Details

sample41.0ms

Algorithm

intervals

Results

22.0ms

256×

body

valid

simplify24.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
2	22	14
3	24	14
done	24	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.2b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`times-frac`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqrt-prod`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num` `sum-log`

Counts

3 → 65

Calls

3 calls:

17.0ms	(+ (* x x) (* y y))
115.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
61.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series408.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (* x x) (* y y))
99.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
261.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.8s

Counts

74 → 74

Iterations

Useful iterations: 3 (818.0ms)

Iter	Nodes	Cost
0	128	1436
1	291	1370
2	855	1241
3	2763	1233
done	5001	1233

prune251.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
33×	`add-sqr-sqrt`
32×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-/r` `associate-/l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `sqrt-div`
3×	`flip3-+` `flip-+`
2×	`associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 89

Calls

3 calls:

17.0ms	(+ (* x x) (* y y))
88.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
65.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series546.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(+ (* x x) (* y y))
341.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
149.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: 3 (544.0ms)

Iter	Nodes	Cost
0	141	2253
1	292	2035
2	727	1965
3	1792	1945
done	5000	1945

prune703.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 17.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`-un-lft-identity` `associate-r*`
14×	`add-cube-cbrt`
13×	`times-frac`
9×	`sqrt-div`
8×	`pow1` `unswap-sqr`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`frac-times` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `associate-r/` `prod-exp` `sum-log` `-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 75

Calls

3 calls:

12.0ms	(+ (* x x) (* y y))
145.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
32.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series460.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (* x x) (* y y))
252.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
167.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.0s

Counts

84 → 84

Iterations

Useful iterations: 3 (642.0ms)

Iter	Nodes	Cost
0	140	1688
1	315	1536
2	794	1451
3	2239	1429
done	5000	1429

prune309.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 17.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-div`
7×	`pow1`
6×	`cbrt-prod`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

34.0ms	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
49.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
39.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series575.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
151.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
137.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
117.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify3.2s

Counts

73 → 73

Iterations

Useful iterations: 3 (310.0ms)

Iter	Nodes	Cost
0	77	1358
1	163	1230
2	426	1156
3	1273	1106
4	4525	1106
done	5002	1106

prune447.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 17.1b

regimes622.0ms

Accuracy

61% (7.7b remaining)

Error of 25.6b against oracle of 17.9b and baseline of 37.7b

bsearch89.0ms

Steps

Iters	Range		Point
10	4.022397810881141e+88	1.565796980266273e+101	1.537188568549187e+101
1	-4.90105109200061e+89	-4.6551667645331244e+89	-4.839580010133739e+89

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	32
1	28	32
done	28	32

end0.0ms

sample785.0ms

Algorithm

intervals

Results

560.0ms

8000×

body

valid