Details

sample30.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	554
2	111
1	33
0	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.2b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
13×	`add-log-exp`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

116.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
385.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
571.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
393.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
163.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
184.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
108.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.6s

Counts

477 → 477

Iterations

Iter	Nodes
done	5001
1	1609
0	602

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize65.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite769.0ms

Algorithm

rewrite-expression-head

Rules

112×	`sqrt-prod`
98×	`*-un-lft-identity`
84×	`times-frac`
68×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
16×	`distribute-lft-out`
14×	`associate-/l*`
12×	`associate-/r*` `sqrt-div`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `add-log-exp` `associate-/l/`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 176

Calls

4 calls:

233.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
265.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
122.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
136.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series439.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
166.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
70.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
71.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.2s

Counts

188 → 188

Iterations

Iter	Nodes
done	5000
2	1095
1	330
0	160

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize91.0ms

Local error

Found 4 expressions with local error:

2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite435.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity` `sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

129.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
96.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
111.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
97.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series268.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
73.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
62.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
66.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	2030
2	401
1	125
0	55

prune549.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
8.3b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

7742×	`times-frac`
4062×	`*-un-lft-identity`
3062×	`add-sqr-sqrt`
3060×	`add-cube-cbrt`
2004×	`sqrt-prod`
501×	`distribute-lft-out`
193×	`div-inv`
185×	`associate-/r/`
89×	`associate-/r*`
82×	`flip3-+` `flip-+`
36×	`add-exp-log`
32×	`associate-/l*`
27×	`add-cbrt-cube`
25×	`div-exp`
16×	`cbrt-undiv`
6×	`pow1` `sqrt-div`
4×	`add-log-exp`
3×	`1-exp` `associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 2367

Calls

4 calls:

246.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
159.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
112.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
461.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
88.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
199.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

simplify4.6s

Counts

2379 → 2379

Iterations

Iter	Nodes
done	5000
0	2509

prune12.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

regimes189.0ms

Accuracy

61.4% (1.0b remaining)

Error of 2.3b against oracle of 1.3b and baseline of 3.8b

bsearch102.0ms

Steps

Iters	Range		Point
9	7.624367775541029e+182	5.1966063590768564e+188	7.725152532273347e+182

simplify14.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample1.2s

Algorithm

intervals

Results

728.0ms	8000×	body	80	valid
273.0ms	8000×	pre	80	true