Details

sample73.0ms

Algorithm

intervals

Results

21.0ms	220×	body	80	valid
9.0ms	17×	body	1280	valid
8.0ms	256×	pre	80	true
4.0ms	10×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify4.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	29
1	39	29
2	183	29
3	3003	29
done	5001	29

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.3b

localize16.0ms

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))

1.3b

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

18.0b

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

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

218.0ms

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

848.0ms

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

77.0ms

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

series966.0ms

Counts

3 → 9

Calls

3 calls:

402.0ms

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

427.0ms

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

137.0ms

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

simplify15.0s

Counts

120 → 120

Iterations

Useful iterations: done (15.0s)

Iter	Nodes	Cost
0	225	4035
1	2011	3821
done	5000	3581

prune490.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.1b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.2b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite1.0s

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-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3--` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip--`

Counts

4 → 295

Calls

4 calls:

277.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
59.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
135.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
532.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

267.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
98.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
441.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
353.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify1.2s

Counts

307 → 307

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	385	9712
done	5000	9243

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.1b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.1b	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
2.2b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
151×	`*-un-lft-identity`
116×	`add-sqr-sqrt`
90×	`associate-r`
75×	`add-cube-cbrt`
22×	`distribute-lft-out`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
9×	`flip3-+` `flip-+`
7×	`pow1`
6×	`div-inv` `add-log-exp`
5×	`associate-/l*`
4×	`cbrt-undiv` `log-prod` `div-exp` `associate-l` `log-pow`
3×	`exp-prod` `prod-exp` `associate-/r*` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `associate-*l/` `associate-/l/`
1×	`+-commutative` `flip3--` `frac-2neg` `div-sub` `associate-r/` `rem-log-exp` `exp-sum` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip--`

Counts

4 → 184

Calls

4 calls:

54.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
123.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
565.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
602.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
414.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
447.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
362.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify3.1s

Counts

196 → 196

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	325	5447
1	4903	5080
done	5001	5036

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.2b	(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
5.7b	(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

6211×	`times-frac`
4294×	`*-un-lft-identity`
3048×	`add-sqr-sqrt`
2585×	`sqrt-prod`
2326×	`add-cube-cbrt`
1077×	`associate-r`
645×	`distribute-lft-out`
339×	`distribute-lft-out--` `difference-of-squares`
262×	`associate-/r/`
174×	`associate-/l*`
134×	`flip3-+` `flip-+`
131×	`div-inv`
36×	`sqrt-div`
32×	`add-exp-log` `add-cbrt-cube`
15×	`cbrt-undiv` `div-exp`
14×	`associate-/r*`
11×	`unswap-sqr`
6×	`pow1` `add-log-exp`
5×	`div-sub`
4×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `associate-r/` `pow-prod-down` `sum-log` `-commutative`

Counts

4 → 2569

Calls

4 calls:

627.0ms	(/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
321.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.4s	(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
321.0ms	(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.8s

Counts

4 → 12

Calls

4 calls:

261.0ms	(/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
361.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
762.0ms	(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
408.0ms	(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify2.7s

Counts

2581 → 2581

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	1739	137324
done	5001	126881

prune9.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.0b

regimes341.0ms

Accuracy

72.3% (1.7b remaining)

Error of 7.5b against oracle of 5.8b and baseline of 12.1b

bsearch4.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	82
1	52	82
done	52	82

end0.0ms

sample2.3s

Algorithm

intervals

Results

627.0ms	549×	body	640	valid
624.0ms	6390×	body	80	valid
268.0ms	8000×	pre	80	true
257.0ms	491×	body	1280	valid
89.0ms	381×	body	320	valid
29.0ms	189×	body	160	valid