Details

sample69.0ms

Algorithm

intervals

Results

18.0ms	231×	body	80	valid
4.0ms	12×	body	1280	valid
4.0ms	14×	body	640	valid
4.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
1.9b	(- (+ x y) (/ (* (- z t) y) (- a t)))
10.7b	(/ (* (- z t) y) (- a t))

rewrite120.0ms

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:

18.0ms	(* (- z t) y)
60.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
41.0ms	(/ (* (- z t) y) (- a t))

series351.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* (- z t) y)
192.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
105.0ms	(/ (* (- z t) y) (- a t))

simplify1.8s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1980
1	392
0	150

prune604.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (- y (* (/ y (- a t)) (- z t))))
0.0b	(/ y (- a t))
5.4b	(- y (* (/ y (- a t)) (- z t)))
11.1b	(* (/ y (- a t)) (- z t))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
31×	`times-frac`
24×	`add-cube-cbrt`
21×	`associate-l`
11×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `sub-neg`
5×	`associate-/r` `flip3--` `associate-r*` `flip--`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/` `associate--r+`
3×	`associate-/l*`
2×	`frac-times` `cbrt-undiv` `associate-+r+` `sum-log` `diff-log` `div-exp` `prod-exp` `associate-*r/` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `clear-num` `associate-+r-` `frac-2neg` `flip3-+` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `distribute-lft-out`

Counts

4 → 119

Calls

4 calls:

19.0ms	(+ x (- y (* (/ y (- a t)) (- z t))))
18.0ms	(/ y (- a t))
5.0ms	(- y (* (/ y (- a t)) (- z t)))
49.0ms	(* (/ y (- a t)) (- z t))

series916.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(+ x (- y (* (/ y (- a t)) (- z t))))
37.0ms	(/ y (- a t))
181.0ms	(- y (* (/ y (- a t)) (- z t)))
559.0ms	(* (/ y (- a t)) (- z t))

simplify1.1s

Counts

131 → 131

Iterations

Iter	Nodes
done	5002
2	2084
1	494
0	187

prune735.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
3.0b	(* (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (* (- z t) (/ (cbrt y) (cbrt (- a t)))))
15.7b	(- y (* (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (* (- z t) (/ (cbrt y) (cbrt (- a t))))))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
39×	`add-cbrt-cube`
37×	`prod-exp` `cbrt-unprod`
17×	`cbrt-undiv` `div-exp`
13×	`frac-times` `associate-l`
12×	`cbrt-div`
11×	`flip3--` `flip--`
9×	`pow1` `associate-*r/`
8×	`associate-/r/`
7×	`add-sqr-sqrt` `-un-lft-identity` `associate-l/` `add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
3×	`pow-prod-down`
2×	`pow1/3`
1×	`sub-neg` `times-frac` `diff-log` `associate-r` `*-commutative` `div-inv`

Counts

4 → 99

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
181.0ms	(* (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (* (- z t) (/ (cbrt y) (cbrt (- a t)))))
10.0ms	(- y (* (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (* (- z t) (/ (cbrt y) (cbrt (- a t))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

280.0ms	(cbrt y)
270.0ms	(cbrt y)
262.0ms	(* (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (* (- z t) (/ (cbrt y) (cbrt (- a t)))))
266.0ms	(- y (* (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))) (* (- z t) (/ (cbrt y) (cbrt (- a t))))))

simplify1.8s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	3463
1	636
0	191

prune775.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
11.1b	(* (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))) (- z t))
14.8b	(- y (* (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))) (- z t)))

rewrite536.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-exp-log`
35×	`prod-exp`
26×	`add-cbrt-cube`
15×	`div-exp` `cbrt-unprod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-prod`
9×	`frac-times` `pow1`
7×	`cbrt-undiv` `flip3--` `add-cube-cbrt` `flip--`
6×	`associate-*l/` `add-log-exp`
5×	`sub-neg` `associate-r` `associate-*r/`
4×	`distribute-rgt-in` `rec-exp` `cbrt-div` `distribute-lft-in` `1-exp` `associate--r+`
3×	`pow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`diff-log` `associate-l` `*-commutative`

Counts

4 → 99

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
520.0ms	(* (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))) (- z t))
5.0ms	(- y (* (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))) (- z t)))

series920.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(cbrt (- a t))
231.0ms	(cbrt (- a t))
267.0ms	(* (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))) (- z t))
199.0ms	(- y (* (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))) (- z t)))

simplify1.7s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
2	3809
1	707
0	227

prune661.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 4.4b

regimes829.0ms

Accuracy

6.2% (5.0b remaining)

Error of 8.6b against oracle of 3.7b and baseline of 9.0b

bsearch48.0ms

Steps

Iters	Range		Point
3	4.0356565631473004e-100	5.070879917928193e-100	4.776220601035188e-100
3	-7.713673533084189e-160	-5.677852690405708e-160	-7.329630304780208e-160

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample1.7s

Algorithm

intervals

Results

489.0ms	453×	body	640	valid
485.0ms	7334×	body	80	valid
102.0ms	263×	body	1280	valid
70.0ms	394×	body	320	valid
28.0ms	18×	body	2560	valid
24.0ms	251×	body	160	valid