Details

sample67.0ms

Algorithm

intervals

Results

18.0ms	251×	body	80	valid
16.0ms	19×	body	640	valid
2.0ms	7×	body	1280	valid
2.0ms	11×	body	160	valid
2.0ms	7×	body	320	valid
1.0ms	3×	body	2560	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	245
1	20	245
2	43	245
3	103	245
4	266	245
5	656	245
6	1598	245
done	5001	245

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
2.8b	(+ x (/ (* (- y x) (- z t)) (- a t)))
18.7b	(/ (* (- y x) (- z t)) (- a t))

rewrite92.0ms

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:

34.0ms	(* (- y x) (- z t))
32.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
24.0ms	(/ (* (- y x) (- z t)) (- a t))

series515.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(* (- y x) (- z t))
291.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
156.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify1.7s

Counts

90 → 90

Iterations

Useful iterations: 2 (518.0ms)

Iter	Nodes	Cost
0	162	25515
1	480	22392
2	1904	21992
done	5000	21992

prune684.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.3b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
2.4b	(/ (- y x) (/ (- a t) (- z t)))
2.8b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite204.0ms

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:

24.0ms	(/ (- a t) (- z t))
32.0ms	(/ (- y x) (/ (- a t) (- z t)))
116.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series626.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- a t) (- z t))
269.0ms	(/ (- y x) (/ (- a t) (- z t)))
282.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify3.6s

Counts

283 → 283

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	354	130065
1	1146	121883
2	3727	119516
done	5000	119231

prune1.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.5b	(* (- y x) (/ (- z t) (- a t)))
2.8b	(+ x (* (- y x) (/ (- z t) (- a t))))

rewrite130.0ms

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:

34.0ms	(/ (- z t) (- a t))
75.0ms	(* (- y x) (/ (- z t) (- a t)))
12.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

series504.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(/ (- z t) (- a t))
167.0ms	(* (- y x) (/ (- z t) (- a t)))
247.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

simplify2.0s

Counts

128 → 128

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	183	36295
1	504	33341
2	1724	32855
done	5001	32775

prune876.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- y x)) (cbrt (- y x)))
1.3b	(/ (/ (- a t) (- z t)) (cbrt (- y x)))
1.5b	(/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (/ (- a t) (- z t)) (cbrt (- y x))))
7.6b	(+ x (/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (/ (- a t) (- z t)) (cbrt (- y x)))))

rewrite527.0ms

Algorithm

rewrite-expression-head

Rules

1623×	`times-frac`
1181×	`add-sqr-sqrt` `*-un-lft-identity`
498×	`cbrt-prod`
477×	`add-cube-cbrt`
350×	`distribute-lft-out--`
348×	`difference-of-squares`
262×	`associate-/r*`
57×	`associate-/r/`
40×	`flip3--` `flip--`
32×	`add-exp-log` `associate-/l*`
30×	`cbrt-div`
29×	`div-inv`
18×	`add-cbrt-cube`
15×	`cbrt-undiv` `div-exp`
11×	`pow1`
10×	`swap-sqr`
9×	`associate-/l/`
8×	`frac-times` `associate-r` `associate-l`
6×	`pow1/3` `add-log-exp`
4×	`associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `unswap-sqr`
2×	`clear-num` `frac-2neg` `div-sub` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `+-commutative` `sum-log` `flip3-+` `pow-plus` `*-commutative` `flip-+` `distribute-lft-out`

Counts

4 → 913

Calls

4 calls:

31.0ms	(* (cbrt (- y x)) (cbrt (- y x)))
48.0ms	(/ (/ (- a t) (- z t)) (cbrt (- y x)))
88.0ms	(/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (/ (- a t) (- z t)) (cbrt (- y x))))
223.0ms	(+ x (/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (/ (- a t) (- z t)) (cbrt (- y x)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (cbrt (- y x)) (cbrt (- y x)))
300.0ms	(/ (/ (- a t) (- z t)) (cbrt (- y x)))
320.0ms	(/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (/ (- a t) (- z t)) (cbrt (- y x))))
244.0ms	(+ x (/ (* (cbrt (- y x)) (cbrt (- y x))) (/ (/ (- a t) (- z t)) (cbrt (- y x)))))

simplify4.2s

Counts

925 → 925

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	960	622729
1	2841	571479
done	5001	566521

prune4.9s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 4.0b

regimes847.0ms

Accuracy

18.5% (6.2b remaining)

Error of 10.3b against oracle of 4.2b and baseline of 11.7b

bsearch113.0ms

Steps

Iters	Range		Point
7	2.0561356340656335e-220	2.274793818262475e-218	2.2402489003734661e-218
8	-1.6666483488478152e-138	-3.805722520557681e-141	-8.219955541919714e-141

simplify11.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	23	747
1	30	747
done	30	747

end0.0ms

sample1.8s

Algorithm

intervals

Results

586.0ms	526×	body	640	valid
551.0ms	7699×	body	80	valid
131.0ms	264×	body	1280	valid
61.0ms	395×	body	320	valid
26.0ms	248×	body	160	valid
6.0ms	19×	body	2560	valid