Details

sample83.0ms

Algorithm

intervals

Results

51.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify112.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

112.0ms

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.6b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite546.0ms

Algorithm

rewrite-expression-head

Rules

4338×	`*-un-lft-identity`
2696×	`times-frac`
2176×	`distribute-lft-out`
779×	`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`
5×	`fma-def`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 1234

Calls

4 calls:

Slowest

211.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
127.0ms	(+ (+ 1.0 (+ beta alpha)) 2)
109.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
37.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

223.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
171.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
141.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
23.0ms	(+ (+ 1.0 (+ beta alpha)) 2)

simplify7.9m

Counts

2152 → 1246

Calls

2152 calls:

Slowest

1.2s	(/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
1.1s	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
1.1s	(/ (/ (/ (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
1.1s	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
1.0s	(/ (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 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

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite457.0ms

Algorithm

rewrite-expression-head

Rules

3887×	`*-un-lft-identity`
2732×	`times-frac`
1531×	`distribute-lft-out`
1080×	`add-sqr-sqrt`
792×	`add-cube-cbrt`
288×	`distribute-lft-out--`
172×	`associate-/l*`
144×	`difference-of-squares`
104×	`associate-/r/`
52×	`flip3-+` `flip-+` `div-inv`
22×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
11×	`cbrt-undiv` `div-exp`
6×	`associate-/l/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `flip--`
1×	`div-sub`

Counts

4 → 1277

Calls

4 calls:

Slowest

153.0ms	(/ (/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (+ (+ beta alpha) 2)) (- 2 (+ beta alpha)))
102.0ms	(/ (- 2 (+ beta alpha)) (+ (+ 1.0 (+ beta alpha)) 2))
78.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (+ (+ beta alpha) 2))
65.0ms	(/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2))

series588.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

230.0ms	(/ (/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (+ (+ beta alpha) 2)) (- 2 (+ beta alpha)))
197.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (+ (+ beta alpha) 2))
99.0ms	(/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2))
62.0ms	(/ (- 2 (+ beta alpha)) (+ (+ 1.0 (+ beta alpha)) 2))