Details

sample22.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	110	35
3	480	35
4	2398	35
done	5001	35

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.4b

localize18.0ms

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))
5.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite655.0ms

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:

56.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
169.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
253.0ms	(/ (/ (/ (+ (+ (+ 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))
143.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
135.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
149.0ms	(/ (/ (/ (+ (+ (+ 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))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify551.0ms

Counts

477 → 477

Iterations

Useful iterations: done (525.0ms)

Iter	Nodes	Cost
0	603	25954
1	1491	25182
done	5002	25025

prune999.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize16.0ms

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))))
5.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite347.0ms

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×	`sqrt-div` `associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 176

Calls

4 calls:

109.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
108.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
61.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series296.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
100.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
49.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify953.0ms

Counts

188 → 188

Iterations

Useful iterations: 3 (396.0ms)

Iter	Nodes	Cost
0	160	5606
1	326	5098
2	828	4954
3	2423	4918
done	5001	4918

prune484.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize17.0ms

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) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (- (+ alpha beta) (* 2.0 1.0))))
2.4b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
5.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite871.0ms

Algorithm

rewrite-expression-head

Rules

4776×	`times-frac`
2643×	`*-un-lft-identity`
1673×	`add-sqr-sqrt` `add-cube-cbrt`
485×	`distribute-lft-out`
363×	`associate-/r/`
361×	`difference-of-squares`
182×	`div-inv`
100×	`associate-/l*`
99×	`flip3--` `flip--`
84×	`flip3-+` `flip-+`
32×	`add-exp-log` `add-cbrt-cube`
25×	`associate-/r*`
19×	`cbrt-undiv` `div-exp`
13×	`add-log-exp`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 1685

Calls

4 calls:

55.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
304.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (- (+ alpha beta) (* 2.0 1.0))))
172.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
143.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
220.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (- (+ alpha beta) (* 2.0 1.0))))
169.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify814.0ms

Counts

1697 → 1697

Iterations

Useful iterations: 0 (273.0ms)

Iter	Nodes	Cost
0	2253	157982
done	5000	157982

prune5.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) (* 2.0 1.0)))
2.4b	(* (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0))) (/ 1 (- (+ alpha beta) (* 2.0 1.0)))))
5.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite7.6s

Algorithm

rewrite-expression-head

Rules

8670×	`times-frac`
3912×	`*-un-lft-identity`
3768×	`add-sqr-sqrt`
3188×	`add-cube-cbrt`
2255×	`associate-r`
1185×	`sqrt-prod`
978×	`cbrt-prod`
527×	`associate-/r/`
399×	`add-exp-log`
347×	`distribute-lft-out`
267×	`div-exp`
258×	`associate-l`
236×	`cbrt-div`
228×	`div-inv`
195×	`add-cbrt-cube`
165×	`flip3--` `flip--`
138×	`cbrt-undiv`
125×	`flip3-+` `flip-+`
95×	`unswap-sqr`
78×	`prod-exp`
49×	`frac-times`
42×	`cbrt-unprod`
25×	`associate-r/` `associate-l/`
15×	`rec-exp` `1-exp`
8×	`pow1`
4×	`sqrt-div` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow1/3` `pow-prod-down` `*-commutative`

Counts

4 → 2765

Calls

4 calls:

8.0ms	(cbrt (+ (+ alpha beta) (* 2.0 1.0)))
7.0s	(* (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0))) (/ 1 (- (+ alpha beta) (* 2.0 1.0)))))
58.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series348.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (+ (+ alpha beta) (* 2.0 1.0)))
153.0ms	(* (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0))) (/ 1 (- (+ alpha beta) (* 2.0 1.0)))))
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
54.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.6s

Counts

2777 → 2777

Iterations

Useful iterations: 0 (489.0ms)

Iter	Nodes	Cost
0	4092	256302
done	5000	256302

prune12.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.8b

regimes78.0ms

Accuracy

55.4% (1.1b remaining)

Error of 2.3b against oracle of 1.1b and baseline of 3.7b

bsearch77.0ms

Steps

Iters	Range		Point
9	1.68690722297182e+158	2.212909629018009e+163	6.85580170450604e+160

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	104
1	44	104
done	44	104

end0.0ms

sample521.0ms

Algorithm

intervals

Results

290.0ms	8000×	body	80	valid
93.0ms	8000×	pre	80	true