Details

Time bar (total: 5.8s)

sample65.0ms

Algorithm
intervals
Results
33.0ms77×body1280valid
12.0ms54×body640valid
6.0ms21×body2560valid
2.0ms78×body80valid
2.0ms16×body320valid
1.0ms10×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: 52.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
2.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.5b
(sqrt (+ (* x x) 1.0))

rewrite21.0ms

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:
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series275.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ x (sqrt (+ (* x x) 1.0)))
171.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify145.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (140.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune147.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize11.0ms

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)))

rewrite206.0ms

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:
114.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
73.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series292.0ms

Counts
2 → 6
Calls
2 calls:
153.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
139.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify120.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
08542089
146421654
250011654

prune426.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (/ 0.5 x))
0.2b
(/ 0.125 (pow x 3))
10.2b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
36×times-frac
29×add-sqr-sqrt add-cube-cbrt
12×unpow-prod-down cube-prod associate-/r*
9×add-exp-log
6×log-prod
5×add-cbrt-cube distribute-lft-out add-log-exp
4×pow1 cube-mult unpow3 sqr-pow
3×div-exp associate-/l*
2×log-div flip3-+ flip-+ distribute-lft-out--
1×cbrt-undiv +-commutative pow-to-exp frac-2neg rem-log-exp pow-exp clear-num sum-log log-pow div-inv
Counts
3 → 94
Calls
3 calls:
6.0ms
(+ x (/ 0.5 x))
4.0ms
(/ 0.125 (pow x 3))
109.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series233.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ x (/ 0.5 x))
39.0ms
(/ 0.125 (pow x 3))
156.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0389596
11807553
25001553

prune184.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
12.2b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
19.0b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite402.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
110×*-un-lft-identity
102×add-sqr-sqrt
76×add-cube-cbrt
47×unpow-prod-down
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
19×associate-/r*
17×sqr-pow
15×add-exp-log
14×cube-prod distribute-lft-out--
13×associate-/l*
12×log-prod
10×difference-of-squares
9×add-log-exp
8×neg-mul-1 frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×cube-mult flip3-- unpow3 flip--
3×diff-log associate--r+
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num div-inv associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 223
Calls
4 calls:
6.0ms
(/ (- 0.0625) (pow x 5))
4.0ms
(/ 0.125 (pow x 3))
195.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
186.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ (- 0.0625) (pow x 5))
35.0ms
(/ 0.125 (pow x 3))
178.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
52.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify100.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08371970
138171891
250021883

prune563.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes91.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.2b

bsearch90.0ms

Steps
ItersRangePoint
11
0.08347146558812443
3.320253512051989e+22
0.9004884393655546
9
-5.7596417613087905
-6.7357437175194845e-09
-1.03811431304858

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
956.0ms2308×body1280valid
373.0ms1563×body640valid
216.0ms786×body2560valid
113.0ms767×body320valid
67.0ms2171×body80valid
33.0ms405×body160valid