Details

sample58.0ms

Algorithm

intervals

Results

17.0ms	238×	body	80	valid
5.0ms	18×	body	640	valid
4.0ms	10×	body	1280	valid
3.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid

simplify2.9s

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: 14.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.3b	(+ x (* (- y z) (/ (- t x) (- a z))))
4.3b	(* (- y z) (/ (- t x) (- a z)))

rewrite198.0ms

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:

48.0ms	(/ (- t x) (- a z))
15.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
127.0ms	(* (- y z) (/ (- t x) (- a z)))

series524.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (- t x) (- a z))
224.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
228.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.8s

Counts

128 → 128

Iterations

Useful iterations: 2 (459.0ms)

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

prune535.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
0.9b	(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
8.7b	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

rewrite594.0ms

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:

4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
512.0ms	(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
11.0ms	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

259.0ms	(cbrt (- a z))
203.0ms	(cbrt (- a z))
426.0ms	(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
301.0ms	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

simplify881.0ms

Counts

518 → 518

Iterations

Useful iterations: done (857.0ms)

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

prune2.7s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
0.6b	(* (cbrt (- a z)) (cbrt (- a z)))
0.9b	(* (/ (/ (- y z) (cbrt (- a z))) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))
9.4b	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (- a z)))))

rewrite450.0ms

Algorithm

rewrite-expression-head

Rules

132×	`cbrt-div`
128×	`times-frac`
127×	`add-sqr-sqrt`
117×	`*-un-lft-identity`
84×	`associate-l`
80×	`cbrt-prod`
54×	`associate-r`
51×	`add-cube-cbrt`
47×	`add-exp-log`
41×	`flip3--` `flip--`
37×	`frac-times`
32×	`distribute-lft-out--`
30×	`associate-/r/` `difference-of-squares`
28×	`add-cbrt-cube`
19×	`associate-*l/`
17×	`cbrt-undiv` `div-exp`
15×	`prod-exp` `cbrt-unprod`
13×	`pow1` `associate-*r/`
10×	`swap-sqr`
7×	`pow1/3` `unswap-sqr`
6×	`add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 241

Calls

4 calls:

25.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
42.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
356.0ms	(* (/ (/ (- y z) (cbrt (- a z))) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))
9.0ms	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (- a z)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
191.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
495.0ms	(* (/ (/ (- y z) (cbrt (- a z))) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))
255.0ms	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (- a z)))))

simplify779.0ms

Counts

253 → 253

Iterations

Useful iterations: done (769.0ms)

Iter	Nodes	Cost
0	430	7428
1	1288	7080
done	5000	6466

prune1.8s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
2.9b	(* (/ (- y z) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (/ (/ (- t x) (cbrt (- a z))) (cbrt (- a z))) (cbrt (cbrt (- a z)))))
8.7b	(+ x (* (/ (- y z) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (/ (/ (- t x) (cbrt (- a z))) (cbrt (- a z))) (cbrt (cbrt (- a z))))))

rewrite4.4s

Algorithm

rewrite-expression-head

Rules

11811×	`times-frac`
9674×	`cbrt-prod`
8070×	`add-sqr-sqrt`
7880×	`*-un-lft-identity`
4120×	`associate-r`
3826×	`add-cube-cbrt`
2027×	`distribute-lft-out--` `difference-of-squares`
230×	`cbrt-div`
208×	`associate-/r/`
108×	`flip3--` `flip--`
101×	`div-inv`
58×	`add-exp-log`
44×	`unswap-sqr`
32×	`add-cbrt-cube`
26×	`cbrt-undiv` `div-exp`
17×	`associate-l`
16×	`prod-exp` `cbrt-unprod`
6×	`pow1` `add-log-exp`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 4258

Calls

4 calls:

4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
2.8s	(* (/ (- y z) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (/ (/ (- t x) (cbrt (- a z))) (cbrt (- a z))) (cbrt (cbrt (- a z)))))
8.0ms	(+ x (* (/ (- y z) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (/ (/ (- t x) (cbrt (- a z))) (cbrt (- a z))) (cbrt (cbrt (- a z))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

213.0ms	(cbrt (- a z))
198.0ms	(cbrt (- a z))
493.0ms	(* (/ (- y z) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (/ (/ (- t x) (cbrt (- a z))) (cbrt (- a z))) (cbrt (cbrt (- a z)))))
216.0ms	(+ x (* (/ (- y z) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (/ (/ (- t x) (cbrt (- a z))) (cbrt (- a z))) (cbrt (cbrt (- a z))))))

simplify2.7s

Counts

4270 → 4270

Iterations

Useful iterations: 0 (558.0ms)

Iter	Nodes	Cost
0	5413	170352
done	5413	170352

prune23.3s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 5.2b

regimes482.0ms

Accuracy

57% (3.6b remaining)

Error of 7.8b against oracle of 4.2b and baseline of 12.5b

bsearch3.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	93
1	39	70
done	39	70

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.1s	7738×	body	80	valid
219.0ms	465×	body	640	valid
84.0ms	268×	body	1280	valid
80.0ms	428×	body	320	valid
32.0ms	269×	body	160	valid
4.0ms	12×	body	2560	valid