Details

Time bar (total: 18.4s)

sample178.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
19.0ms283×body80nan

simplify35.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b
(/ (- 1.0 x) (+ 1.0 x))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
45×add-sqr-sqrt
41×times-frac
26×sqrt-prod
24×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
5×add-exp-log add-cbrt-cube associate-/l*
4×pow1 associate-/r* associate-/r/
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num flip--
Counts
3 → 97
Calls
3 calls:
40.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
53.0ms
(/ (- 1.0 x) (+ 1.0 x))

series232.0ms

Counts
3 → 9
Calls
3 calls:
144.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
7.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
80.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify1.6s

Counts
106 → 106
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01681479
13641398
213121313
done50011311

prune659.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
0.0b
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
0.0b
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
0.0b
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

rewrite482.0ms

Algorithm
rewrite-expression-head
Rules
184×*-un-lft-identity
91×times-frac
79×add-sqr-sqrt
55×distribute-lft-out
51×associate-*l*
44×unpow-prod-down cube-prod
36×add-cube-cbrt
19×distribute-lft-out-- difference-of-squares
11×add-exp-log sum-cubes add-cbrt-cube
9×pow1 associate-/r*
6×flip3-+ flip-+
5×sqrt-div associate-/l*
4×expm1-log1p-u frac-times associate-*r/ associate-/r/ log1p-expm1-u add-log-exp
3×associate-*r*
2×cbrt-undiv sqrt-pow1 div-exp pow-prod-down associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×distribute-rgt-in flip3-- frac-2neg distribute-lft-in pow1/2 div-sub clear-num sqrt-prod *-commutative flip--
Counts
4 → 183
Calls
4 calls:
77.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
1.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
97.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
290.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series420.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
15.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
76.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
117.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify3.1s

Counts
195 → 195
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
02534707
18334097
241213812
done50003812

prune1.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (- x 1.0))
0.0b
(* x (- x 1.0))
0.0b
(* (- 1.0 x) (- (pow 1.0 4) (* (* x (- x 1.0)) (* x (- x 1.0)))))
0.0b
(* (* x (- x 1.0)) (* x (- x 1.0)))

rewrite375.0ms

Algorithm
rewrite-expression-head
Rules
86×prod-diff
76×add-sqr-sqrt
75×distribute-rgt-in distribute-lft-in
68×*-un-lft-identity
62×add-cube-cbrt
49×pow1
22×add-exp-log add-cbrt-cube
20×associate-*r/ pow-prod-down
17×associate-*r*
14×flip3-- flip--
12×associate-*l*
11×prod-exp cbrt-unprod
10×sub-neg
8×frac-times
7×unpow-prod-down
6×difference-of-squares
4×expm1-log1p-u associate-*l/ pow-sqr *-commutative pow-prod-up log1p-expm1-u add-log-exp
3×distribute-lft-out-- unswap-sqr sqr-pow
2×pow-plus
1×pow2 swap-sqr
Counts
4 → 231
Calls
4 calls:
48.0ms
(* x (- x 1.0))
47.0ms
(* x (- x 1.0))
112.0ms
(* (- 1.0 x) (- (pow 1.0 4) (* (* x (- x 1.0)) (* x (- x 1.0)))))
143.0ms
(* (* x (- x 1.0)) (* x (- x 1.0)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* x (- x 1.0))
88.0ms
(* x (- x 1.0))
91.0ms
(* (- 1.0 x) (- (pow 1.0 4) (* (* x (- x 1.0)) (* x (- x 1.0)))))
68.0ms
(* (* x (- x 1.0)) (* x (- x 1.0)))

simplify1.1s

Counts
243 → 243
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03105537
110204701
done50014010

prune1.9s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize132.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- x 1.0) (- x 1.0))
0.0b
(/ (* (- (* 1.0 1.0) (* x x)) (- (pow 1.0 8) (* (* (- x 1.0) x) (pow (* x (- x 1.0)) 3)))) (* (fma (* x x) (* (- x 1.0) (- x 1.0)) (pow 1.0 4)) (+ 1.0 x)))
0.0b
(pow (* x (- x 1.0)) 3)
0.1b
(* (* (- x 1.0) x) (pow (* x (- x 1.0)) 3))

rewrite311.0ms

Algorithm
rewrite-expression-head
Rules
41×add-exp-log
36×*-un-lft-identity
32×add-sqr-sqrt
26×add-cbrt-cube
22×add-cube-cbrt
20×prod-exp
19×flip3-- flip--
18×prod-diff
16×associate-*r/
14×pow1
13×associate-*r*
12×frac-times associate-*l/
11×distribute-rgt-in distribute-lft-in
9×cbrt-unprod
8×cube-div associate-/l/
7×swap-sqr
6×associate-*l* pow-exp distribute-lft-out--
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp difference-of-squares
3×pow-to-exp pow-unpow
2×cube-mult sub-neg unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down associate-/r/ *-commutative rem-cube-cbrt sqr-pow
1×pow2 frac-2neg flip3-+ times-frac pow-plus clear-num associate-/r* pow-sqr pow-prod-up flip-+ div-inv associate-/l* unswap-sqr
Counts
4 → 161
Calls
4 calls:
78.0ms
(* (- x 1.0) (- x 1.0))
97.0ms
(/ (* (- (* 1.0 1.0) (* x x)) (- (pow 1.0 8) (* (* (- x 1.0) x) (pow (* x (- x 1.0)) 3)))) (* (fma (* x x) (* (- x 1.0) (- x 1.0)) (pow 1.0 4)) (+ 1.0 x)))
20.0ms
(pow (* x (- x 1.0)) 3)
102.0ms
(* (* (- x 1.0) x) (pow (* x (- x 1.0)) 3))

series521.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (- x 1.0) (- x 1.0))
286.0ms
(/ (* (- (* 1.0 1.0) (* x x)) (- (pow 1.0 8) (* (* (- x 1.0) x) (pow (* x (- x 1.0)) 3)))) (* (fma (* x x) (* (- x 1.0) (- x 1.0)) (pow 1.0 4)) (+ 1.0 x)))
88.0ms
(pow (* x (- x 1.0)) 3)
103.0ms
(* (* (- x 1.0) x) (pow (* x (- x 1.0)) 3))

simplify919.0ms

Counts
173 → 173
Iterations

Useful iterations: done (907.0ms)

IterNodesCost
03184286
110533872
done50013044

prune1.9s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify18.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03468
14168
24268
done4268

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.4s8000×body80valid
575.0ms8118×body80nan