Details

sample78.0ms

Algorithm

intervals

Results

21.0ms	203×	body	80	valid
10.0ms	18×	body	1280	valid
9.0ms	256×	pre	80	true
6.0ms	13×	body	640	valid
5.0ms	16×	body	320	valid
1.0ms	6×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	102	29
3	453	29
4	2483	29
done	5001	29

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize32.0ms

Local error

Found 3 expressions with local error:

0.1b

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

1.6b

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

20.7b

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite987.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`add-cbrt-cube` `add-exp-log`
14×	`associate-/r/`
11×	`flip3-+` `flip-+` `distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `associate-/r*` `div-exp` `div-inv`
5×	`add-log-exp`
4×	`frac-times`
3×	`pow1` `flip3--` `flip--`
2×	`clear-num` `frac-2neg` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 111

Calls

3 calls:

249.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

672.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

62.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series1.0s

Counts

3 → 9

Calls

3 calls:

427.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

450.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

135.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.1s

Counts

120 → 120

Iterations

Useful iterations: 2 (705.0ms)

Iter	Nodes	Cost
0	225	4035
1	697	3821
2	4479	3581
done	5001	3581

prune573.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.5b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite744.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac`
290×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/l*`
24×	`associate-/r/`
20×	`add-cbrt-cube` `add-exp-log`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/`
1×	`+-commutative` `sum-log` `flip3--` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

4 → 295

Calls

4 calls:

39.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
178.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
392.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
112.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
238.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
404.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
255.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify590.0ms

Counts

307 → 307

Iterations

Useful iterations: done (570.0ms)

Iter	Nodes	Cost
0	381	9700
1	1138	9275
done	5001	8945

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.5b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
4.5b	(log (exp (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
274×	`*-un-lft-identity`
195×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
27×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
21×	`associate-/l*`
18×	`add-cbrt-cube` `add-exp-log`
14×	`flip3-+` `flip-+`
11×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`log-prod` `associate-/r` `associate-l*` `log-pow`
3×	`exp-prod` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `div-sub` `associate-*l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `rem-log-exp` `exp-sum` `pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 271

Calls

4 calls:

225.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
410.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
104.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
468.0ms	(log (exp (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

267.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
356.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
256.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
281.0ms	(log (exp (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

simplify566.0ms

Counts

283 → 283

Iterations

Useful iterations: done (551.0ms)

Iter	Nodes	Cost
0	392	9601
1	1163	9170
done	5001	8766

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize75.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(* (+ beta alpha) (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
5.0b	(+ (* (+ beta alpha) (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite4.5s

Algorithm

rewrite-expression-head

Rules

90×	`add-exp-log`
51×	`add-cbrt-cube`
43×	`prod-exp` `cbrt-unprod`
27×	`cbrt-undiv` `div-exp`
13×	`*-un-lft-identity`
9×	`frac-times` `pow1`
8×	`cbrt-prod`
7×	`add-sqr-sqrt` `flip3-+` `add-cube-cbrt` `flip-+`
6×	`associate-*r/` `add-log-exp`
5×	`associate-*l/`
4×	`cbrt-div` `associate-l`
3×	`pow-prod-down` `distribute-lft-out`
2×	`pow1/3`
1×	`+-commutative` `sum-log` `associate-r` `*-commutative`

Counts

4 → 97

Calls

4 calls:

68.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
60.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.1s	(* (+ beta alpha) (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
2.2s	(+ (* (+ beta alpha) (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

237.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
241.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
338.0ms	(* (+ beta alpha) (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
261.0ms	(+ (* (+ beta alpha) (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify2.5s

Counts

109 → 109

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	267	6726
1	892	6288
2	4822	3609
done	5001	3603

prune791.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

regimes410.0ms

Accuracy

19.9% (5.3b remaining)

Error of 11.3b against oracle of 5.9b and baseline of 12.6b

bsearch103.0ms

Steps

Iters	Range		Point
8	1.538992510133342e+149	5.820374342875008e+152	1.142935579114712e+152

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	52
1	38	52
2	39	52
done	39	52

end0.0ms

sample2.2s

Algorithm

intervals

Results

681.0ms	6318×	body	80	valid
329.0ms	8000×	pre	80	true
308.0ms	512×	body	1280	valid
251.0ms	598×	body	640	valid
139.0ms	363×	body	320	valid
35.0ms	209×	body	160	valid