Details

sample36.0ms

Algorithm

intervals

Results

13.0ms	263×	body	80	valid
2.0ms	11×	body	320	valid
2.0ms	9×	body	640	valid
1.0ms	6×	body	1280	valid
0.0ms	2×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	3019
5	643
4	223
3	109
2	52
1	22
0	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
0.8b	(- (+ x y) (/ (* (- z t) y) (- a t)))
10.4b	(/ (* (- z t) y) (- a t))

rewrite103.0ms

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`
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 → 70

Calls

3 calls:

17.0ms	(* (- z t) y)
66.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
18.0ms	(/ (* (- z t) y) (- a t))

series325.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* (- z t) y)
193.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
86.0ms	(/ (* (- z t) y) (- a t))

simplify1.8s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1980
1	392
0	150

prune585.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.5b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
4.9b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite187.0ms

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/`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sum-log` `sub-neg` `pow-prod-down` `associate--l+` `*-commutative`

Counts

4 → 127

Calls

4 calls:

6.0ms	(cbrt (- a t))
6.0ms	(cbrt (- a t))
129.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
35.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series852.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(cbrt (- a t))
226.0ms	(cbrt (- a t))
190.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
202.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify2.6s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
2	3750
1	800
0	274

prune938.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.7b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
5.6b	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

14×	`frac-sub`
10×	`frac-times` `associate-*l/`
9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity` `flip3-+` `add-cube-cbrt` `flip-+`
6×	`associate-*r/`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`pow1/3`
2×	`diff-log`
1×	`sum-log` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 61

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)
36.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

series985.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(cbrt y)
286.0ms	(cbrt y)
228.0ms	(cbrt y)
202.0ms	(- (+ x y) (* (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt y) (cbrt y)) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt y) (cbrt (cbrt (- a t))))))

simplify1.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1908
1	430
0	151

prune709.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.7b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
2.8b	(* (/ (- z t) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
5.4b	(- (+ x y) (* (/ (- z t) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

rewrite706.0ms

Algorithm

rewrite-expression-head

Rules

332×	`cbrt-div`
139×	`frac-times`
112×	`flip3--` `flip--`
89×	`associate-l`
82×	`associate-/r/`
60×	`add-exp-log`
52×	`cbrt-prod` `add-sqr-sqrt`
47×	`associate-l/` `associate-r/`
41×	`*-un-lft-identity` `times-frac`
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`
6×	`pow1` `frac-sub` `distribute-lft-out--` `difference-of-squares`
4×	`unswap-sqr`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sum-log` `sub-neg` `pow-prod-down` `associate--l+` `*-commutative`

Counts

4 → 218

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
618.0ms	(* (/ (- z t) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
63.0ms	(- (+ x y) (* (/ (- z t) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

series707.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(cbrt (- a t))
180.0ms	(cbrt (- a t))
164.0ms	(* (/ (- z t) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
166.0ms	(- (+ x y) (* (/ (- z t) (* (* (cbrt (cbrt (- a t))) (cbrt (cbrt (- a t)))) (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

simplify1.5s

Counts

230 → 230

Iterations

Iter	Nodes
done	5000
1	1360
0	421

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.7b

regimes884.0ms

Accuracy

27.7% (5.1b remaining)

Error of 9.5b against oracle of 4.3b and baseline of 11.4b

bsearch108.0ms

Steps

Iters	Range		Point
8	8.391520337805593e-109	2.206490995737268e-106	1.027335171522284e-108
6	-4.151288806614406e-87	-6.816939173909149e-88	-7.132241680778371e-88

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample1.6s

Algorithm

intervals

Results

570.0ms	7354×	body	80	valid
444.0ms	434×	body	320	valid
104.0ms	257×	body	1280	valid
95.0ms	450×	body	640	valid
43.0ms	249×	body	160	valid
5.0ms	17×	body	2560	valid