Details

sample45.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify118.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

118.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize29.0ms

Local error

Found 4 expressions with local error:

3.1b	(/ (+ 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)

rewrite445.0ms

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

204.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
79.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
76.0ms	(+ (+ 1.0 (+ beta alpha)) 2)
29.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series562.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

215.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
204.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
119.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
24.0ms	(+ (+ 1.0 (+ beta alpha)) 2)

simplify8.6m

Counts

2211 → 1246

Calls

2211 calls:

Slowest

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

prune15.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.4b

localize54.0ms

Local error

Found 4 expressions with local error:

10.6b	(/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha)))))
3.1b	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.1b	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
0.2b	(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha)))

rewrite653.0ms

Algorithm

rewrite-expression-head

Rules

19596×	`times-frac`
18914×	`*-un-lft-identity`
7243×	`distribute-lft-out`
6418×	`add-sqr-sqrt`
6412×	`add-cube-cbrt`
5164×	`sqrt-prod`
369×	`div-inv`
289×	`associate-/r/`
215×	`associate-/r*`
134×	`flip3-+` `flip-+`
36×	`add-exp-log`
32×	`associate-/l*`
27×	`add-cbrt-cube`
25×	`div-exp`
16×	`cbrt-undiv`
6×	`pow1` `sqrt-div`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`1-exp` `associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `hypot-def`

Counts

4 → 5621

Calls

4 calls:

Slowest

76.0ms	(/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha)))))
27.0ms	(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha)))
9.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
5.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series620.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

275.0ms	(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha)))
185.0ms	(/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha)))))
85.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
74.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))