Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify218.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	17	19
2	35	19
3	67	19
4	111	19
5	158	19
6	173	19
7	174	19
done	174	19

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
3.8b	(- (* x x) (* (* y 4.0) y))
28.6b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

9.0ms	(+ (* x x) (* (* y 4.0) y))
8.0ms	(- (* x x) (* (* y 4.0) y))
57.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series196.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (* x x) (* (* y 4.0) y))
60.0ms	(- (* x x) (* (* y 4.0) y))
87.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify2.7s

Counts

64 → 64

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	87	1404
1	233	1375
2	769	1233
3	2891	1226
done	5001	1210

prune188.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
20.9b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
21.8b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-cube-cbrt` `associate-/r/` `add-log-exp`
7×	`times-frac`
6×	`associate-/r*`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`pow1` `prod-exp` `cbrt-unprod` `div-inv`
3×	`distribute-rgt-out--`
2×	`frac-2neg` `clear-num` `associate-/l*` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 79

Calls

4 calls:

15.0ms	(+ (* x x) (* (* y 4.0) y))
110.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
29.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
17.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* x x) (* (* y 4.0) y))
90.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
66.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
54.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify1.4s

Counts

91 → 91

Iterations

Useful iterations: 2 (373.0ms)

Iter	Nodes	Cost
0	142	2132
1	384	2013
2	1397	1747
done	5000	1747

prune226.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))))
0.2b	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y)))
20.6b	(/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))
21.8b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
46×	`times-frac`
38×	`add-sqr-sqrt`
32×	`add-cbrt-cube`
29×	`*-un-lft-identity`
24×	`add-cube-cbrt`
22×	`div-exp`
13×	`prod-exp`
12×	`cbrt-undiv`
11×	`associate-/r*`
8×	`div-inv`
7×	`cbrt-unprod` `associate-/l*`
6×	`add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`rec-exp` `1-exp`
3×	`frac-2neg` `clear-num` `associate-/r/`
2×	`flip3-+` `flip-+` `associate-/l/` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `frac-sub` `flip--` `inv-pow`

Counts

4 → 129

Calls

4 calls:

124.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))))
46.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y)))
58.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))
17.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))))
90.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y)))
78.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))
70.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify1.4s

Counts

141 → 141

Iterations

Useful iterations: 2 (498.0ms)

Iter	Nodes	Cost
0	220	3773
1	557	3491
2	1964	3046
done	5001	3046

prune400.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* x x)))
0.2b	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y)))
20.6b	(/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))
21.8b	(/ (+ (* x x) (* (* y 4.0) y)) (* x x))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
72×	`times-frac`
41×	`add-cbrt-cube`
40×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
34×	`div-exp`
17×	`cbrt-undiv`
16×	`prod-exp` `associate-/r*`
12×	`div-inv` `associate-/l*`
8×	`cbrt-unprod`
7×	`rec-exp` `1-exp`
6×	`pow1`
4×	`frac-2neg` `clear-num` `associate-/l/` `add-log-exp`
2×	`pow-flip` `flip3-+` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 164

Calls

4 calls:

45.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* x x)))
61.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y)))
70.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))
39.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (* x x))

series321.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* x x)))
82.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y)))
73.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))
92.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (* x x))

simplify1.9s

Counts

176 → 176

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	238	3994
1	575	3701
2	1866	3102
done	5001	3084

prune452.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes201.0ms

Accuracy

56.4% (13.4b remaining)

Error of 13.9b against oracle of 0.4b and baseline of 31.2b

bsearch288.0ms

Steps

Iters	Range		Point
9	9556.682540875734	15966983906.555069	98355.24381927797
9	4.924640387312937e-45	2.5480243600333034e-37	8.134021215145638e-38
9	1.5895540584967369e-59	9.417139633880594e-52	1.5753976874379915e-55
7	-4.0684965810982345e-160	-4.482309770999907e-162	-1.636890293131895e-160
10	-2.7913152028957945e+157	-7.954806027061161e+143	-4.75816735826197e+148

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	30	92
1	35	92
done	35	92

end0.0ms

sample933.0ms

Algorithm

intervals

Results

619.0ms

8000×

body

valid