Details

Time bar (total: 3.4s)

sample52.0ms

Algorithm
intervals
Results
24.0ms809×body80nan
9.0ms256×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)

rewrite54.0ms

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:
22.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
3.0ms
(sqrt (- 1.0 (* x x)))
19.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series569.0ms

Counts
4 → 12
Calls
4 calls:
282.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
56.0ms
(sqrt (- 1.0 (* x x)))
103.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
127.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify50.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
05121017
11798965
25002961

prune286.0ms

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

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (sqrt x))
0.2b
(/ 1.0 (sqrt x))
0.2b
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.5b
(* (/ 1 (sqrt x)) (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
116×times-frac
105×add-sqr-sqrt
102×*-un-lft-identity
95×sqrt-prod
82×add-cube-cbrt
22×associate-*l*
21×add-exp-log
18×associate-/r*
15×add-cbrt-cube
13×associate-*r* associate-/l*
9×distribute-lft-out
8×pow1
7×difference-of-squares
6×div-exp div-inv
5×unswap-sqr
4×cbrt-undiv prod-exp add-log-exp
3×frac-times pow-flip frac-2neg associate-*r/ clear-num
2×rec-exp flip3-+ sqrt-div 1-exp frac-add cbrt-unprod flip-+ associate-/l/
1×distribute-rgt-in sqrt-undiv distribute-rgt-out flip3-- distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative flip-- inv-pow
Counts
4 → 218
Calls
4 calls:
4.0ms
(/ 1 (sqrt x))
4.0ms
(/ 1.0 (sqrt x))
7.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
59.0ms
(* (/ 1 (sqrt x)) (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))

series334.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ 1 (sqrt x))
38.0ms
(/ 1.0 (sqrt x))
67.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
202.0ms
(* (/ 1 (sqrt x)) (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))

simplify86.0ms

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
08092152
138101930
250011871

prune505.0ms

Filtered
230 candidates to 140 candidates (60.9%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New2300230
Fresh000
Picked011
Done000
Total2301231

Merged error: 0b

Counts
231 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01712
11712

end0.0ms

sample1.4s

Algorithm
intervals
Results
709.0ms23458×body80nan
294.0ms8000×body80valid