Details

sample55.0ms

Algorithm

intervals

Results

15.0ms	254×	body	80	valid
9.0ms	5×	body	1280	valid
4.0ms	18×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	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: 21.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
1.1b	(+ x (/ (* (- y x) (- z t)) (- a t)))
15.3b	(/ (* (- y x) (- z t)) (- a t))

rewrite128.0ms

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:

51.0ms	(* (- y x) (- z t))
30.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
42.0ms	(/ (* (- y x) (- z t)) (- a t))

series463.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* (- y x) (- z t))
246.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
162.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify2.1s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1904
1	480
0	162

prune732.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.9b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.9b	(/ (- y x) (/ (- a t) (- z t)))
1.1b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite198.0ms

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:

23.0ms	(/ (- a t) (- z t))
45.0ms	(/ (- y x) (/ (- a t) (- z t)))
113.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series663.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- a t) (- z t))
320.0ms	(/ (- y x) (/ (- a t) (- z t)))
265.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify2.6s

Counts

283 → 283

Iterations

Iter	Nodes
done	5000
2	3727
1	1146
0	354

prune1.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.9b

localize36.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ x (/ (/ (- y x) (* (cbrt (/ (- a t) (- z t))) (cbrt (/ (- a t) (- z t))))) (cbrt (/ (- a t) (- z t)))))
2.6b	(cbrt (/ (- a t) (- z t)))
2.6b	(cbrt (/ (- a t) (- z t)))
2.6b	(cbrt (/ (- a t) (- z t)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
97×	`add-sqr-sqrt`
93×	`cbrt-prod`
75×	`times-frac`
37×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`cbrt-div` `flip3--` `pow1/3` `div-inv` `flip--`
2×	`div-sub`
1×	`+-commutative` `associate-+r-` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 133

Calls

4 calls:

205.0ms	(+ x (/ (/ (- y x) (* (cbrt (/ (- a t) (- z t))) (cbrt (/ (- a t) (- z t))))) (cbrt (/ (- a t) (- z t)))))
8.0ms	(cbrt (/ (- a t) (- z t)))
11.0ms	(cbrt (/ (- a t) (- z t)))
9.0ms	(cbrt (/ (- a t) (- z t)))

series1.5s

Counts

4 → 12

Calls

4 calls:

220.0ms	(+ x (/ (/ (- y x) (* (cbrt (/ (- a t) (- z t))) (cbrt (/ (- a t) (- z t))))) (cbrt (/ (- a t) (- z t)))))
402.0ms	(cbrt (/ (- a t) (- z t)))
436.0ms	(cbrt (/ (- a t) (- z t)))
424.0ms	(cbrt (/ (- a t) (- z t)))

simplify2.1s

Counts

145 → 145

Iterations

Iter	Nodes
done	5011
3	2362
2	856
1	400
0	191

prune1.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
0.9b	(/ (- y x) (/ (* (cbrt (- a t)) (cbrt (- a t))) (/ (- z t) (cbrt (- a t)))))
7.2b	(+ x (/ (- y x) (/ (* (cbrt (- a t)) (cbrt (- a t))) (/ (- z t) (cbrt (- a t))))))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

771×	`times-frac`
444×	`*-un-lft-identity`
442×	`add-sqr-sqrt`
178×	`add-cube-cbrt`
160×	`cbrt-prod`
132×	`distribute-lft-out--` `difference-of-squares`
51×	`associate-/r*`
22×	`add-exp-log`
19×	`associate-/r/`
16×	`cbrt-div` `add-cbrt-cube`
13×	`div-inv`
11×	`cbrt-undiv` `div-exp`
9×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`associate-/l*`
4×	`pow1`
2×	`pow1/3` `div-sub` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 378

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
60.0ms	(/ (- y x) (/ (* (cbrt (- a t)) (cbrt (- a t))) (/ (- z t) (cbrt (- a t)))))
183.0ms	(+ x (/ (- y x) (/ (* (cbrt (- a t)) (cbrt (- a t))) (/ (- z t) (cbrt (- a t))))))

series912.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt (- a t))
226.0ms	(cbrt (- a t))
270.0ms	(/ (- y x) (/ (* (cbrt (- a t)) (cbrt (- a t))) (/ (- z t) (cbrt (- a t)))))
234.0ms	(+ x (/ (- y x) (/ (* (cbrt (- a t)) (cbrt (- a t))) (/ (- z t) (cbrt (- a t))))))

simplify1.8s

Counts

390 → 390

Iterations

Iter	Nodes
done	5000
1	1965
0	595

prune2.6s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.9b

regimes929.0ms

Accuracy

9.1% (6.6b remaining)

Error of 10.4b against oracle of 3.7b and baseline of 11.0b

bsearch132.0ms

Steps

Iters	Range		Point
6	4.3349714367632944e-150	2.1863104960864863e-149	7.094564478841642e-150
8	2.3320124297926875e-300	1.7474270508966551e-296	7.138856904617574e-300

simplify19.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	7870×	body	80	valid
116.0ms	263×	body	1280	valid
101.0ms	458×	body	640	valid
65.0ms	374×	body	320	valid
29.0ms	258×	body	160	valid
7.0ms	23×	body	2560	valid