Details

sample38.0ms

Algorithm

intervals

Results

11.0ms	257×	body	80	valid
2.0ms	12×	body	640	valid
2.0ms	8×	body	1280	valid
1.0ms	13×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	2560	valid

simplify2.8s

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	334	13
5	976	13
6	4035	13
done	5000	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
1.7b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.7b	(* (- y z) (/ (- t x) (- a z)))

rewrite162.0ms

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:

47.0ms	(/ (- t x) (- a z))
16.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
88.0ms	(* (- y z) (/ (- t x) (- a z)))

series604.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(/ (- t x) (- a z))
279.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
228.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify2.2s

Counts

128 → 128

Iterations

Useful iterations: 2 (441.0ms)

Iter	Nodes	Cost
0	183	1813
1	500	1716
2	2672	1606
done	5002	1606

prune469.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
2.3b	(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
6.1b	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

rewrite729.0ms

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:

12.0ms	(cbrt (- a z))
9.0ms	(cbrt (- a z))
598.0ms	(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
28.0ms	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

215.0ms	(cbrt (- a z))
213.0ms	(cbrt (- a z))
509.0ms	(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
261.0ms	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

simplify890.0ms

Counts

518 → 518

Iterations

Useful iterations: done (872.0ms)

Iter	Nodes	Cost
0	524	12813
1	1724	12646
done	5000	12300

prune2.7s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.0b

localize45.0ms

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))))
7.1b	(+ 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))))))

rewrite108.0ms

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:

22.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
21.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
22.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
12.0ms	(+ 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))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

401.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
348.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
389.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
254.0ms	(+ 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))))))

simplify3.0s

Counts

188 → 188

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	233	4432
1	478	4264
2	1176	3757
3	4909	3707
done	5000	3677

prune1.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.4b	(/ 1 (/ (- a z) (- t x)))
3.2b	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
6.7b	(* (- y z) (/ 1 (/ (- a z) (- t x))))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
338×	`add-sqr-sqrt`
326×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-r`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`add-exp-log` `associate-/r*`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-l` `unswap-sqr`
4×	`rec-exp` `1-exp`
3×	`cbrt-unprod`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 344

Calls

4 calls:

37.0ms	(/ (- a z) (- t x))
44.0ms	(/ 1 (/ (- a z) (- t x)))
15.0ms	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
134.0ms	(* (- y z) (/ 1 (/ (- a z) (- t x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (- a z) (- t x))
293.0ms	(/ 1 (/ (- a z) (- t x)))
243.0ms	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
502.0ms	(* (- y z) (/ 1 (/ (- a z) (- t x))))

simplify795.0ms

Counts

356 → 356

Iterations

Useful iterations: done (779.0ms)

Iter	Nodes	Cost
0	393	6138
1	1159	5194
done	5001	4824

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.7b

regimes588.0ms

Accuracy

66.5% (2.7b remaining)

Error of 6.1b against oracle of 3.4b and baseline of 11.6b

bsearch4.0ms

simplify12.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	25	69
1	34	57
done	34	57

end0.0ms

sample1.9s

Algorithm

intervals

Results

944.0ms	7790×	body	80	valid
102.0ms	515×	body	640	valid
100.0ms	269×	body	1280	valid
60.0ms	391×	body	320	valid
47.0ms	24×	body	2560	valid
23.0ms	240×	body	160	valid