Details

Time bar (total: 1.5s)

sample18.0ms

Algorithm
intervals
Results
4.0ms256×body80valid
4.0ms244×body80nan

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
073
1113
2113

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt sqrt-prod
2×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
1×add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp difference-of-squares
Counts
1 → 16
Calls
1 calls:
5.0ms
(sqrt (- 1.0 (* x x)))

series60.0ms

Counts
1 → 3
Calls
1 calls:
60.0ms
(sqrt (- 1.0 (* x x)))

simplify87.0ms

Algorithm
egg-herbie
Counts
19 → 19
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0157124
1534121
22617120
35002119

prune47.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (sqrt 1.0)))
0.0b
(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
54×add-sqr-sqrt
52×associate-*r*
32×add-cube-cbrt *-un-lft-identity
28×sqrt-prod
20×unpow-prod-down
12×add-exp-log
9×unswap-sqr
8×unpow2 sqr-pow
7×add-cbrt-cube
4×pow1 prod-exp add-log-exp
3×associate-*r/ div-exp associate-*l*
2×cbrt-unprod
1×cbrt-undiv +-commutative pow-to-exp flip3-+ pow-prod-down frac-add pow-exp sum-log *-commutative flip-+ div-inv
Counts
2 → 92
Calls
2 calls:
32.0ms
(* 1/2 (/ (pow x 2) (sqrt 1.0)))
24.0ms
(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

series366.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(* 1/2 (/ (pow x 2) (sqrt 1.0)))
297.0ms
(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

simplify74.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0465718
12261638
25003638

prune240.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02012
12012

end0.0ms

sample491.0ms

Algorithm
intervals
Results
134.0ms8000×body80valid
126.0ms8107×body80nan