Details

Time bar (total: 1.8m)

sample39.0ms

Algorithm
intervals
Results
27.0ms256×body80valid

simplify20.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
19.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
0.0b
(/ x (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
87×*-un-lft-identity
63×add-sqr-sqrt
62×times-frac
35×add-cube-cbrt
27×fma-def
14×difference-of-squares
12×distribute-lft-out
11×associate-/r*
9×add-exp-log distribute-lft-out--
7×add-cbrt-cube difference-of-sqr-1
6×associate-/r/ associate-/l*
5×add-log-exp
4×pow1 div-inv
3×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- flip-+ flip--
1×+-commutative rec-exp sum-log 1-exp frac-add pow-flip inv-pow
Counts
3 → 136
Calls
3 calls:
Slowest
67.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
8.0ms
(/ 1 (- x 1))
7.0ms
(/ x (+ x 1))

series141.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
89.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
29.0ms
(/ x (+ x 1))
23.0ms
(/ 1 (- x 1))

simplify4.5s

Counts
138 → 145
Calls
138 calls:
Slowest
355.0ms
(/ (* (* 1 1) 1) (* (* (- x 1) (- x 1)) (- x 1)))
349.0ms
(- (+ (* 2 (pow x 2)) (+ (* 2 (pow x 4)) 1)))
327.0ms
(/ (* (* x x) x) (* (* (+ x 1) (+ x 1)) (+ x 1)))
226.0ms
(+ (* 1 (+ x 1)) (* (- x 1) x))
216.0ms
(- (+ x (pow x 3)) (pow x 2))

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (+ (/ 1 (- x 1)) (/ x (+ x 1))))
0.0b
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
0.0b
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
0.0b
(+ (/ 1 (- x 1)) (/ x (+ x 1)))

rewrite702.0ms

Algorithm
rewrite-expression-head
Rules
157×*-un-lft-identity
95×times-frac
81×frac-times fma-def
75×add-sqr-sqrt
51×flip3-+ frac-add flip-+
38×add-cube-cbrt
32×distribute-lft-out
27×associate-*l/
23×pow1
18×difference-of-squares
17×distribute-lft-out--
15×associate-*r/
10×add-log-exp
9×add-cbrt-cube difference-of-sqr-1 associate-*r* add-exp-log
7×div-inv
6×pow-plus associate-/r/ pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×+-commutative sum-log flip3-- pow-prod-down prod-exp cbrt-unprod flip--
2×pow2 pow-sqr
1×distribute-rgt-in distribute-lft-in associate-*l* pow3 *-commutative unswap-sqr
Counts
4 → 246
Calls
4 calls:
Slowest
520.0ms
(* (* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (+ (/ 1 (- x 1)) (/ x (+ x 1))))
60.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
59.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
58.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))

series346.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
114.0ms
(* (* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (+ (/ 1 (- x 1)) (/ x (+ x 1))))
88.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
74.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))
70.0ms
(+ (/ 1 (- x 1)) (/ x (+ x 1)))

simplify48.6s

Counts
267 → 258
Calls
267 calls:
Slowest
1.1s
(* (* (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (/ x (+ x 1)) (/ x (+ x 1)))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (/ x (+ x 1)) (/ x (+ x 1))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (/ x (+ x 1)) (/ x (+ x 1)))))
1.0s
(* (* (+ (pow (/ 1 (- x 1)) 3) (pow (/ x (+ x 1)) 3)) (+ (* 1 (+ x 1)) (* (- x 1) x))) (+ (pow (/ 1 (- x 1)) 3) (pow (/ x (+ x 1)) 3)))
846.0ms
(* (* (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (/ x (+ x 1)) (/ x (+ x 1)))) (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (+ (* 1 (+ x 1)) (* (- x 1) x)))
757.0ms
(* (* (* (* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1))))) (* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1))))) (* (* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (+ (/ 1 (- x 1)) (/ x (+ x 1)))))
727.0ms
(* (* (+ (* 1 (+ x 1)) (* (- x 1) x)) (+ (pow (/ 1 (- x 1)) 3) (pow (/ x (+ x 1)) 3))) (+ (pow (/ 1 (- x 1)) 3) (pow (/ x (+ x 1)) 3)))

prune2.7s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize150.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1 (- x 1)) (/ 1 (- x 1)))
0.0b
(/ (/ 1 (- x 1)) (* (- x 1) (- x 1)))
0.0b
(/ (/ 1 (- x 1)) (* (- x 1) (- x 1)))
0.0b
(* (/ x (+ x 1)) (/ x (+ x 1)))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
322×times-frac
282×*-un-lft-identity
280×add-sqr-sqrt
136×add-cube-cbrt
100×add-exp-log
65×swap-sqr
54×pow1 associate-/l* difference-of-squares
52×add-cbrt-cube
45×associate-*r* associate-*l*
44×div-exp
40×associate-/r/
30×difference-of-sqr-1 distribute-lft-out--
28×prod-exp
20×cbrt-undiv flip3-- flip--
18×distribute-lft-out
16×div-inv pow-flip inv-pow pow-div
13×unswap-sqr
12×rec-exp 1-exp cbrt-unprod
10×frac-times pow-prod-up
8×pow-sqr
6×pow2 pow-plus associate-*l/ associate-*r/
4×expm1-log1p-u flip3-+ pow-prod-down flip-+ insert-posit16 log1p-expm1-u add-log-exp
2×clear-num associate-/r* frac-2neg *-commutative associate-/l/
1×un-div-inv
Counts
4 → 437
Calls
4 calls:
Slowest
72.0ms
(* (/ 1 (- x 1)) (/ 1 (- x 1)))
45.0ms
(/ (/ 1 (- x 1)) (* (- x 1) (- x 1)))
42.0ms
(/ (/ 1 (- x 1)) (* (- x 1) (- x 1)))
30.0ms
(* (/ x (+ x 1)) (/ x (+ x 1)))

series135.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
36.0ms
(* (/ x (+ x 1)) (/ x (+ x 1)))
36.0ms
(/ (/ 1 (- x 1)) (* (- x 1) (- x 1)))
32.0ms
(/ (/ 1 (- x 1)) (* (- x 1) (- x 1)))
31.0ms
(* (/ 1 (- x 1)) (/ 1 (- x 1)))

simplify40.4s

Counts
550 → 449
Calls
550 calls:
Slowest
705.0ms
(* (/ 1 (- (* x x) (* 1 1))) (/ 1 (- (* x x) (* 1 1))))
609.0ms
(/ (/ 1 (- (pow x 3) (pow 1 3))) (- x 1))
497.0ms
(* (/ (* (* 1 1) 1) (* (* (- x 1) (- x 1)) (- x 1))) (* (* (/ 1 (- x 1)) (/ 1 (- x 1))) (/ 1 (- x 1))))
477.0ms
(* (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))))
450.0ms
(+ (* 2 (/ 1 (pow x 3))) (+ (* 3 (/ 1 (pow x 4))) (/ 1 (pow x 2))))

prune7.6s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample838.0ms

Algorithm
intervals
Results
706.0ms8000×body80valid