Details

Time bar (total: 4.0s)

sample51.0ms

Algorithm
intervals
Results
23.0ms773×body80nan
12.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0127
1167
2167

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b
(/ (sqrt (- 1.0 (* x x))) x)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
33×times-frac
32×add-sqr-sqrt
26×add-cube-cbrt
20×sqrt-prod
8×log-prod distribute-lft-out
7×add-exp-log associate-/l*
6×pow1 add-cbrt-cube add-log-exp
5×div-inv difference-of-squares
4×sqrt-div
3×log-div associate-/r*
2×distribute-rgt-out flip3-- flip3-+ frac-add flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num sum-log log-pow
Counts
4 → 98
Calls
4 calls:
23.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
3.0ms
(sqrt (- 1.0 (* x x)))
21.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series614.0ms

Counts
4 → 12
Calls
4 calls:
307.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
60.0ms
(sqrt (- 1.0 (* x x)))
112.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
135.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify54.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
05121016
11814965
25002961

prune300.0ms

Filtered
110 candidates to 88 candidates (80.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New1091110
Fresh000
Picked101
Done000
Total1101111

Merged error: 0b

Counts
111 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (sqrt 1.0) x))
0.2b
(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
0.2b
(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
0.5b
(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
292×sqrt-prod
274×add-sqr-sqrt
232×times-frac
181×*-un-lft-identity
127×add-cube-cbrt
58×associate-*r*
46×associate-*l*
28×difference-of-squares
25×unswap-sqr
20×add-exp-log add-cbrt-cube
16×associate-/l*
14×distribute-lft-out--
13×distribute-lft-out
12×associate-/r*
7×pow1
6×cbrt-undiv sqrt-div div-exp
4×sqrt-undiv prod-exp cbrt-unprod div-inv associate-/l/ add-log-exp
2×flip3-- frac-2neg clear-num flip--
1×frac-times rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sqrt-unprod associate-*r/ pow-prod-down associate-*l/ *-commutative flip-+
Counts
4 → 322
Calls
4 calls:
5.0ms
(sqrt (- (sqrt 1.0) x))
9.0ms
(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
10.0ms
(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
65.0ms
(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

series532.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sqrt (- (sqrt 1.0) x))
118.0ms
(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
128.0ms
(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
215.0ms
(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

simplify139.0ms

Algorithm
egg-herbie
Counts
334 → 334
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
09174291
143574071
250023959

prune761.0ms

Filtered
334 candidates to 166 candidates (49.7%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New3340334
Fresh000
Picked011
Done000
Total3341335

Merged error: 0b

Counts
335 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01714
11714

end0.0ms

sample1.4s

Algorithm
intervals
Results
704.0ms23979×body80nan
283.0ms8000×body80valid