Details

sample31.0ms

Algorithm

intervals

Results

13.0ms

321×

body

valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	13	9
2	20	9
3	34	9
4	53	9
5	64	9
6	75	9
7	96	9
8	136	9
9	377	9
10	1759	9
done	5001	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (- 1.0 x) y)
0.0b	(+ (* (- 1.0 x) y) (* x z))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`*-un-lft-identity`
5×	`associate-l`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
3×	`associate-r`
2×	`associate-*l/`
1×	`+-commutative` `flip3--` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

23.0ms	(* (- 1.0 x) y)
23.0ms	(+ (* (- 1.0 x) y) (* x z))

series73.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(* (- 1.0 x) y)
40.0ms	(+ (* (- 1.0 x) y) (* x z))

simplify609.0ms

Counts

39 → 39

Iterations

Useful iterations: done (607.0ms)

Iter	Nodes	Cost
0	71	405
1	189	375
2	737	347
done	5001	345

prune102.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 x))
0.0b	(sqrt (- 1.0 x))
0.1b	(* (sqrt (- 1.0 x)) y)
0.1b	(* (sqrt (- 1.0 x)) (* (sqrt (- 1.0 x)) y))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
21×	`sqrt-prod`
19×	`*-un-lft-identity`
18×	`sqrt-div`
16×	`associate-l`
13×	`pow1`
11×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
10×	`associate-*l/`
9×	`flip3--` `flip--`
4×	`frac-times` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `-commutative` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

12.0ms	(sqrt (- 1.0 x))
10.0ms	(sqrt (- 1.0 x))
37.0ms	(* (sqrt (- 1.0 x)) y)
77.0ms	(* (sqrt (- 1.0 x)) (* (sqrt (- 1.0 x)) y))

series237.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (- 1.0 x))
47.0ms	(sqrt (- 1.0 x))
103.0ms	(* (sqrt (- 1.0 x)) y)
41.0ms	(* (sqrt (- 1.0 x)) (* (sqrt (- 1.0 x)) y))

simplify995.0ms

Counts

103 → 103

Iterations

Useful iterations: done (990.0ms)

Iter	Nodes	Cost
0	136	1246
1	336	1132
2	1310	922
done	5000	916

prune364.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* y (sqrt (- (* 1.0 1.0) (* x x)))) (sqrt (+ 1.0 x)))
0.0b	(sqrt (- 1.0 x))
0.0b	(sqrt (+ 1.0 x))
0.0b	(* (sqrt (- 1.0 x)) (/ (* y (sqrt (- (* 1.0 1.0) (* x x)))) (sqrt (+ 1.0 x))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity` `sqrt-prod`
25×	`add-sqr-sqrt`
18×	`add-exp-log` `add-cbrt-cube`
15×	`add-cube-cbrt`
14×	`times-frac` `sqrt-div`
13×	`associate-r`
8×	`pow1` `associate-l`
7×	`associate-/r*`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r/` `flip--` `distribute-lft-out` `add-log-exp`
3×	`flip3-+` `associate-*r/` `flip-+`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/` `div-inv` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

4 → 109

Calls

4 calls:

44.0ms	(/ (* y (sqrt (- (* 1.0 1.0) (* x x)))) (sqrt (+ 1.0 x)))
7.0ms	(sqrt (- 1.0 x))
7.0ms	(sqrt (+ 1.0 x))
72.0ms	(* (sqrt (- 1.0 x)) (/ (* y (sqrt (- (* 1.0 1.0) (* x x)))) (sqrt (+ 1.0 x))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (* y (sqrt (- (* 1.0 1.0) (* x x)))) (sqrt (+ 1.0 x)))
46.0ms	(sqrt (- 1.0 x))
49.0ms	(sqrt (+ 1.0 x))
274.0ms	(* (sqrt (- 1.0 x)) (/ (* y (sqrt (- (* 1.0 1.0) (* x x)))) (sqrt (+ 1.0 x))))

simplify1.2s

Counts

121 → 121

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	200	2241
1	530	2045
2	2545	1809
done	5002	1805

prune443.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* (sqrt y) (- 1.0 x)) (sqrt y)) (* x z))
0.1b	(* (sqrt y) (- 1.0 x))
0.2b	(* (* (sqrt y) (- 1.0 x)) (sqrt y))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`associate-r`
10×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`add-cube-cbrt`
7×	`associate-l` `sqrt-prod`
5×	`add-log-exp`
4×	`associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `associate-l/` `-commutative` `flip--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 64

Calls

3 calls:

56.0ms	(+ (* (* (sqrt y) (- 1.0 x)) (sqrt y)) (* x z))
34.0ms	(* (sqrt y) (- 1.0 x))
44.0ms	(* (* (sqrt y) (- 1.0 x)) (sqrt y))

series182.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(+ (* (* (sqrt y) (- 1.0 x)) (sqrt y)) (* x z))
45.0ms	(* (sqrt y) (- 1.0 x))
43.0ms	(* (* (sqrt y) (- 1.0 x)) (sqrt y))

simplify938.0ms

Counts

73 → 73

Iterations

Useful iterations: done (935.0ms)

Iter	Nodes	Cost
0	126	925
1	349	853
2	1768	659
done	5000	645

prune133.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	11	9
done	11	9

end0.0ms

sample1.1s

Algorithm

intervals

Results

634.0ms

10154×

body

valid