Details

Time bar (total: 9.2m)

sample44.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
7.0ms256×pre80true

simplify125.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
125.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize31.0ms

Local error

Found 4 expressions with local error:

3.2b
(/ (+ 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 (+ beta alpha)) 2)
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite440.0ms

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
166.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
93.0ms
(+ (+ 1.0 (+ beta alpha)) 2)
79.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
36.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series557.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
238.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
176.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
127.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
15.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify8.1m

Counts
2152 → 1246
Calls
2152 calls:
Slowest
1.2s
(/ (/ (/ (cbrt (+ 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))) (+ 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))
1.0s
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
996.0ms
(/ (/ (- 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))

prune14.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

3.2b
(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
0.1b
(/ (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b
(/ 1 (+ 2 (+ beta alpha)))
0.0b
(+ (+ 1.0 (+ beta alpha)) 2)

rewrite449.0ms

Algorithm
rewrite-expression-head
Rules
246×*-un-lft-identity
133×times-frac
124×distribute-lft-out
58×add-sqr-sqrt
51×add-cube-cbrt
39×add-exp-log
25×add-cbrt-cube
21×associate-*r*
20×associate-/r/
17×div-exp
14×associate-/l*
13×flip3-+ flip-+ add-log-exp
11×associate-/r*
10×cbrt-undiv div-inv
8×prod-exp
7×pow1
6×sum-log
5×fma-def
4×expm1-log1p-u associate-*l* cbrt-unprod insert-posit16 log1p-expm1-u
3×rec-exp 1-exp unswap-sqr
2×frac-times clear-num frac-2neg associate-*l/
1×+-commutative associate-+l+ pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow associate-/l/
Counts
4 → 230
Calls
4 calls:
Slowest
184.0ms
(/ (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
121.0ms
(+ (+ 1.0 (+ beta alpha)) 2)
101.0ms
(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
38.0ms
(/ 1 (+ 2 (+ beta alpha)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
268.0ms
(/ (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
128.0ms
(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
45.0ms
(/ 1 (+ 2 (+ beta alpha)))
15.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify46.4s

Counts
268 → 242
Calls
268 calls:
Slowest
694.0ms
(/ (* (* (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))) (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))) (* (* (+ (+ 1.0 (+ beta alpha)) 2) (+ (+ 1.0 (+ beta alpha)) 2)) (+ (+ 1.0 (+ beta alpha)) 2)))
600.0ms
(/ (/ 1 (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
592.0ms
(/ (/ 1 (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
580.0ms
(- (- (+ (log (+ 1.0 (fma beta alpha (+ beta alpha)))) (- 0 (log (+ 2 (+ beta alpha))))) (log (+ 2 (+ beta alpha)))) (log (+ (+ 1.0 (+ beta alpha)) 2)))
569.0ms
(/ (/ (/ 1 (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))

prune2.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

3.2b
(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
3.2b
(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
0.1b
(/ (sqrt (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))))))
0.1b
(/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))))

rewrite707.0ms

Algorithm
rewrite-expression-head
Rules
3821×*-un-lft-identity
3559×times-frac
2057×sqrt-prod
1931×distribute-lft-out
839×add-sqr-sqrt
825×add-cube-cbrt
395×associate-/r/
206×div-inv
194×flip3-+ flip-+
103×associate-/r*
42×associate-*r*
29×add-exp-log
21×add-cbrt-cube
20×associate-/l*
17×sqrt-div
8×pow1 div-exp associate-*l* prod-exp
6×cbrt-undiv unswap-sqr
4×expm1-log1p-u frac-times associate-*l/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l/
2×rec-exp clear-num frac-2neg 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative
Counts
4 → 1594
Calls
4 calls:
Slowest
275.0ms
(/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))))
170.0ms
(/ (sqrt (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))))))
63.0ms
(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
57.0ms
(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

series835.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
373.0ms
(/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))))
181.0ms
(/ (sqrt (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))) (/ (+ (+ 1.0 (+ beta alpha)) 2) (sqrt (/ (* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))))))
157.0ms
(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
124.0ms
(* (+ 1.0 (fma beta alpha (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))