Details

sample33.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	22
3	22
2	21
1	15
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.7b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

13.0ms	(+ (* x x) (* y y))
83.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series362.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (* x x) (* y y))
68.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
247.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.3s

Counts

74 → 74

Iterations

Iter	Nodes
done	5002
3	4285
2	926
1	295
0	128

prune459.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.0b

localize32.0ms

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)))
33.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite113.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`frac-times` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-unprod` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 75

Calls

3 calls:

6.0ms	(+ (* x x) (* y y))
71.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
33.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series337.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* x x) (* y y))
183.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
116.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.9s

Counts

84 → 84

Iterations

Iter	Nodes
done	5012
3	3085
2	818
1	321
0	140

prune428.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.0b

localize28.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ (sqrt (+ (+ (* z z) (* x x)) (* y y))) (sqrt 3.0))
33.7b	(sqrt (+ (+ (* z z) (* x x)) (* y y)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 78

Calls

2 calls:

73.0ms	(/ (sqrt (+ (+ (* z z) (* x x)) (* y y))) (sqrt 3.0))
41.0ms	(sqrt (+ (+ (* z z) (* x x)) (* y y)))

series432.0ms

Counts

2 → 6

Calls

2 calls:

307.0ms	(/ (sqrt (+ (+ (* z z) (* x x)) (* y y))) (sqrt 3.0))
124.0ms	(sqrt (+ (+ (* z z) (* x x)) (* y y)))

simplify2.8s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
4	4293
3	1362
2	485
1	217
0	119

prune380.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.2b

localize6.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ (- z) (sqrt 3.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
44×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
33×	`sqrt-prod`
21×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-/l*`
7×	`neg-mul-1`
6×	`associate-/r*`
3×	`add-cbrt-cube` `add-exp-log`
1×	`neg-sub0` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `distribute-frac-neg` `div-inv` `add-log-exp`

Counts

1 → 90

Calls

1 calls:

14.0ms

(/ (- z) (sqrt 3.0))

series98.0ms

Counts

1 → 3

Calls

1 calls:

97.0ms

(/ (- z) (sqrt 3.0))

simplify1.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	1590
2	606
1	258
0	131

prune349.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 5.1b

regimes1.3s

Accuracy

37.7% (20.1b remaining)

Error of 26.1b against oracle of 6.0b and baseline of 38.3b

bsearch107.0ms

Steps

Iters	Range		Point
7	1.1699726614989072e+126	1.5995148681347137e+128	8.320790080049102e+126
9	-4.064102892713862e+80	-1.8599689544989674e+74	-3.917725958087788e+80

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

907.0ms

8000×

body

valid