Details

sample70.0ms

Algorithm

intervals

Results

41.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify135.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

135.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.6b

localize31.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.0b	(+ (+ 1.0 (+ beta alpha)) 2)

rewrite1000.0ms

Algorithm

rewrite-expression-head

Rules

4332×	`*-un-lft-identity`
2696×	`times-frac`
2173×	`distribute-lft-out`
778×	`add-sqr-sqrt` `add-cube-cbrt`
166×	`associate-/l*`
102×	`associate-/r/`
53×	`flip3-+` `flip-+`
51×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
6×	`sum-log`
4×	`pow1` `insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 1221

Calls

4 calls:

Slowest

339.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
257.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
170.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
102.0ms	(+ (+ 1.0 (+ beta alpha)) 2)

series508.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

191.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
177.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
123.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
16.0ms	(+ (+ 1.0 (+ beta alpha)) 2)

simplify7.2m

Counts

2150 → 1233

Calls

2150 calls:

Slowest

996.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
982.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
948.0ms	(/ (/ (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
918.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 1.0 (+ beta alpha)) 2))
915.0ms	(/ (/ (- 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

prune13.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.8b

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta)))
0.1b	(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 1.0 (+ 2 (+ alpha beta)))) (+ 2 (+ alpha beta)))
0.0b	(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 1.0 (+ 2 (+ alpha beta))))
0.0b	(+ (+ (* beta alpha) (+ alpha beta)) 1.0)

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

4588×	`*-un-lft-identity`
2782×	`times-frac`
2340×	`distribute-lft-out`
797×	`add-sqr-sqrt` `add-cube-cbrt`
192×	`associate-/l*`
104×	`associate-/r/`
54×	`flip3-+` `flip-+`
52×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
6×	`sum-log`
4×	`pow1` `insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 1265

Calls

4 calls:

Slowest

423.0ms	(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 1.0 (+ 2 (+ alpha beta)))) (+ 2 (+ alpha beta)))
347.0ms	(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 1.0 (+ 2 (+ alpha beta))))
234.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta)))
92.0ms	(+ (+ (* beta alpha) (+ alpha beta)) 1.0)

series956.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

647.0ms	(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 1.0 (+ 2 (+ alpha beta)))) (+ 2 (+ alpha beta)))
166.0ms	(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 1.0 (+ 2 (+ alpha beta))))
114.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta)))
29.0ms	(+ (+ (* beta alpha) (+ alpha beta)) 1.0)