Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	202×	body	80	valid
5.0ms	256×	pre	80	true
5.0ms	27×	body	1280	valid
2.0ms	16×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	6×	body	160	valid

simplify916.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	52	13
4	73	13
5	118	13
6	149	13
7	177	13
8	208	13
9	246	13
10	274	13
11	285	13
12	297	13
13	301	13
done	301	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

80.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
183.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series147.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
79.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts

71 → 71

Iterations

Useful iterations: 3 (703.0ms)

Iter	Nodes	Cost
0	124	1134
1	320	1074
2	886	1014
3	2832	1006
done	5000	1006

prune209.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.2b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
31×	`times-frac`
28×	`add-sqr-sqrt`
24×	`distribute-lft-out`
23×	`add-cube-cbrt`
10×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 89

Calls

3 calls:

49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
226.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series293.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(/ alpha (+ (+ alpha beta) 2.0))
85.0ms	(/ beta (+ (+ alpha beta) 2.0))
118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: 3 (576.0ms)

Iter	Nodes	Cost
0	153	1237
1	326	1164
2	775	1090
3	2063	1082
done	5000	1082

prune355.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(cbrt (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
0.0b	(pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite894.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `times-frac`
18×	`cbrt-prod`
12×	`unpow-prod-down` `cube-prod` `distribute-lft-out`
10×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `associate-/r*` `distribute-lft-out--`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `flip--` `associate-/l*`
2×	`cube-mult` `cbrt-div` `unpow3` `associate-/r/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 112

Calls

4 calls:

52.0ms	(/ beta (+ (+ alpha beta) 2.0))
250.0ms	(cbrt (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
288.0ms	(pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)
299.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series623.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ beta (+ (+ alpha beta) 2.0))
150.0ms	(cbrt (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
295.0ms	(pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)
109.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify960.0ms

Counts

124 → 124

Iterations

Useful iterations: done (953.0ms)

Iter	Nodes	Cost
0	200	2172
1	468	1916
2	1266	1748
done	5001	1721

prune470.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.3b	(/ (/ beta (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
0.3b	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite539.0ms

Algorithm

rewrite-expression-head

Rules

560×	`*-un-lft-identity`
496×	`times-frac`
310×	`sqrt-prod`
233×	`add-sqr-sqrt`
228×	`add-cube-cbrt`
198×	`distribute-lft-out`
36×	`associate-/l*`
24×	`associate-/r/`
22×	`sqrt-div`
21×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
12×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

4 → 396

Calls

4 calls:

38.0ms	(/ alpha (+ (+ alpha beta) 2.0))
135.0ms	(/ (/ beta (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
55.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
277.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series323.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ alpha (+ (+ alpha beta) 2.0))
63.0ms	(/ (/ beta (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
97.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
98.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.6s

Counts

408 → 408

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	401	10674
1	891	8946
2	1870	8439
done	5000	8068

prune823.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

Details

sample33.0ms

simplify916.0ms

prune3.0ms

localize15.0ms

rewrite268.0ms

series147.0ms

simplify1.7s

prune209.0ms

localize12.0ms

rewrite325.0ms

series293.0ms

simplify1.6s

prune355.0ms

localize16.0ms

rewrite894.0ms

series623.0ms

simplify960.0ms

prune470.0ms

localize31.0ms

rewrite539.0ms

series323.0ms

simplify1.6s

prune823.0ms

regimes145.0ms

bsearch3.0ms