Details

Time bar (total: 10.4s)

sample97.0ms

Algorithm
intervals
Results
25.0ms256×body160nan
23.0ms530×body80nan
15.0ms256×body80valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1129
done129

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
30.4b
(sqrt (- (* x x) 1.0))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt *-un-lft-identity
add-cube-cbrt sqrt-prod add-log-exp
pow1 fma-def
add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
+-commutative rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 sum-log flip-- flip-+ distribute-lft-out difference-of-squares
Counts
2 → 35
Calls
2 calls:
23.0ms
(+ x (sqrt (- (* x x) 1.0)))
40.0ms
(sqrt (- (* x x) 1.0))

series182.0ms

Counts
2 → 6
Calls
2 calls:
105.0ms
(+ x (sqrt (- (* x x) 1.0)))
76.0ms
(sqrt (- (* x x) 1.0))

simplify1.4s

Counts
41 → 41
Iterations

Useful iterations: done (1.4s)

IterNodesCost
095483
1458428
done5000392

prune157.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ 0.125 (pow x 3))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down cube-prod associate-/r*
add-exp-log
cube-mult unpow3 sqr-pow
div-exp add-cbrt-cube associate-/l*
pow1 cbrt-undiv expm1-log1p-u pow-to-exp frac-2neg pow-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 67
Calls
1 calls:
9.0ms
(/ 0.125 (pow x 3))

series61.0ms

Counts
1 → 3
Calls
1 calls:
61.0ms
(/ 0.125 (pow x 3))

simplify5.0s

Counts
70 → 70
Iterations

Useful iterations: done (5.0s)

IterNodesCost
098740
14173598
done5000580

prune190.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
11414
done1414

end0.0ms

sample3.2s

Algorithm
intervals
Results
951.0ms8000×body80valid
808.0ms7613×body160nan
740.0ms16341×body80nan