Details

Time bar (total: 11.2s)

sample289.0ms

Algorithm
intervals
Results
65.0ms284×body80nan
39.0ms256×body80valid

simplify80.0ms

Counts
1 → 1
Iterations
IterNodes
done23
323
221
118
09

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
79×*-un-lft-identity
56×add-sqr-sqrt
49×times-frac
30×sqrt-prod
26×add-cube-cbrt
18×difference-of-squares
13×distribute-lft-out
9×distribute-lft-out--
6×associate-/l*
5×add-cbrt-cube add-exp-log
4×pow1 associate-/r* associate-/r/
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub div-exp flip--
Counts
3 → 109
Calls
3 calls:
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))
10.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
19.0ms
(/ (- 1 x) (+ 1 x))

series107.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))
59.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
42.0ms
(/ (- 1 x) (+ 1 x))

simplify1.2s

Counts
118 → 118
Iterations
IterNodes
done2001
32001
2795
1360
0174

prune410.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
627×*-un-lft-identity
510×times-frac
358×add-sqr-sqrt
324×prod-diff
323×add-cube-cbrt
129×distribute-lft-out
86×associate-/r/
51×div-inv
43×flip3-+ flip-+
23×sqrt-prod
18×fma-neg
16×distribute-lft-out--
12×distribute-rgt-out-- difference-of-squares
10×add-exp-log
8×associate-/r* add-cbrt-cube
6×pow1 associate-/l* add-log-exp
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u
3×div-exp
2×cbrt-undiv clear-num frac-2neg flip3-- frac-sub flip-- sub-div
1×rem-sqrt-square rec-exp sub-neg sqrt-pow1 pow1/2 diff-log 1-exp pow-flip inv-pow
Counts
4 → 495
Calls
4 calls:
79.0ms
(sqrt (- (/ 1 (+ 1 x)) (/ x (+ 1 x))))
16.0ms
(/ x (+ 1 x))
17.0ms
(/ 1 (+ 1 x))
95.0ms
(- (/ 1 (+ 1 x)) (/ x (+ 1 x)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(sqrt (- (/ 1 (+ 1 x)) (/ x (+ 1 x))))
41.0ms
(/ x (+ 1 x))
25.0ms
(/ 1 (+ 1 x))
52.0ms
(- (/ 1 (+ 1 x)) (/ x (+ 1 x)))

simplify1.3s

Counts
507 → 507
Iterations
IterNodes
done2004
22004
11083
0486

prune1.6s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt x)
0.7b
(cbrt x)
0.7b
(cbrt x)
58.1b
(fma (- (/ (cbrt x) (+ 1 x))) (/ (* (cbrt x) (cbrt x)) 1) (* (/ (cbrt x) (+ 1 x)) (/ (* (cbrt x) (cbrt x)) 1)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 53
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
2.0ms
(cbrt x)
1.0ms
(fma (- (/ (cbrt x) (+ 1 x))) (/ (* (cbrt x) (cbrt x)) 1) (* (/ (cbrt x) (+ 1 x)) (/ (* (cbrt x) (cbrt x)) 1)))

series972.0ms

Counts
4 → 12
Calls
4 calls:
264.0ms
(cbrt x)
257.0ms
(cbrt x)
269.0ms
(cbrt x)
181.0ms
(fma (- (/ (cbrt x) (+ 1 x))) (/ (* (cbrt x) (cbrt x)) 1) (* (/ (cbrt x) (+ 1 x)) (/ (* (cbrt x) (cbrt x)) 1)))

simplify1.4s

Counts
65 → 65
Iterations
IterNodes
done2000
42000
3878
2250
195
050

prune571.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify9.0ms

Iterations
IterNodes
done38
238
133
022

end0.0ms

sample2.6s

Algorithm
intervals
Results
1000.0ms8000×body80valid
943.0ms8057×body80nan