Details

Time bar (total: 7.0s)

sample62.0ms

Algorithm
intervals
Results
29.0ms72×body1280valid
11.0ms45×body640valid
5.0ms20×body2560valid
5.0ms37×body320valid
2.0ms69×body80valid
1.0ms13×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: 53.6b

localize7.0ms

Local error

Found 3 expressions with local error:

1.2b
(+ x (sqrt (+ (* x x) 1.0)))
3.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.8b
(sqrt (+ (* x x) 1.0))

rewrite46.0ms

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:
17.0ms
(+ x (sqrt (+ (* x x) 1.0)))
19.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
9.0ms
(sqrt (+ (* x x) 1.0))

series248.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(+ x (sqrt (+ (* x x) 1.0)))
155.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
37.0ms
(sqrt (+ (* x x) 1.0))

simplify143.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (137.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune141.0ms

Pruning

4 alts after pruning (4 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)))

rewrite270.0ms

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:
164.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
86.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series269.0ms

Counts
2 → 6
Calls
2 calls:
141.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
128.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify112.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08542089
146421654
250011654

prune416.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/6 (pow x 3))
0.1b
(/ x (/ 1.0 x))
11.8b
(+ (- (* (- (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))))))
13.6b
(/ (+ (- (* (- (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)))

rewrite138.0ms

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:
13.0ms
(* 1/6 (pow x 3))
8.0ms
(/ x (/ 1.0 x))
27.0ms
(+ (- (* (- (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))))))
83.0ms
(/ (+ (- (* (- (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)))

series625.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* 1/6 (pow x 3))
27.0ms
(/ x (/ 1.0 x))
174.0ms
(+ (- (* (- (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))))))
391.0ms
(/ (+ (- (* (- (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)))

simplify48.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09742798
150012465

prune589.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/6 (pow x 3))
0.4b
(/ 1 (/ (/ 1.0 x) x))
11.8b
(+ (- (* (- (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))) (- (/ 1 (/ (/ 1.0 x) x))))))
13.6b
(/ (+ (- (* (- (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))) (- (/ 1 (/ (/ 1.0 x) x)))))) (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (pow (sqrt 1.0) 3)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
396×times-frac
201×add-sqr-sqrt
194×add-cube-cbrt *-un-lft-identity
44×associate-/r*
40×add-exp-log
20×add-cbrt-cube
19×div-exp
18×div-inv
12×associate-*r*
10×associate-*l/
8×cbrt-undiv associate-*r/ frac-add distribute-neg-frac add-log-exp
6×flip3-+ prod-exp flip-+ associate-/l/ associate-/l*
5×pow1 flip3-- flip--
4×unpow-prod-down cube-prod unswap-sqr
3×rec-exp 1-exp 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 pow-flip distribute-lft-in unpow3 div-sub neg-log *-commutative inv-pow
Counts
4 → 282
Calls
4 calls:
12.0ms
(* 1/6 (pow x 3))
19.0ms
(/ 1 (/ (/ 1.0 x) x))
27.0ms
(+ (- (* (- (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))) (- (/ 1 (/ (/ 1.0 x) x))))))
81.0ms
(/ (+ (- (* (- (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))) (- (/ 1 (/ (/ 1.0 x) x)))))) (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (pow (sqrt 1.0) 3)))

series619.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* 1/6 (pow x 3))
29.0ms
(/ 1 (/ (/ 1.0 x) x))
172.0ms
(+ (- (* (- (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))) (- (/ 1 (/ (/ 1.0 x) x))))))
387.0ms
(/ (+ (- (* (- (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))) (- (/ 1 (/ (/ 1.0 x) x)))))) (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (pow (sqrt 1.0) 3)))

simplify76.0ms

Algorithm
egg-herbie
Counts
294 → 294
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
016104317
150013647

prune923.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes63.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.9b

bsearch77.0ms

Steps
ItersRangePoint
10
1.6041137143851903e-12
1.537653969837454
0.8901203005302397
9
-11413.0783357711
-0.00024241826916865248
-1.0196250072526523

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
949.0ms2347×body1280valid
358.0ms1520×body640valid
202.0ms774×body2560valid
115.0ms845×body320valid
64.0ms2136×body80valid
29.0ms378×body160valid