Details

Time bar (total: 4.6s)

sample51.0ms

Algorithm
intervals
Results
23.0ms741×body80nan
9.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0127
1167
2167

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

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:
7.0ms
(sqrt (- 1.0 (* x x)))
12.0ms
(/ (sqrt (- 1.0 (* x x))) x)
35.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
34.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series529.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(sqrt (- 1.0 (* x x)))
121.0ms
(/ (sqrt (- 1.0 (* x x))) x)
91.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
267.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify50.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
05121016
11814965
25001961

prune276.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (pow x 4) (* (pow (sqrt 1.0) 3) (+ (sqrt 1.0) 1.0)))
0.0b
(* 1/2 (/ (pow x 2) (* (sqrt 1.0) (+ (sqrt 1.0) 1.0))))
0.0b
(/ (pow x 2) (* (sqrt 1.0) (+ (sqrt 1.0) 1.0)))
0.2b
(- (- (log (+ (sqrt 1.0) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (+ (sqrt 1.0) 1.0))))) (+ (* 1/8 (/ (pow x 4) (* (pow (sqrt 1.0) 3) (+ (sqrt 1.0) 1.0)))) (log x)))

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
24×add-sqr-sqrt div-exp
23×*-un-lft-identity times-frac add-cbrt-cube
22×prod-exp
17×add-cube-cbrt
16×associate--l+
15×unpow-prod-down associate-/l*
14×associate-*r*
12×add-log-exp
11×pow-to-exp pow-exp
7×log-prod associate-*r/
6×pow1 cbrt-undiv diff-log associate-/r/ cbrt-unprod
5×flip3-+ flip-+ sqr-pow
4×frac-sub
3×flip3-- associate-*l* flip-- div-inv unpow2
2×sub-neg distribute-rgt-out frac-2neg clear-num associate-/r* sum-log
1×associate--l- pow-prod-down distribute-rgt1-in sqrt-prod *-commutative distribute-lft-out associate--r+ distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 148
Calls
4 calls:
20.0ms
(/ (pow x 4) (* (pow (sqrt 1.0) 3) (+ (sqrt 1.0) 1.0)))
50.0ms
(* 1/2 (/ (pow x 2) (* (sqrt 1.0) (+ (sqrt 1.0) 1.0))))
19.0ms
(/ (pow x 2) (* (sqrt 1.0) (+ (sqrt 1.0) 1.0)))
154.0ms
(- (- (log (+ (sqrt 1.0) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (+ (sqrt 1.0) 1.0))))) (+ (* 1/8 (/ (pow x 4) (* (pow (sqrt 1.0) 3) (+ (sqrt 1.0) 1.0)))) (log x)))

series811.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(/ (pow x 4) (* (pow (sqrt 1.0) 3) (+ (sqrt 1.0) 1.0)))
127.0ms
(* 1/2 (/ (pow x 2) (* (sqrt 1.0) (+ (sqrt 1.0) 1.0))))
126.0ms
(/ (pow x 2) (* (sqrt 1.0) (+ (sqrt 1.0) 1.0)))
359.0ms
(- (- (log (+ (sqrt 1.0) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (+ (sqrt 1.0) 1.0))))) (+ (* 1/8 (/ (pow x 4) (* (pow (sqrt 1.0) 3) (+ (sqrt 1.0) 1.0)))) (log x)))

simplify116.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
08352369
141192159
250012145

prune823.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03530
13530

end0.0ms

sample1.5s

Algorithm
intervals
Results
708.0ms24270×body80nan
296.0ms8000×body80valid