Details

sample23.0ms

Algorithm

intervals

Results

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

simplify79.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17
done	5002	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.9b

localize12.0ms

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))
5.5b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

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:

105.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
328.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
477.0ms	(/ (/ (/ (+ (+ (+ 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))
283.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
149.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
161.0ms	(/ (/ (/ (+ (+ (+ 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))
76.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify124.0ms

Counts

477 → 477

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552
done	5002	12552

prune986.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.5b

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))) (* 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
5.5b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

354×	`times-frac`
220×	`*-un-lft-identity`
150×	`add-sqr-sqrt` `add-cube-cbrt`
82×	`associate-/l*`
41×	`add-exp-log`
35×	`distribute-lft-out`
32×	`add-cbrt-cube`
30×	`associate-/r/`
22×	`div-exp`
17×	`flip3-+` `flip-+`
16×	`cbrt-undiv`
15×	`div-inv`
13×	`add-log-exp`
7×	`associate-/r*`
6×	`prod-exp` `sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
2×	`associate-*r/`
1×	`+-commutative` `associate-+l+`

Counts

4 → 291

Calls

4 calls:

106.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
327.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
429.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (* 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
280.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
152.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
155.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (* 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
83.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify77.0ms

Counts

303 → 303

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1121	6337
1	5001	5855
done	5001	5855

prune705.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
5.5b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.5b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite803.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
80×	`sqrt-prod`
70×	`times-frac`
56×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
22×	`distribute-lft-out`
13×	`associate-/r*`
11×	`associate-/l*`
10×	`sqrt-div`
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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`
1×	`sqrt-undiv`

Counts

4 → 159

Calls

4 calls:

363.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
205.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
113.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
116.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series432.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
111.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
53.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
49.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify67.0ms

Counts

171 → 171

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	507	2617
1	1942	2448
2	5003	2394
done	5003	2394

prune471.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (* 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
16.5b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
61×	`add-cbrt-cube`
56×	`*-un-lft-identity`
55×	`times-frac`
50×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
33×	`div-exp`
26×	`prod-exp`
24×	`cbrt-undiv`
22×	`associate-l`
17×	`cbrt-unprod`
15×	`associate-r`
10×	`associate-/r/`
9×	`distribute-lft-out` `difference-of-squares`
8×	`associate-/r` `associate-/l`
7×	`associate-/l/`
6×	`pow1`
5×	`1-exp` `div-inv`
4×	`flip3-+` `associate-*r/` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `frac-2neg` `clear-num` `flip--`
2×	`frac-times` `associate-*l/`
1×	`div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 176

Calls

4 calls:

95.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
530.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
269.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (* 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
287.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

series818.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
419.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
232.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (* 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
122.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

simplify63.0ms

Counts

188 → 188

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	998	4329
1	5001	3526
done	5001	3526

prune506.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.5b

regimes74.0ms

Accuracy

42.5% (1.4b remaining)

Error of 2.6b against oracle of 1.2b and baseline of 3.6b

bsearch47.0ms

Steps

Iters	Range		Point
6	2.425829213074854e+127	3.660299660418296e+128	3.553719024558119e+128

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	34
1	44	34
2	44	34
done	44	34

end0.0ms

sample544.0ms

Algorithm

intervals

Results

280.0ms	8000×	body	80	valid
84.0ms	8000×	pre	80	true