Details

sample38.0ms

Algorithm

intervals

Results

13.0ms	240×	body	80	valid
1.0ms	3×	body	2560	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	640	valid
0.0ms	2×	body	1280	valid
0.0ms	4×	body	160	valid

simplify507.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	505
7	505
6	504
5	497
4	431
3	212
2	66
1	20
0	8

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ (+ x y) y) x) z)
0.0b	(+ (+ (+ (+ (+ x y) y) x) z) x)
0.0b	(+ (+ (+ x y) y) x)
0.0b	(+ (+ x y) y)

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity` `add-log-exp`
34×	`sum-log` `distribute-lft-out`
4×	`add-sqr-sqrt` `pow1` `+-commutative` `associate-+l+` `flip3-+` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `flip-+`

Counts

4 → 72

Calls

4 calls:

636.0ms	(+ (+ (+ (+ x y) y) x) z)
2.4s	(+ (+ (+ (+ (+ x y) y) x) z) x)
140.0ms	(+ (+ (+ x y) y) x)
31.0ms	(+ (+ x y) y)

series200.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (+ (+ (+ x y) y) x) z)
49.0ms	(+ (+ (+ (+ (+ x y) y) x) z) x)
47.0ms	(+ (+ (+ x y) y) x)
49.0ms	(+ (+ x y) y)

simplify672.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	1273
1	292
0	104

prune295.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (* x 3) (+ z (+ y y)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
6×	`sum-log`
1×	`add-sqr-sqrt` `pow1` `+-commutative` `associate-+r+` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `flip-+`

Counts

1 → 14

Calls

1 calls:

71.0ms

(+ (* x 3) (+ z (+ y y)))

series52.0ms

Counts

1 → 3

Calls

1 calls:

52.0ms

(+ (* x 3) (+ z (+ y y)))

simplify1.3s

Counts

17 → 17

Iterations

Iter	Nodes
done	5000
3	3078
2	524
1	129
0	42

prune78.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ (+ (+ x x) (+ y y)) z))
0.0b	(sqrt (+ x (+ (+ (+ x x) (+ y y)) z)))
0.0b	(sqrt (+ x (+ (+ (+ x x) (+ y y)) z)))
0.3b	(* (sqrt (+ x (+ (+ (+ x x) (+ y y)) z))) (sqrt (+ x (+ (+ (+ x x) (+ y y)) z))))

rewrite6.4s

Algorithm

rewrite-expression-head

Rules

501×	`*-un-lft-identity`
361×	`distribute-lft-out`
144×	`sqrt-prod`
56×	`swap-sqr`
29×	`add-log-exp`
28×	`add-sqr-sqrt`
21×	`pow1`
19×	`sum-log`
16×	`sqrt-div`
14×	`add-cube-cbrt`
12×	`associate-r` `associate-l`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `associate-+r+` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 182

Calls

4 calls:

625.0ms	(+ x (+ (+ (+ x x) (+ y y)) z))
1.0s	(sqrt (+ x (+ (+ (+ x x) (+ y y)) z)))
996.0ms	(sqrt (+ x (+ (+ (+ x x) (+ y y)) z)))
3.7s	(* (sqrt (+ x (+ (+ (+ x x) (+ y y)) z))) (sqrt (+ x (+ (+ (+ x x) (+ y y)) z))))

series381.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ x (+ (+ (+ x x) (+ y y)) z))
120.0ms	(sqrt (+ x (+ (+ (+ x x) (+ y y)) z)))
110.0ms	(sqrt (+ x (+ (+ (+ x x) (+ y y)) z)))
94.0ms	(* (sqrt (+ x (+ (+ (+ x x) (+ y y)) z))) (sqrt (+ x (+ (+ (+ x x) (+ y y)) z))))

simplify1.2s

Counts

194 → 194

Iterations

Iter	Nodes
done	5002
2	1799
1	360
0	143

prune622.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ z (+ (* 2 (+ x y)) x))))
0.1b	(sqrt (sqrt (+ x (+ (+ (+ x x) (+ y y)) z))))
0.2b	(* (pow (sqrt (sqrt (+ z (+ (* 2 (+ x y)) x)))) 3) (sqrt (sqrt (+ x (+ (+ (+ x x) (+ y y)) z)))))
0.4b	(pow (sqrt (sqrt (+ z (+ (* 2 (+ x y)) x)))) 3)

rewrite3.7s

Algorithm

rewrite-expression-head

Rules

141×	`sqrt-prod`
85×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
43×	`distribute-lft-out`
36×	`sqrt-div`
29×	`unpow-prod-down` `cube-prod`
26×	`associate-l`
25×	`add-cube-cbrt`
24×	`unswap-sqr`
15×	`associate-r`
12×	`sqrt-pow1`
11×	`pow1`
10×	`add-exp-log`
9×	`flip3-+` `flip-+`
8×	`cube-div`
7×	`add-cbrt-cube`
6×	`pow1/2`
5×	`pow-pow` `sqr-pow`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `associate-l/` `pow-exp` `associate-r/`
1×	`*-commutative` `cbrt-unprod` `sqrt-pow2` `rem-cube-cbrt`

Counts

4 → 178

Calls

4 calls:

68.0ms	(sqrt (sqrt (+ z (+ (* 2 (+ x y)) x))))
993.0ms	(sqrt (sqrt (+ x (+ (+ (+ x x) (+ y y)) z))))
2.5s	(* (pow (sqrt (sqrt (+ z (+ (* 2 (+ x y)) x)))) 3) (sqrt (sqrt (+ x (+ (+ (+ x x) (+ y y)) z)))))
115.0ms	(pow (sqrt (sqrt (+ z (+ (* 2 (+ x y)) x)))) 3)

series1.7s

Counts

4 → 12

Calls

4 calls:

538.0ms	(sqrt (sqrt (+ z (+ (* 2 (+ x y)) x))))
631.0ms	(sqrt (sqrt (+ x (+ (+ (+ x x) (+ y y)) z))))
94.0ms	(* (pow (sqrt (sqrt (+ z (+ (* 2 (+ x y)) x)))) 3) (sqrt (sqrt (+ x (+ (+ (+ x x) (+ y y)) z)))))
481.0ms	(pow (sqrt (sqrt (+ z (+ (* 2 (+ x y)) x)))) 3)

simplify3.0s

Counts

190 → 190

Iterations

Iter	Nodes
done	5001
2	3946
1	828
0	288

prune975.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes291.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
1	11
0	8

end0.0ms

sample957.0ms

Algorithm

intervals

Results

442.0ms	7397×	body	80	valid
74.0ms	203×	body	1280	valid
27.0ms	168×	body	640	valid
16.0ms	131×	body	320	valid
8.0ms	34×	body	2560	valid
6.0ms	71×	body	160	valid