Details

sample49.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify20.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	25
3	25
2	22
1	15
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.1b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

42.0ms	(+ (+ (* x x) (* y y)) (* z z))
6.0ms	(+ (* x x) (* y y))
81.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
54.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series468.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (+ (* x x) (* y y)) (* z z))
33.0ms	(+ (* x x) (* y y))
96.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
280.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.2s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1770
1	358
0	139

prune647.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.1b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.1b	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
58×	`times-frac`
38×	`*-un-lft-identity`
36×	`sqrt-prod`
32×	`add-cube-cbrt`
22×	`associate-r` `associate-l`
21×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
11×	`pow1`
7×	`sqrt-div` `div-exp`
6×	`prod-exp`
4×	`cbrt-undiv` `sqrt-pow1` `cbrt-unprod` `add-log-exp`
3×	`pow1/2`
2×	`frac-times` `rem-sqrt-square` `flip3-+` `1-exp` `pow-prod-down` `associate-l/` `associate-r/` `flip-+` `div-inv`
1×	`*-commutative`

Counts

4 → 125

Calls

4 calls:

208.0ms	(* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
42.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
28.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
61.0ms	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
136.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
150.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
270.0ms	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify5.4s

Counts

137 → 137

Iterations

Iter	Nodes
done	5001
2	4876
1	555
0	179

prune734.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
36.1b	(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
51×	`times-frac` `add-exp-log`
37×	`*-un-lft-identity`
34×	`add-cube-cbrt`
24×	`cbrt-prod`
22×	`associate-r`
20×	`prod-exp`
19×	`add-cbrt-cube`
16×	`div-exp`
9×	`pow1` `unswap-sqr`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*` `add-log-exp`
4×	`rec-exp` `1-exp`
3×	`sqrt-div` `div-inv` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `flip3-+` `pow-prod-down` `associate-l/` `associate-r/` `flip-+` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `pow1/2` `*-commutative` `sqrt-prod`

Counts

4 → 136

Calls

4 calls:

11.0ms	(+ (* x x) (* y y))
132.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
67.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
49.0ms	(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

series844.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* x x) (* y y))
199.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
187.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
418.0ms	(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

simplify2.8s

Counts

148 → 148

Iterations

Iter	Nodes
done	5000
2	4975
1	729
0	228

prune916.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 20.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* z z) (* x x))
0.3b	(/ (sqrt (+ (* y y) (+ (* z z) (* x x)))) (sqrt 3.0))
36.1b	(sqrt (+ (* y y) (+ (* z z) (* x x))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

10.0ms	(+ (* z z) (* x x))
41.0ms	(/ (sqrt (+ (* y y) (+ (* z z) (* x x)))) (sqrt 3.0))
25.0ms	(sqrt (+ (* y y) (+ (* z z) (* x x))))

series447.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (* z z) (* x x))
249.0ms	(/ (sqrt (+ (* y y) (+ (* z z) (* x x)))) (sqrt 3.0))
151.0ms	(sqrt (+ (* y y) (+ (* z z) (* x x))))

simplify1.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1384
1	318
0	141

prune424.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.7b

regimes1.0s

Accuracy

34% (20.4b remaining)

Error of 26.7b against oracle of 6.3b and baseline of 37.2b

bsearch189.0ms

Steps

Iters	Range		Point
8	4.894347796388268e+59	1.6925211481097654e+62	1.5401699409035865e+62
8	1.752738582954229e-256	2.375564426734208e-252	1.7885689886641004e-256
9	-7.070473805980724e-246	-4.361739110048328e-251	-5.954117318185457e-251
8	-4.929461773712573e+105	-2.6664585819665247e+101	-2.2246552119313502e+105

simplify15.0ms

Iterations

Iter	Nodes
done	56
3	56
2	55
1	51
0	41

end0.0ms

sample1.0s

Algorithm

intervals

Results

628.0ms

8000×

body

valid