Details

sample44.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify56.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize49.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.0b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`times-frac`
17×	`*-un-lft-identity` `add-cube-cbrt`
13×	`sqrt-prod`
4×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-/r` `associate-/l`
2×	`rem-sqrt-square` `insert-posit16` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `flip-+`

Counts

2 → 56

Calls

2 calls:

158.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
79.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series448.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
324.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify4.8s

Counts

62 → 62

Iterations

Iter	Nodes
done	5014
3	3110
2	652
1	219
0	109

prune864.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.3b

localize33.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite128.0ms

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-+` `insert-posit16` `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 → 80

Calls

2 calls:

76.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
45.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series633.0ms

Counts

2 → 6

Calls

2 calls:

448.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
185.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify6.8s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
4	4232
3	1354
2	488
1	219
0	121

prune933.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.2b

localize32.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`associate-r`
15×	`*-un-lft-identity`
13×	`times-frac` `add-cube-cbrt`
9×	`sqrt-div`
8×	`unswap-sqr`
7×	`pow1`
6×	`associate-l`
4×	`add-cbrt-cube` `add-exp-log`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`frac-times` `associate-*l/` `insert-posit16` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `div-inv`

Counts

2 → 66

Calls

2 calls:

192.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
64.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series587.0ms

Counts

2 → 6

Calls

2 calls:

368.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
219.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify3.6s

Counts

72 → 72

Iterations

Iter	Nodes
done	5002
3	1650
2	586
1	243
0	120

prune894.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 18.2b

localize11.0ms

Local error

Found 1 expressions with local error:

0.1b	(* z (sqrt 0.3333333333333333))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-r`
4×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
3×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log`
2×	`unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `insert-posit16` `add-log-exp`

Counts

1 → 23

Calls

1 calls:

17.0ms

(* z (sqrt 0.3333333333333333))

series69.0ms

Counts

1 → 3

Calls

1 calls:

68.0ms

(* z (sqrt 0.3333333333333333))

simplify8.3s

Counts

26 → 26

Iterations

Iter	Nodes
done	5001
5	3293
4	1018
3	365
2	158
1	74
0	38

prune200.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 18.2b

regimes3.1s

Accuracy

60.3% (7.9b remaining)

Error of 26.2b against oracle of 18.3b and baseline of 38.2b

bsearch282.0ms

Steps

Iters	Range		Point
6	3.1637000559480493e+109	2.0415539430385264e+110	1.5076748323158748e+110
8	8.055053755439609e-110	1.6612561150022382e-105	9.401516089224205e-110
9	1.2506859338201988e-136	1.1736359054906841e-130	2.0302680281655676e-131
10	-2.4334994185842963e+101	-6.019456552311765e+88	-2.061657435745164e+101

simplify26.0ms

Iterations

Iter	Nodes
done	38
2	38
1	35
0	30

end0.0ms

sample933.0ms

Algorithm

intervals

Results

593.0ms

8000×

body

valid