Details

sample61.0ms

Algorithm

intervals

Results

15.0ms	194×	body	80	valid
8.0ms	20×	body	1280	valid
7.0ms	22×	body	640	valid
6.0ms	256×	pre	80	true
3.0ms	15×	body	320	valid
1.0ms	5×	body	160	valid

simplify2.1s

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: 23.6b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b

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

1.2b

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

20.8b

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

rewrite952.0ms

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:

205.0ms

(/ (/ (* (+ 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)

71.0ms

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

series808.0ms

Counts

3 → 9

Calls

3 calls:

332.0ms

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

372.0ms

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

103.0ms

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

simplify2.6s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	4479
1	697
0	225

prune863.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
0.0b	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
1.2b	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

1250×	`times-frac`
1055×	`*-un-lft-identity`
619×	`add-sqr-sqrt`
461×	`add-cube-cbrt`
218×	`distribute-lft-out`
96×	`associate-/l*`
79×	`distribute-lft-out--` `difference-of-squares`
60×	`associate-/r/`
33×	`div-inv`
30×	`associate-/r*`
26×	`flip3--` `flip--`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`associate-/l/`
4×	`pow1` `flip3-+` `flip-+`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log`

Counts

4 → 645

Calls

4 calls:

117.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
237.0ms	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
61.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
865.0ms	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
340.0ms	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
128.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
382.0ms	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify1.9s

Counts

657 → 657

Iterations

Iter	Nodes
done	5001
1	1924
0	705

prune3.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0b	(/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) 1) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.2b	(+ (* (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) 1) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite899.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
147×	`*-un-lft-identity`
128×	`add-sqr-sqrt`
77×	`add-cube-cbrt`
58×	`associate-l`
41×	`add-exp-log`
29×	`add-cbrt-cube`
26×	`associate-r`
24×	`distribute-lft-out`
19×	`div-exp`
12×	`associate-/r/`
11×	`cbrt-undiv`
10×	`prod-exp` `unswap-sqr`
9×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
8×	`flip3-+` `flip-+`
7×	`associate-/r*` `div-inv`
6×	`pow1` `cbrt-unprod` `add-log-exp`
4×	`1-exp` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `+-commutative` `sum-log` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 214

Calls

4 calls:

160.0ms	(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
70.0ms	(/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i)))
526.0ms	(* (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) 1) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
133.0ms	(+ (* (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) 1) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
111.0ms	(/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i)))
330.0ms	(* (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) 1) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
468.0ms	(+ (* (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) 1) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify1.3s

Counts

226 → 226

Iterations

Iter	Nodes
done	5000
1	1182
0	353

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)) (+ alpha beta))
0.2b	(/ 1 (/ (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)) (+ alpha beta)))
4.6b	(+ (/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

5615×	`times-frac`
3877×	`*-un-lft-identity`
2481×	`add-sqr-sqrt`
1995×	`add-cube-cbrt`
698×	`distribute-lft-out`
299×	`associate-/l*`
243×	`distribute-lft-out--` `difference-of-squares`
210×	`associate-/r/`
108×	`div-inv`
98×	`associate-/r*`
81×	`flip3--` `flip--`
62×	`add-exp-log`
43×	`div-exp`
32×	`add-cbrt-cube`
22×	`flip3-+` `flip-+`
19×	`cbrt-undiv`
6×	`rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
3×	`clear-num` `frac-2neg`
2×	`associate-/l/`
1×	`+-commutative` `sum-log` `pow-flip` `inv-pow`

Counts

4 → 1932

Calls

4 calls:

356.0ms	(/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
146.0ms	(/ (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)) (+ alpha beta))
117.0ms	(/ 1 (/ (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)) (+ alpha beta)))
1.5s	(+ (/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

394.0ms	(/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
182.0ms	(/ (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)) (+ alpha beta))
127.0ms	(/ 1 (/ (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)) (+ alpha beta)))
361.0ms	(+ (/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify2.8s

Counts

1944 → 1944

Iterations

Iter	Nodes
done	5000
0	1899

prune10.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

regimes431.0ms

Accuracy

-4.2% (6.7b remaining)

Error of 12.4b against oracle of 5.7b and baseline of 12.1b

bsearch86.0ms

Steps

Iters	Range		Point
6	1.2666592301982906e+45	6.124437830376974e+45	6.021952390523363e+45

simplify15.0ms

Iterations

Iter	Nodes
done	43
1	43
0	33

end0.0ms

sample1.8s

Algorithm

intervals

Results

551.0ms	6390×	body	80	valid
312.0ms	8000×	pre	80	true
274.0ms	539×	body	640	valid
211.0ms	522×	body	1280	valid
112.0ms	350×	body	320	valid
77.0ms	199×	body	160	valid