Details

Time bar (total: 5.0s)

sample64.0ms

Algorithm
intervals
Results
33.0ms81×body1280valid
12.0ms49×body640valid
5.0ms20×body2560valid
4.0ms28×body320valid
2.0ms67×body80valid
1.0ms11×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
3.0b
(log (+ x (sqrt (+ (* x x) 1.0))))
16.1b
(sqrt (+ (* x x) 1.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
6.0ms
(+ x (sqrt (+ (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series270.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
164.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify136.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (130.0ms)

IterNodesCost
0309394
11021364
24731348
35002347

prune148.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
182×add-sqr-sqrt
140×unpow-prod-down cube-prod
118×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×add-exp-log unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow-to-exp pow-exp add-log-exp
4×pow1
3×associate-*r/ associate-*l*
2×diff-log frac-sub cbrt-unprod
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 286
Calls
2 calls:
15.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
51.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series296.0ms

Counts
2 → 6
Calls
2 calls:
156.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
140.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify116.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08542089
146421654
250011654

prune429.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.09375 (pow x 4))
0.1b
(- (log 2) (- (- (/ 0.09375 (pow x 4)) (log x)) (/ (/ 0.25 x) x)))
0.1b
(/ (/ 0.25 x) x)
7.4b
(- (- (/ 0.09375 (pow x 4)) (log x)) (/ (/ 0.25 x) x))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
99×times-frac
90×*-un-lft-identity
74×add-sqr-sqrt
63×add-cube-cbrt
23×distribute-lft-out--
16×associate-/l*
14×add-exp-log
13×add-log-exp
12×unpow-prod-down
11×pow1 add-cbrt-cube
10×associate-/r*
9×diff-log
7×associate--l+ log-pow
6×div-exp div-inv
5×sub-neg
4×cbrt-undiv associate--r+ difference-of-squares sqr-pow
3×log-prod flip3-- flip--
2×frac-2neg clear-num frac-sub
1×associate--l- pow-to-exp pow-exp associate-/l/ associate--r-
Counts
4 → 170
Calls
4 calls:
4.0ms
(/ 0.09375 (pow x 4))
39.0ms
(- (log 2) (- (- (/ 0.09375 (pow x 4)) (log x)) (/ (/ 0.25 x) x)))
6.0ms
(/ (/ 0.25 x) x)
36.0ms
(- (- (/ 0.09375 (pow x 4)) (log x)) (/ (/ 0.25 x) x))

series225.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ 0.09375 (pow x 4))
94.0ms
(- (log 2) (- (- (/ 0.09375 (pow x 4)) (log x)) (/ (/ 0.25 x) x)))
24.0ms
(/ (/ 0.25 x) x)
67.0ms
(- (- (/ 0.09375 (pow x 4)) (log x)) (/ (/ 0.25 x) x))

simplify65.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
07211389
126641284
250011281

prune434.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
0.5b
(/ 0.125 (pow x 3))
10.9b
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
33×*-un-lft-identity
29×add-cube-cbrt
12×unpow-prod-down cube-prod associate-/r*
9×add-exp-log
8×add-log-exp
6×log-prod
5×add-cbrt-cube
4×pow1 cube-mult log-div flip3-- unpow3 frac-sub flip-- difference-of-squares sqr-pow
3×diff-log div-exp associate-/l*
2×sub-neg associate--r+ distribute-lft-out--
1×cbrt-undiv pow-to-exp frac-2neg rem-log-exp pow-exp clear-num log-pow div-inv associate--r-
Counts
3 → 105
Calls
3 calls:
17.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
5.0ms
(/ 0.125 (pow x 3))
17.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

series237.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
41.0ms
(/ 0.125 (pow x 3))
154.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

simplify72.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0475884
12181836
25002836

prune235.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes68.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.6b

bsearch72.0ms

Steps
ItersRangePoint
8
0.22405535791780642
145.42571904303156
0.963811647786171
8
-914.1439753575298
-0.11986014733990268
-1.0090202414523164

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04829
14829

end0.0ms

sample1.9s

Algorithm
intervals
Results
973.0ms2365×body1280valid
374.0ms1569×body640valid
212.0ms787×body2560valid
107.0ms806×body320valid
67.0ms2104×body80valid
28.0ms369×body160valid