Details

Time bar (total: 15.8s)

sample95.0ms

Algorithm
intervals
Results
44.0ms74×body1280valid
19.0ms54×body640valid
12.0ms28×body2560valid
4.0ms23×body320valid
3.0ms62×body80valid
2.0ms15×body160valid

simplify1.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
4.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.8b
(sqrt (+ (* x x) 1.0))

rewrite84.0ms

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:
28.0ms
(+ x (sqrt (+ (* x x) 1.0)))
41.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
13.0ms
(sqrt (+ (* x x) 1.0))

series320.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(+ x (sqrt (+ (* x x) 1.0)))
198.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
63.0ms
(sqrt (+ (* x x) 1.0))

simplify81.0ms

Counts
51 → 51

prune162.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

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)))

rewrite287.0ms

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:
171.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
92.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series332.0ms

Counts
2 → 6
Calls
2 calls:
162.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
171.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify103.0ms

Counts
292 → 292

prune659.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (/ 1.0 16.0)) (pow x 5))
0.3b
(/ (/ 1.0 8.0) (pow x 3))
13.4b
(log (- (/ (/ 1.0 8.0) (pow x 3)) (- (/ (/ 1.0 2.0) x) (/ (- (/ 1.0 16.0)) (pow x 5)))))
18.7b
(- (/ (/ 1.0 8.0) (pow x 3)) (- (/ (/ 1.0 2.0) x) (/ (- (/ 1.0 16.0)) (pow x 5))))

rewrite3.6s

Algorithm
rewrite-expression-head
Rules
705×times-frac
402×*-un-lft-identity
382×add-sqr-sqrt
326×add-cube-cbrt
139×unpow-prod-down
114×distribute-rgt-neg-in
104×distribute-lft-neg-in
49×sqr-pow
46×cube-prod
43×associate-/l*
37×div-inv
30×distribute-lft-out--
23×add-exp-log
20×log-prod
19×associate-/r*
18×difference-of-squares
14×cube-mult unpow3
12×div-exp
11×add-cbrt-cube
9×add-log-exp
8×neg-mul-1 frac-sub
5×pow1 log-div
4×cbrt-undiv flip3-- flip--
3×pow-to-exp diff-log pow-exp associate--r+
2×neg-sub0 sub-neg frac-2neg div-sub clear-num associate-/l/ associate--r-
1×distribute-frac-neg rem-log-exp log-pow distribute-neg-frac
Counts
4 → 535
Calls
4 calls:
38.0ms
(/ (- (/ 1.0 16.0)) (pow x 5))
16.0ms
(/ (/ 1.0 8.0) (pow x 3))
1.9s
(log (- (/ (/ 1.0 8.0) (pow x 3)) (- (/ (/ 1.0 2.0) x) (/ (- (/ 1.0 16.0)) (pow x 5)))))
1.6s
(- (/ (/ 1.0 8.0) (pow x 3)) (- (/ (/ 1.0 2.0) x) (/ (- (/ 1.0 16.0)) (pow x 5))))

series424.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ (- (/ 1.0 16.0)) (pow x 5))
40.0ms
(/ (/ 1.0 8.0) (pow x 3))
236.0ms
(log (- (/ (/ 1.0 8.0) (pow x 3)) (- (/ (/ 1.0 2.0) x) (/ (- (/ 1.0 16.0)) (pow x 5)))))
81.0ms
(- (/ (/ 1.0 8.0) (pow x 3)) (- (/ (/ 1.0 2.0) x) (/ (- (/ 1.0 16.0)) (pow x 5))))

simplify99.0ms

Counts
547 → 547

prune2.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 3.0 32.0) (pow x 4))
0.1b
(- (log 2) (- (- (/ (/ 3.0 32.0) (pow x 4)) (log x)) (/ (/ (/ 1.0 4.0) x) x)))
0.1b
(/ (/ (/ 1.0 4.0) x) x)
5.4b
(- (- (/ (/ 3.0 32.0) (pow x 4)) (log x)) (/ (/ (/ 1.0 4.0) x) x))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
562×times-frac
300×*-un-lft-identity
289×add-sqr-sqrt
273×add-cube-cbrt
56×associate-/l*
42×unpow-prod-down
26×add-exp-log div-inv
23×distribute-lft-out--
18×add-cbrt-cube
15×div-exp
14×sqr-pow
13×add-log-exp
11×pow1
10×associate-/r*
9×cbrt-undiv diff-log
7×associate--l+ log-pow
5×sub-neg difference-of-squares
4×associate--r+
3×log-prod flip3-- flip--
2×pow-to-exp frac-2neg pow-exp clear-num frac-sub associate-/l/
1×associate--l- associate--r-
Counts
4 → 378
Calls
4 calls:
15.0ms
(/ (/ 3.0 32.0) (pow x 4))
1.2s
(- (log 2) (- (- (/ (/ 3.0 32.0) (pow x 4)) (log x)) (/ (/ (/ 1.0 4.0) x) x)))
23.0ms
(/ (/ (/ 1.0 4.0) x) x)
691.0ms
(- (- (/ (/ 3.0 32.0) (pow x 4)) (log x)) (/ (/ (/ 1.0 4.0) x) x))

series352.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ (/ 3.0 32.0) (pow x 4))
164.0ms
(- (log 2) (- (- (/ (/ 3.0 32.0) (pow x 4)) (log x)) (/ (/ (/ 1.0 4.0) x) x)))
45.0ms
(/ (/ (/ 1.0 4.0) x) x)
93.0ms
(- (- (/ (/ 3.0 32.0) (pow x 4)) (log x)) (/ (/ (/ 1.0 4.0) x) x))

simplify58.0ms

Counts
390 → 390

prune1.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes169.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.7b

bsearch103.0ms

Steps
ItersRangePoint
9
3.244205803610274e-06
1902.9075791774285
0.9479026978334683
8
-45.38980787391071
-0.005411406272604966
-0.998226736869587

simplify66.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s2333×body1280valid
905.0ms1587×body640valid
346.0ms777×body2560valid
180.0ms2109×body80valid
173.0ms755×body320valid
51.0ms439×body160valid