Details

Time bar (total: 16.2s)

sample140.0ms

Algorithm
intervals
Results
50.0ms501×body80nan
43.0ms243×body160nan
26.0ms256×body80valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
82237
7713
6239
597
460
335
219
116
07

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1)))
31.8b
(sqrt (- (* x x) 1))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity sqrt-prod
5×add-sqr-sqrt
4×add-log-exp
3×pow1 add-cube-cbrt
2×add-cbrt-cube sqrt-div add-exp-log insert-posit16 difference-of-squares
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ flip3-- pow1/2 difference-of-sqr-1 flip-+ flip-- distribute-lft-out
Counts
2 → 32
Calls
2 calls:
24.0ms
(+ x (sqrt (- (* x x) 1)))
17.0ms
(sqrt (- (* x x) 1))

series137.0ms

Counts
2 → 6
Calls
2 calls:
79.0ms
(+ x (sqrt (- (* x x) 1)))
58.0ms
(sqrt (- (* x x) 1))

simplify1.4s

Counts
38 → 38
Iterations
IterNodes
43053
31225
2471
1208
091

prune364.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.5b
(* (sqrt (+ x 1)) (sqrt (- x 1)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×sqrt-prod
12×sqrt-div
11×*-un-lft-identity
10×associate-*r*
7×associate-*l*
6×pow1 add-cube-cbrt
4×frac-times flip3-+ add-cbrt-cube add-exp-log flip-+ add-log-exp unswap-sqr
3×flip3-- pow-prod-down flip--
2×sqrt-pow1 pow1/2 associate-*l/ associate-*r/ insert-posit16 difference-of-squares
1×+-commutative sum-log sqrt-unprod difference-of-sqr-1 prod-exp *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 56
Calls
2 calls:
5.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
32.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))

series173.0ms

Counts
2 → 6
Calls
2 calls:
80.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
92.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify3.8s

Counts
62 → 62
Iterations
IterNodes
45995
31834
2693
1295
0132

prune534.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (sqrt (- x 1)))
0.5b
(cbrt (sqrt (- x 1)))
0.5b
(cbrt (sqrt (- x 1)))
0.5b
(* (cbrt (sqrt (- x 1))) (cbrt (sqrt (- x 1))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
94×cbrt-prod
76×add-sqr-sqrt
65×sqrt-prod
51×*-un-lft-identity
22×add-cube-cbrt
19×swap-sqr
18×cbrt-div sqrt-div
16×difference-of-squares
13×associate-*r* associate-*l*
11×pow1
9×flip3-- pow1/3 difference-of-sqr-1 flip-- distribute-lft-out-- unswap-sqr
6×add-exp-log
4×frac-times add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 144
Calls
4 calls:
3.0ms
(cbrt (sqrt (- x 1)))
7.0ms
(cbrt (sqrt (- x 1)))
3.0ms
(cbrt (sqrt (- x 1)))
46.0ms
(* (cbrt (sqrt (- x 1))) (cbrt (sqrt (- x 1))))

series472.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(cbrt (sqrt (- x 1)))
109.0ms
(cbrt (sqrt (- x 1)))
110.0ms
(cbrt (sqrt (- x 1)))
150.0ms
(* (cbrt (sqrt (- x 1))) (cbrt (sqrt (- x 1))))

simplify834.0ms

Counts
156 → 156
Iterations
IterNodes
32046
2799
1340
0165

prune2.0s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations
IterNodes
218
118
012

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s7683×body160nan
1.1s16041×body80nan
856.0ms8000×body80valid