Details

sample74.0ms

Algorithm

intervals

Results

16.0ms	208×	body	80	valid
7.0ms	256×	pre	80	true
6.0ms	15×	body	1280	valid
5.0ms	15×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	5×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize22.0ms

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))

2.3b

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

22.2b

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

rewrite966.0ms

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:

217.0ms

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

667.0ms

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

72.0ms

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

series958.0ms

Counts

3 → 9

Calls

3 calls:

388.0ms

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

437.0ms

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

132.0ms

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

simplify3.3s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	4479
1	697
0	225

prune883.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.5b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite876.0ms

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:

42.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
244.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
399.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
158.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
244.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
349.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
453.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify1.5s

Counts

307 → 307

Iterations

Iter	Nodes
done	5001
1	1142
0	385

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize119.0ms

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	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (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)))))
4.8b	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (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)

rewrite4.7s

Algorithm

rewrite-expression-head

Rules

207×	`add-exp-log`
94×	`prod-exp`
87×	`div-exp`
84×	`add-cbrt-cube`
58×	`cbrt-unprod`
51×	`cbrt-undiv`
13×	`*-un-lft-identity`
12×	`1-exp`
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 → 121

Calls

4 calls:

90.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
64.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.3s	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (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	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (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)

series1.3s

Counts

4 → 12

Calls

4 calls:

299.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
224.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
344.0ms	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (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)))))
419.0ms	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (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)

simplify2.8s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
1	1213
0	337

prune805.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize97.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b	(cbrt (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
1.7b	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (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 (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))))
4.8b	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (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 (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))))) 1.0)

rewrite5.1s

Algorithm

rewrite-expression-head

Rules

207×	`add-exp-log`
94×	`prod-exp`
87×	`div-exp`
84×	`add-cbrt-cube`
82×	`cbrt-div`
58×	`cbrt-unprod`
51×	`cbrt-undiv`
37×	`frac-times`
33×	`flip3-+` `flip-+`
19×	`associate-*l/`
14×	`associate-*r/`
12×	`1-exp`
10×	`*-un-lft-identity`
9×	`pow1`
6×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
5×	`cbrt-prod`
4×	`associate-l`
3×	`pow-prod-down`
2×	`pow1/3` `distribute-lft-out`
1×	`+-commutative` `sum-log` `associate-r` `pow3` `*-commutative` `rem-cbrt-cube`

Counts

4 → 143

Calls

4 calls:

65.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
630.0ms	(cbrt (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
2.3s	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (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 (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))))
2.1s	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (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 (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))))) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

278.0ms	(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
271.0ms	(cbrt (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
358.0ms	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (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 (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))))
451.0ms	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (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 (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))))) 1.0)

simplify2.7s

Counts

155 → 155

Iterations

Iter	Nodes
done	5000
1	1364
0	432

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

regimes411.0ms

Accuracy

13.3% (5.8b remaining)

Error of 11.8b against oracle of 5.9b and baseline of 12.7b

bsearch182.0ms

Steps

Iters	Range		Point
9	2.5571677378596085e+141	6.851744006698495e+147	6.818670779247876e+145

simplify31.0ms

Iterations

Iter	Nodes
done	54
1	54
0	41

end0.0ms

sample2.5s

Algorithm

intervals

Results

707.0ms	6316×	body	80	valid
691.0ms	8000×	pre	80	true
305.0ms	519×	body	1280	valid
198.0ms	582×	body	640	valid
136.0ms	385×	body	320	valid
34.0ms	198×	body	160	valid