful iterations: done (1.7s)

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

prune628.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
0.5b	(cbrt (- y z))
1.3b	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.5b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
35×	`add-cbrt-cube`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
15×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
14×	`associate-l`
9×	`pow1` `add-cube-cbrt`
8×	`times-frac`
6×	`cbrt-div` `add-log-exp`
5×	`frac-times` `associate-*r/`
3×	`flip3--` `pow-prod-down` `associate-*l/` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `associate-/r/`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 103

Calls

4 calls:

4.0ms	(cbrt (- y z))
7.0ms	(cbrt (- y z))
209.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
10.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

228.0ms	(cbrt (- y z))
227.0ms	(cbrt (- y z))
435.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
230.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify1.5s

Counts

115 → 115

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	225	3755
1	600	3566
2	2220	2466
done	5001	2157

prune502.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.7b	(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
6.9b	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

rewrite624.0ms

Algorithm

rewrite-expression-head

Rules

772×	`times-frac`
686×	`add-sqr-sqrt`
600×	`*-un-lft-identity`
487×	`cbrt-prod`
374×	`associate-l`
270×	`add-cube-cbrt`
165×	`distribute-lft-out--` `difference-of-squares`
46×	`associate-r`
25×	`add-exp-log`
24×	`cbrt-div`
21×	`unswap-sqr`
20×	`associate-/r/`
16×	`add-cbrt-cube`
12×	`flip3--` `flip--`
10×	`div-inv`
9×	`cbrt-undiv` `div-exp`
6×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`pow1/3`
1×	`+-commutative` `frac-times` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative` `flip-+`

Counts

4 → 506

Calls

4 calls:

5.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
542.0ms	(* (/ (/ (- 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)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

198.0ms	(cbrt (- a z))
190.0ms	(cbrt (- a z))
432.0ms	(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
217.0ms	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

simplify1.2s

Counts

518 → 518

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	524	12813
1	1669	12630
done	5000	12272

prune2.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 2.2b

regimes503.0ms

Accuracy

11.5% (7.7b remaining)

Error of 11.1b against oracle of 3.4b and baseline of 12.1b

bsearch133.0ms

Steps

Iters	Range		Point
7	1.0702432537069418e+178	1.8974423033311793e+179	8.311607488137995e+178
9	-1.816126690174146e+173	-5.346400383434256e+167	-2.065198081982861e+170

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	67
1	42	67
done	42	67

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	7750×	body	80	valid
126.0ms	445×	body	640	valid
73.0ms	267×	body	1280	valid
71.0ms	442×	body	320	valid
57.0ms	255×	body	160	valid
4.0ms	14×	body	2560	valid