Details

Time bar (total: 1.9s)

sample18.0ms

Algorithm
intervals
Results
6.0ms245×body80nan
4.0ms256×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
073
1113
2133
3133

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)))

rewrite4.0ms

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 expm1-log1p-u rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- log1p-expm1-u add-log-exp difference-of-squares
Counts
1 → 18
Calls
1 calls:
4.0ms
(sqrt (- 1.0 (* x x)))

series60.0ms

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

simplify82.0ms

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 3 (78.0ms)

IterNodesCost
0165131
1568128
22782126
35001123

prune52.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
200×times-frac
182×associate-*r*
175×add-sqr-sqrt
128×unpow-prod-down
106×add-cube-cbrt *-un-lft-identity
76×sqrt-prod
48×cube-prod
42×sqr-pow
36×add-exp-log
28×unswap-sqr
14×prod-exp
13×add-cbrt-cube
12×div-exp
8×unpow2
7×pow1 cube-mult pow-to-exp unpow3 pow-exp
6×associate-*l*
5×add-log-exp
4×associate-*r/ cbrt-unprod
3×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv pow-prod-down *-commutative div-inv
1×+-commutative fma-def flip3-+ frac-add sum-log flip-+
Counts
3 → 273
Calls
3 calls:
13.0ms
(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))
50.0ms
(* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3)))
22.0ms
(* 1/2 (/ (pow x 2) (sqrt 1.0)))

series523.0ms

Counts
3 → 9
Calls
3 calls:
299.0ms
(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))
147.0ms
(* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3)))
76.0ms
(* 1/2 (/ (pow x 2) (sqrt 1.0)))

simplify55.0ms

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010241989
150021720

prune579.0ms

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

sample440.0ms

Algorithm
intervals
Results
133.0ms8000×body80valid
128.0ms8243×body80nan