Details

Time bar (total: 6.9s)

sample68.0ms

Algorithm
intervals
Results
31.0ms74×body1280valid
16.0ms55×body640valid
7.0ms28×body2560valid
3.0ms22×body320valid
2.0ms66×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: 55.3b

localize6.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
2.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.1b
(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))

series278.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(+ x (sqrt (+ (* x x) 1.0)))
175.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
48.0ms
(sqrt (+ (* x x) 1.0))

simplify142.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (132.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune144.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

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)))

rewrite208.0ms

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:
112.0ms
(- (+ (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)))

series321.0ms

Counts
2 → 6
Calls
2 calls:
177.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
144.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify149.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
08542089
146421654
250011654

prune424.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/6 (pow x 3))
0.1b
(/ x (/ 1.0 x))
14.6b
(+ (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3)))) (* (pow (sqrt 1.0) 3) (+ (* (log (sqrt 1.0)) (log (sqrt 1.0))) (- (/ x (/ 1.0 x))))))
16.6b
(/ (+ (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3)))) (* (pow (sqrt 1.0) 3) (+ (* (log (sqrt 1.0)) (log (sqrt 1.0))) (- (/ x (/ 1.0 x)))))) (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (pow (sqrt 1.0) 3)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
59×add-sqr-sqrt
52×add-cube-cbrt *-un-lft-identity
24×add-exp-log
16×add-cbrt-cube
14×associate-/r*
12×associate-*r*
10×associate-*l/
8×associate-*r/ frac-add distribute-neg-frac add-log-exp
7×div-exp
6×flip3-+ prod-exp flip-+ div-inv associate-/l/ associate-/l*
5×cbrt-undiv flip3-- flip--
4×pow1 unpow-prod-down cube-prod unswap-sqr
3×associate-*l* associate-/r/
2×neg-sub0 pow-to-exp associate-+l- associate-+r+ frac-2neg pow-exp clear-num sum-log cbrt-unprod sqr-pow
1×+-commutative distribute-rgt-in cube-mult distribute-lft-in unpow3 div-sub neg-log *-commutative
Counts
4 → 152
Calls
4 calls:
6.0ms
(* 1/6 (pow x 3))
4.0ms
(/ x (/ 1.0 x))
9.0ms
(+ (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3)))) (* (pow (sqrt 1.0) 3) (+ (* (log (sqrt 1.0)) (log (sqrt 1.0))) (- (/ x (/ 1.0 x))))))
37.0ms
(/ (+ (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3)))) (* (pow (sqrt 1.0) 3) (+ (* (log (sqrt 1.0)) (log (sqrt 1.0))) (- (/ x (/ 1.0 x)))))) (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (pow (sqrt 1.0) 3)))

series725.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* 1/6 (pow x 3))
25.0ms
(/ x (/ 1.0 x))
208.0ms
(+ (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3)))) (* (pow (sqrt 1.0) 3) (+ (* (log (sqrt 1.0)) (log (sqrt 1.0))) (- (/ x (/ 1.0 x))))))
449.0ms
(/ (+ (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3)))) (* (pow (sqrt 1.0) 3) (+ (* (log (sqrt 1.0)) (log (sqrt 1.0))) (- (/ x (/ 1.0 x)))))) (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (pow (sqrt 1.0) 3)))

simplify47.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09742798
150012465

prune628.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- 0.0625) (pow x 5))
0.4b
(/ 0.125 (pow x 3))
14.1b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
20.2b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite386.0ms

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))
174.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
190.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series332.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ (- 0.0625) (pow x 5))
35.0ms
(/ 0.125 (pow x 3))
189.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
53.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify99.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
08371970
138171891
250021883

prune714.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.8b

bsearch74.0ms

Steps
ItersRangePoint
8
0.003342748024832997
13.582308112339199
0.8940970356054183
9
-118.89002763209811
-0.00028315217264546786
-1.0102938707423672

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
955.0ms2324×body1280valid
377.0ms1603×body640valid
220.0ms825×body2560valid
117.0ms800×body320valid
62.0ms2044×body80valid
31.0ms404×body160valid