Details

sample30.0ms

Algorithm

intervals

Results

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

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	111	35
3	550	35
4	4087	35
done	5000	35

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize28.0ms

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))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.7s

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-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

139.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
377.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
754.0ms	(/ (/ (/ (+ (+ (+ 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))
402.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
204.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
235.0ms	(/ (/ (/ (+ (+ (+ 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))
101.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.6s

Counts

477 → 477

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	603	25954
1	1443	25182
2	4754	24241
done	5001	23501

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
0.0b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.3s

Algorithm

rewrite-expression-head

Rules

18109×	`times-frac`
9724×	`*-un-lft-identity`
6724×	`add-sqr-sqrt` `add-cube-cbrt`
1500×	`distribute-lft-out`
792×	`associate-/l*`
684×	`div-inv`
572×	`associate-/r/`
245×	`flip3-+` `flip-+`
154×	`add-exp-log`
134×	`div-exp`
84×	`associate-/r*`
61×	`add-cbrt-cube`
41×	`cbrt-undiv`
30×	`1-exp`
12×	`rec-exp`
6×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 4911

Calls

4 calls:

354.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
336.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
1.1s	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
424.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

217.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
210.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
693.0ms	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
98.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify3.0s

Counts

4923 → 4923

Iterations

Useful iterations: 0 (872.0ms)

Iter	Nodes	Cost
0	5274	351082
done	5274	351082

prune23.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (cbrt 1)) (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
0.1b	(/ (/ 1 (* (cbrt 1) (cbrt 1))) (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

12733×	`times-frac`
6141×	`*-un-lft-identity`
5301×	`sqrt-prod`
5009×	`add-sqr-sqrt` `add-cube-cbrt`
1188×	`cbrt-prod`
566×	`distribute-lft-out`
485×	`div-inv`
409×	`associate-/r/`
268×	`associate-/r*`
190×	`flip3-+` `flip-+`
75×	`add-exp-log`
47×	`div-exp`
37×	`associate-/l*`
35×	`add-cbrt-cube`
31×	`sqrt-div`
23×	`cbrt-undiv`
6×	`rec-exp` `1-exp` `prod-exp` `associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`
2×	`cbrt-unprod`

Counts

4 → 4216

Calls

4 calls:

475.0ms	(/ (/ 1 (cbrt 1)) (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
399.0ms	(/ (/ 1 (* (cbrt 1) (cbrt 1))) (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
444.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
503.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series799.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(/ (/ 1 (cbrt 1)) (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
333.0ms	(/ (/ 1 (* (cbrt 1) (cbrt 1))) (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
97.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
104.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.9s

Counts

4228 → 4228

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	3647	286778
done	5001	269745

prune28.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite742.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-prod` `times-frac`
7×	`distribute-lft-out`
6×	`add-exp-log` `cbrt-div` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`pow1` `associate-/l*` `add-log-exp`
3×	`pow1/3` `associate-/r*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 77

Calls

4 calls:

447.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
86.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
92.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
112.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series389.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
106.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
88.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
96.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.0s

Counts

89 → 89

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	141	2116
1	367	2064
2	1241	1904
done	5001	1848

prune912.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes101.0ms

Accuracy

59.2% (1.6b remaining)

Error of 1.7b against oracle of 0.0b and baseline of 4.1b

bsearch105.0ms

Steps

Iters	Range		Point
7	9.711408253067022e+141	2.2840282335092652e+144	1.4606790468840281e+143

simplify17.0ms

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	36	107
1	48	94
done	48	94

end0.0ms

sample1.4s

Algorithm

intervals

Results

720.0ms	8000×	body	80	valid
391.0ms	8000×	pre	80	true