Details

sample46.0ms

Algorithm

intervals

Results

19.0ms	258×	body	80	valid
2.0ms	9×	body	1280	valid
2.0ms	12×	body	320	valid
2.0ms	9×	body	640	valid
1.0ms	10×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	1598
5	656
4	266
3	103
2	43
1	20
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
2.2b	(+ x (/ (* (- y x) (- z t)) (- a t)))
17.1b	(/ (* (- y x) (- z t)) (- a t))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

52.0ms	(* (- y x) (- z t))
22.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
23.0ms	(/ (* (- y x) (- z t)) (- a t))

series458.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* (- y x) (- z t))
249.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
144.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify1.6s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1904
1	480
0	162

prune709.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.8b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
2.2b	(+ x (/ (- y x) (/ (- a t) (- z t))))
2.7b	(/ (- y x) (/ (- a t) (- z t)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+r-` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

18.0ms	(/ (- a t) (- z t))
108.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
30.0ms	(/ (- y x) (/ (- a t) (- z t)))

series627.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(/ (- a t) (- z t))
269.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
269.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify2.1s

Counts

283 → 283

Iterations

Iter	Nodes
done	5002
2	3788
1	1146
0	354

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
0.9b	(/ (- y x) (* (/ (cbrt (- a t)) (cbrt (- z t))) (/ (cbrt (- a t)) (cbrt (- z t)))))
2.2b	(+ x (/ (/ (- y x) (* (/ (cbrt (- a t)) (cbrt (- z t))) (/ (cbrt (- a t)) (cbrt (- z t))))) (/ (cbrt (- a t)) (cbrt (- z t)))))

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
14×	`add-cbrt-cube`
10×	`cbrt-prod`
9×	`cbrt-undiv` `div-exp`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`times-frac` `associate-/l*`
4×	`pow1` `cbrt-div` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `div-sub` `associate-/r/` `flip--`
2×	`pow1/3` `associate-/l/`
1×	`frac-times` `+-commutative` `clear-num` `associate-+r-` `associate-/r` `sum-log` `frac-2neg` `flip3-+` `associate-l/` `associate-*r/` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 80

Calls

4 calls:

3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))
56.0ms	(/ (- y x) (* (/ (cbrt (- a t)) (cbrt (- z t))) (/ (cbrt (- a t)) (cbrt (- z t)))))
282.0ms	(+ x (/ (/ (- y x) (* (/ (cbrt (- a t)) (cbrt (- z t))) (/ (cbrt (- a t)) (cbrt (- z t))))) (/ (cbrt (- a t)) (cbrt (- z t)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

215.0ms	(cbrt (- z t))
222.0ms	(cbrt (- z t))
425.0ms	(/ (- y x) (* (/ (cbrt (- a t)) (cbrt (- z t))) (/ (cbrt (- a t)) (cbrt (- z t)))))
288.0ms	(+ x (/ (/ (- y x) (* (/ (cbrt (- a t)) (cbrt (- z t))) (/ (cbrt (- a t)) (cbrt (- z t))))) (/ (cbrt (- a t)) (cbrt (- z t)))))

simplify2.0s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1565
1	549
0	213

prune695.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.8b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.2b	(+ x (* (- y x) (/ (- z t) (- a t))))
2.6b	(* (- y x) (/ (- z t) (- a t)))

rewrite111.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `associate-l` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`frac-times` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-r/` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

23.0ms	(/ (- z t) (- a t))
11.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
72.0ms	(* (- y x) (/ (- z t) (- a t)))

series850.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ (- z t) (- a t))
276.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
510.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify1.6s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	1720
1	503
0	183

prune676.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 2.8b

regimes887.0ms

Accuracy

14.6% (6.2b remaining)

Error of 10.4b against oracle of 4.2b and baseline of 11.5b

bsearch129.0ms

Steps

Iters	Range		Point
5	2.837789130114876e-223	8.100114978727542e-223	7.273457157218697e-223
10	-1.6522177722814347e-125	-2.530256043446995e-142	-4.911453117926139e-142

simplify13.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample1.3s

Algorithm

intervals

Results

582.0ms	7760×	body	80	valid
117.0ms	469×	body	640	valid
97.0ms	415×	body	320	valid
64.0ms	255×	body	1280	valid
58.0ms	279×	body	160	valid
4.0ms	14×	body	2560	valid