Details

Time bar (total: 6.8s)

sample29.0ms

Algorithm
intervals
Results
8.0ms60×body640valid
4.0ms122×body80valid
4.0ms40×body320valid
4.0ms21×body1280valid
1.0ms13×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1317
2437
3577
4737
5927
61267
71587
82077
92097
102097

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: 9.1b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.7b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
32×times-frac
24×add-sqr-sqrt
13×distribute-lft-out
12×add-cube-cbrt
10×distribute-lft-out-- add-log-exp
5×add-exp-log add-cbrt-cube
4×associate-/r* difference-of-squares
3×pow1 frac-add associate-/l*
2×sub-neg associate-+l+ flip3-- flip3-+ diff-log sum-log associate-/r/ frac-sub flip-- flip-+
1×cbrt-undiv +-commutative associate-+l- frac-2neg div-exp clear-num div-inv
Counts
3 → 77
Calls
3 calls:
5.0ms
(/ 1.0 (+ x 1.0))
18.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
37.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series296.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(/ 1.0 (+ x 1.0))
42.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
223.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify43.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0403659
11378627
25001617

prune149.0ms

Filtered
86 candidates to 62 candidates (72.1%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New82486
Fresh000
Picked101
Done000
Total83487

Merged error: 0.1b

Counts
87 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
1.7b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
1.7b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
1.7b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
137×*-un-lft-identity
48×times-frac
32×distribute-lft-out
28×distribute-lft-out--
19×add-log-exp
12×frac-add
9×cbrt-prod
6×associate-+l+ sum-log
5×add-sqr-sqrt add-cube-cbrt cbrt-div
4×pow1 add-exp-log flip3-- flip3-+ frac-sub add-cbrt-cube flip-- flip-+
3×+-commutative associate-+l- sub-neg diff-log
1×pow1/3
Counts
4 → 94
Calls
4 calls:
31.0ms
(cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
35.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
32.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
36.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
451.0ms
(cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
211.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
401.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
221.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify47.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
04211383
113941299
250011241

prune214.0ms

Filtered
106 candidates to 72 candidates (67.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1060106
Fresh033
Picked011
Done000
Total1064110

Merged error: 0.1b

Counts
110 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ 1.0 (+ x 1.0)))
0.0b
(sqrt (/ 1.0 (+ x 1.0)))
0.2b
(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
7.2b
(+ (- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
134×sqrt-prod
116×*-un-lft-identity
94×add-sqr-sqrt
92×times-frac
60×add-cube-cbrt
29×swap-sqr
25×distribute-lft-out
21×pow1 associate-*r* associate-*l*
12×associate-/r/
10×sqrt-pow1 pow1/2 sqrt-div
9×add-log-exp unswap-sqr
7×flip3-+ flip-+
6×add-exp-log add-cbrt-cube div-inv
5×frac-add pow-prod-up
4×rem-sqrt-square
3×pow-prod-down pow-sqr frac-sub
2×frac-times associate-+l+ associate-*r/ associate-*l/ sum-log
1×+-commutative pow2 associate-+l- sub-neg flip3-- pow-plus sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative flip-- cbrt-unprod
Counts
4 → 189
Calls
4 calls:
5.0ms
(sqrt (/ 1.0 (+ x 1.0)))
5.0ms
(sqrt (/ 1.0 (+ x 1.0)))
21.0ms
(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
34.0ms
(+ (- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series390.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(sqrt (/ 1.0 (+ x 1.0)))
88.0ms
(sqrt (/ 1.0 (+ x 1.0)))
74.0ms
(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
141.0ms
(+ (- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify87.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06011683
128781525
250021483

prune322.0ms

Filtered
201 candidates to 128 candidates (63.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2001201
Fresh112
Picked101
Done101
Total2032205

Merged error: 0.1b

Counts
205 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ 1.0 (+ x 1.0)))
0.1b
(* (* (sqrt 1.0) (sqrt (/ 1.0 (+ x 1.0)))) x)
3.4b
(/ (+ (* (- (* (* (sqrt 1.0) (sqrt (/ 1.0 (+ x 1.0)))) x) (* (sqrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (sqrt (+ x 1.0)) x) 1.0)) (* (* (sqrt (+ x 1.0)) x) (- x 1.0)))
10.2b
(+ (* (- (* (* (sqrt 1.0) (sqrt (/ 1.0 (+ x 1.0)))) x) (* (sqrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (sqrt (+ x 1.0)) x) 1.0))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
185×associate-*l/
112×sqrt-div
56×frac-add
46×flip3-+ flip-+
36×frac-times
35×flip3-- associate-*r/ flip--
30×associate-/l/
24×frac-sub
21×*-un-lft-identity
18×add-exp-log add-sqr-sqrt sqrt-prod add-cbrt-cube
16×times-frac
15×add-cube-cbrt
10×pow1 associate-/r/
6×prod-exp cbrt-unprod add-log-exp
4×associate-+l+
3×cbrt-undiv div-exp associate-*r* pow-prod-down distribute-lft-out associate-/l*
2×distribute-rgt-in sub-neg rem-sqrt-square distribute-lft-in div-inv
1×+-commutative frac-2neg sqrt-pow1 pow1/2 associate-*l* clear-num associate-/r* sum-log *-commutative
Counts
4 → 153
Calls
4 calls:
6.0ms
(sqrt (/ 1.0 (+ x 1.0)))
15.0ms
(* (* (sqrt 1.0) (sqrt (/ 1.0 (+ x 1.0)))) x)
34.0ms
(/ (+ (* (- (* (* (sqrt 1.0) (sqrt (/ 1.0 (+ x 1.0)))) x) (* (sqrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (sqrt (+ x 1.0)) x) 1.0)) (* (* (sqrt (+ x 1.0)) x) (- x 1.0)))
22.0ms
(+ (* (- (* (* (sqrt 1.0) (sqrt (/ 1.0 (+ x 1.0)))) x) (* (sqrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (sqrt (+ x 1.0)) x) 1.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
98.0ms
(sqrt (/ 1.0 (+ x 1.0)))
178.0ms
(* (* (sqrt 1.0) (sqrt (/ 1.0 (+ x 1.0)))) x)
1.0s
(/ (+ (* (- (* (* (sqrt 1.0) (sqrt (/ 1.0 (+ x 1.0)))) x) (* (sqrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (sqrt (+ x 1.0)) x) 1.0)) (* (* (sqrt (+ x 1.0)) x) (- x 1.0)))
398.0ms
(+ (* (- (* (* (sqrt 1.0) (sqrt (/ 1.0 (+ x 1.0)))) x) (* (sqrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (sqrt (+ x 1.0)) x) 1.0))

simplify70.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
015474557
150014296

prune744.0ms

Filtered
165 candidates to 139 candidates (84.2%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1641165
Fresh011
Picked011
Done000
Total1643167

Merged error: 0.1b

Counts
167 → 3

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 27.0b

bsearch154.0ms

Steps
ItersRangePoint
10
14.716166499582775
2.5158614700293387e+20
111.33784045281939
11
-2193661101726697.2
-1.4639597033977343e-08
-0.9978403496791813

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05532
15532

end0.0ms

sample729.0ms

Algorithm
intervals
Results
253.0ms1887×body640valid
150.0ms4126×body80valid
99.0ms939×body320valid
93.0ms551×body1280valid
37.0ms499×body160valid