Details

sample23.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify268.0ms

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	114	19
5	166	19
6	195	19
7	199	19
done	199	19

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
4.8b	(- (* x x) (* (* y 4.0) y))
29.5b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite89.0ms

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:

21.0ms	(+ (* x x) (* (* y 4.0) y))
14.0ms	(- (* x x) (* (* y 4.0) y))
52.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series191.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(+ (* x x) (* (* y 4.0) y))
60.0ms	(- (* x x) (* (* y 4.0) y))
71.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify799.0ms

Counts

64 → 64

Iterations

Useful iterations: done (796.0ms)

Iter	Nodes	Cost
0	87	1404
1	254	1375
2	1196	1235
done	5001	1233

prune232.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* x x) (* (* y 4.0) y))
29.5b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
29.5b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
29.5b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r` `associate-/l`
6×	`associate-/r/` `associate-/l/` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
3×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 108

Calls

4 calls:

13.0ms	(- (* x x) (* (* y 4.0) y))
30.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
34.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
33.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* x x) (* (* y 4.0) y))
69.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
73.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
86.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify760.0ms

Counts

120 → 120

Iterations

Useful iterations: done (754.0ms)

Iter	Nodes	Cost
0	82	3148
1	237	3096
2	1163	2816
done	5001	2810

prune548.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize64.0ms

Local error

Found 4 expressions with local error:

29.2b	(cbrt (- (* x x) (* (* y 4.0) y)))
29.2b	(cbrt (- (* x x) (* (* y 4.0) y)))
29.5b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
29.5b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`cbrt-prod` `associate-/r` `associate-/l`
4×	`pow1` `cbrt-div` `flip3--` `associate-/r/` `flip--` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `pow1/3` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 90

Calls

4 calls:

10.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
8.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
35.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
32.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
148.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
123.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
77.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify785.0ms

Counts

102 → 102

Iterations

Useful iterations: done (777.0ms)

Iter	Nodes	Cost
0	111	2530
1	280	2486
2	1176	2258
done	5000	2232

prune655.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
0.9b	(/ 1 (+ (* x x) (* (* y 4.0) y)))
4.8b	(- (* x x) (* (* y 4.0) y))
29.9b	(* (- (* x x) (* (* y 4.0) y)) (/ 1 (+ (* x x) (* (* y 4.0) y))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `flip3-+` `associate-l` `associate-/r` `flip--` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 98

Calls

4 calls:

15.0ms	(+ (* x x) (* (* y 4.0) y))
24.0ms	(/ 1 (+ (* x x) (* (* y 4.0) y)))
14.0ms	(- (* x x) (* (* y 4.0) y))
100.0ms	(* (- (* x x) (* (* y 4.0) y)) (/ 1 (+ (* x x) (* (* y 4.0) y))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* x x) (* (* y 4.0) y))
52.0ms	(/ 1 (+ (* x x) (* (* y 4.0) y)))
47.0ms	(- (* x x) (* (* y 4.0) y))
94.0ms	(* (- (* x x) (* (* y 4.0) y)) (/ 1 (+ (* x x) (* (* y 4.0) y))))

simplify1.9s

Counts

110 → 110

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	127	2193
1	360	2072
2	2151	1773
done	5001	1767

prune299.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes174.0ms

Accuracy

61.6% (12.2b remaining)

Error of 12.6b against oracle of 0.4b and baseline of 32.2b

bsearch230.0ms

Steps

Iters	Range		Point
9	5.544110015415869e+89	8.73093819312065e+95	6.052303689076668e+95
9	2.507054277993032e-156	3.616730134671116e-149	1.2958981514480286e-152
8	-2.895351554843775e-99	-1.1436941264463758e-103	-6.621300319852041e-102
10	-7.015537041391403e+155	-1.2785578264641574e+145	-1.517398075841732e+145

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	235
1	42	235
done	42	235

end0.0ms

sample827.0ms

Algorithm

intervals

Results

558.0ms

8000×

body

valid