Details

sample78.0ms

Algorithm

intervals

Results

18.0ms	237×	body	80	valid
5.0ms	16×	body	640	valid
3.0ms	9×	body	1280	valid
2.0ms	13×	body	160	valid
2.0ms	7×	body	320	valid
0.0ms	1×	body	2560	valid

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
7	2087
6	873
5	342
4	176
3	101
2	50
1	22
0	11

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize52.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
3.9b	(- (+ x y) (/ (* (- z t) y) (- a t)))
9.9b	(/ (* (- z t) y) (- a t))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
10×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1` `associate-/r` `times-frac` `associate-l*` `distribute-lft-out--`
4×	`flip3--` `associate-*l/` `flip--` `difference-of-squares`
3×	`associate-r` `insert-posit16`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `associate-/r/` `frac-sub` `cbrt-unprod` `associate-/l/`
1×	`clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `pow-prod-down` `associate--l+` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 73

Calls

3 calls:

36.0ms	(* (- z t) y)
111.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
56.0ms	(/ (* (- z t) y) (- a t))

series462.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* (- z t) y)
279.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
137.0ms	(/ (* (- z t) y) (- a t))

simplify3.0s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1411
1	395
0	153

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.4b

localize78.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.6b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
7.4b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity`
30×	`associate-r`
27×	`cbrt-prod`
25×	`add-exp-log`
23×	`add-cube-cbrt`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
9×	`add-log-exp`
8×	`prod-exp` `cbrt-unprod`
7×	`frac-times` `cbrt-undiv` `div-exp`
6×	`pow1` `frac-sub` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
5×	`associate-l/` `associate-r/`
4×	`insert-posit16`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sum-log` `sub-neg` `pow-prod-down` `associate--l+` `*-commutative`

Counts

4 → 131

Calls

4 calls:

12.0ms	(cbrt (- a t))
13.0ms	(cbrt (- a t))
246.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
93.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

320.0ms	(cbrt (- a t))
277.0ms	(cbrt (- a t))
190.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
261.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify5.7s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	3089
1	790
0	277

prune2.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.3b

localize147.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
2.2b	(* (/ (- z t) (* (* (cbrt (cbrt (- a t))) (cbrt (- a t))) (* (cbrt (cbrt (- a t))) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
8.6b	(- (+ x y) (* (/ (- z t) (* (* (cbrt (cbrt (- a t))) (cbrt (- a t))) (* (cbrt (cbrt (- a t))) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

332×	`cbrt-div`
139×	`frac-times`
112×	`flip3--` `flip--`
89×	`associate-l`
82×	`associate-/r/`
63×	`add-sqr-sqrt`
60×	`add-exp-log`
55×	`cbrt-prod`
48×	`times-frac`
47×	`associate-l/` `associate-r/`
41×	`*-un-lft-identity`
39×	`associate-r`
38×	`add-cbrt-cube`
29×	`add-cube-cbrt`
28×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
8×	`unswap-sqr`
6×	`pow1` `frac-sub` `distribute-lft-out--` `difference-of-squares`
4×	`insert-posit16`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sum-log` `sub-neg` `pow-prod-down` `associate--l+` `*-commutative`

Counts

4 → 226

Calls

4 calls:

7.0ms	(cbrt (- a t))
12.0ms	(cbrt (- a t))
841.0ms	(* (/ (- z t) (* (* (cbrt (cbrt (- a t))) (cbrt (- a t))) (* (cbrt (cbrt (- a t))) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
80.0ms	(- (+ x y) (* (/ (- z t) (* (* (cbrt (cbrt (- a t))) (cbrt (- a t))) (* (cbrt (cbrt (- a t))) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

315.0ms	(cbrt (- a t))
286.0ms	(cbrt (- a t))
202.0ms	(* (/ (- z t) (* (* (cbrt (cbrt (- a t))) (cbrt (- a t))) (* (cbrt (cbrt (- a t))) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
276.0ms	(- (+ x y) (* (/ (- z t) (* (* (cbrt (cbrt (- a t))) (cbrt (- a t))) (* (cbrt (cbrt (- a t))) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

simplify2.7s

Counts

238 → 238

Iterations

Iter	Nodes
done	5000
1	1419
0	464

prune4.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.3b

localize208.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (/ y (cbrt (- a t))))
5.7b	(cbrt (/ y (cbrt (- a t))))
6.7b	(/ (- z t) (* (/ (cbrt (- a t)) (cbrt (/ y (cbrt (- a t))))) (/ (cbrt (- a t)) (cbrt (/ y (cbrt (- a t)))))))
8.3b	(- (+ x y) (* (/ (- z t) (* (/ (cbrt (- a t)) (cbrt (/ y (cbrt (- a t))))) (/ (cbrt (- a t)) (cbrt (/ y (cbrt (- a t))))))) (cbrt (/ y (cbrt (- a t))))))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

90×	`cbrt-prod`
53×	`times-frac`
52×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`add-cube-cbrt`
22×	`add-exp-log`
14×	`add-cbrt-cube`
10×	`cbrt-div`
9×	`cbrt-undiv` `div-exp` `add-log-exp`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`associate-/r/`
6×	`frac-sub`
5×	`associate-/l*`
4×	`pow1` `flip3--` `prod-exp` `cbrt-unprod` `insert-posit16` `flip--`
3×	`frac-times` `flip3-+` `associate-l/` `associate-r/` `flip-+` `div-inv`
2×	`pow1/3` `diff-log` `associate-/l/`
1×	`clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `div-sub` `associate--l+`

Counts

4 → 139

Calls

4 calls:

20.0ms	(cbrt (/ y (cbrt (- a t))))
15.0ms	(cbrt (/ y (cbrt (- a t))))
175.0ms	(/ (- z t) (* (/ (cbrt (- a t)) (cbrt (/ y (cbrt (- a t))))) (/ (cbrt (- a t)) (cbrt (/ y (cbrt (- a t)))))))
89.0ms	(- (+ x y) (* (/ (- z t) (* (/ (cbrt (- a t)) (cbrt (/ y (cbrt (- a t))))) (/ (cbrt (- a t)) (cbrt (/ y (cbrt (- a t))))))) (cbrt (/ y (cbrt (- a t))))))

series2.2s

Counts

4 → 12

Calls

4 calls:

499.0ms	(cbrt (/ y (cbrt (- a t))))
448.0ms	(cbrt (/ y (cbrt (- a t))))
868.0ms	(/ (- z t) (* (/ (cbrt (- a t)) (cbrt (/ y (cbrt (- a t))))) (/ (cbrt (- a t)) (cbrt (/ y (cbrt (- a t)))))))
409.0ms	(- (+ x y) (* (/ (- z t) (* (/ (cbrt (- a t)) (cbrt (/ y (cbrt (- a t))))) (/ (cbrt (- a t)) (cbrt (/ y (cbrt (- a t))))))) (cbrt (/ y (cbrt (- a t))))))

simplify5.7s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
2	2679
1	823
0	352

prune2.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.3b

regimes3.3s

Accuracy

12.9% (6.2b remaining)

Error of 10.3b against oracle of 4.0b and baseline of 11.2b

bsearch160.0ms

Steps

Iters	Range		Point
9	8.926486449435712e+126	2.8364102844858466e+132	2.9186525251190146e+129
7	-1.3939370376628877e+50	-2.6305624027095992e+48	-1.3731458525563276e+50

simplify49.0ms

Iterations

Iter	Nodes
done	45
1	45
0	34

end0.0ms

sample1.8s

Algorithm

intervals

Results

929.0ms	7361×	body	80	valid
144.0ms	433×	body	640	valid
111.0ms	392×	body	320	valid
71.0ms	268×	body	1280	valid
47.0ms	245×	body	160	valid
6.0ms	20×	body	2560	valid