Details

Time bar (total: 7.4m)

sample60.0ms

Algorithm
intervals
Results
33.0ms256×body80valid
9.0ms256×pre80true

simplify152.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
152.0ms
(/ (/ (/ (+ (+ (+ 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: 4.3b

localize34.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (+ 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)

rewrite810.0ms

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
316.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
188.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
147.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
84.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

series529.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
209.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
166.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
129.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
25.0ms
(+ (+ 1.0 (+ beta alpha)) 2)

simplify7.1m

Counts
2150 → 1233
Calls
2150 calls:
Slowest
1.1s
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (cbrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
999.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
965.0ms
(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
931.0ms
(/ (/ (/ (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
888.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))

prune13.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.0b

localize82.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta)))
0.1b
(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta))) (- 2 (+ alpha beta)))
0.0b
(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta)))
0.0b
(* (/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta))) (- 2 (+ alpha beta))) (/ (- 2 (+ beta alpha)) (+ (+ 1.0 (+ beta alpha)) 2)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
6831×*-un-lft-identity
4944×times-frac
2638×distribute-lft-out
1980×add-sqr-sqrt
1390×add-cube-cbrt
822×associate-*l*
558×distribute-lft-out--
279×difference-of-squares
178×associate-/r/
166×associate-/l*
89×div-inv
88×flip3-+ flip-+
52×add-cbrt-cube add-exp-log
42×associate-*r*
26×cbrt-undiv div-exp
16×associate-/r*
8×prod-exp cbrt-unprod unswap-sqr
6×pow1
4×insert-posit16 add-log-exp associate-/l/
3×clear-num frac-2neg
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 2104
Calls
4 calls:
Slowest
575.0ms
(* (/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta))) (- 2 (+ alpha beta))) (/ (- 2 (+ beta alpha)) (+ (+ 1.0 (+ beta alpha)) 2)))
347.0ms
(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta))) (- 2 (+ alpha beta)))
262.0ms
(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta)))
192.0ms
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
620.0ms
(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta)))
228.0ms
(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta))) (- 2 (+ alpha beta)))
193.0ms
(* (/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta))) (+ 2 (+ alpha beta))) (- 2 (+ alpha beta))) (/ (- 2 (+ beta alpha)) (+ (+ 1.0 (+ beta alpha)) 2)))
115.0ms
(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ 2 (+ alpha beta)))