Details

Time bar (total: 13.4s)

sample69.0ms

Algorithm
intervals
Results
32.0ms70×body1280valid
13.0ms51×body640valid
6.0ms20×body2560valid
3.0ms23×body320valid
3.0ms80×body80valid
1.0ms12×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 50.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.9b
(+ x (sqrt (+ (* x x) 1.0)))
3.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.6b
(sqrt (+ (* x x) 1.0))

rewrite61.0ms

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:
34.0ms
(+ x (sqrt (+ (* x x) 1.0)))
17.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms
(sqrt (+ (* x x) 1.0))

series323.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
204.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
58.0ms
(sqrt (+ (* x x) 1.0))

simplify710.0ms

Counts
51 → 51
Iterations

Useful iterations: done (708.0ms)

IterNodesCost
0133761
1319691
21350618
done5002606

prune168.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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))))
0.2b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite312.0ms

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:
175.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
117.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series354.0ms

Counts
2 → 6
Calls
2 calls:
207.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
147.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify592.0ms

Counts
292 → 292
Iterations

Useful iterations: done (579.0ms)

IterNodesCost
03364436
19903368
done50003059

prune636.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.3b
(/ 0.125 (pow x 3))
11.2b
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

rewrite975.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
54×*-un-lft-identity
51×times-frac
30×add-cube-cbrt
15×add-log-exp
14×unpow-prod-down cube-prod
12×associate-/r*
10×add-exp-log distribute-lft-out difference-of-squares
6×log-prod add-cbrt-cube sqr-pow
5×pow1 sum-log
4×cube-mult unpow3 distribute-lft-out--
3×div-exp associate-/l*
2×associate-+r- log-div flip3-+ diff-log flip-+
1×cbrt-undiv +-commutative pow-to-exp sub-neg associate-+r+ flip3-- frac-2neg rem-log-exp pow-exp clear-num log-pow frac-sub flip-- div-inv
Counts
4 → 125
Calls
4 calls:
367.0ms
(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
70.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
13.0ms
(/ 0.125 (pow x 3))
517.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

series416.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
100.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
44.0ms
(/ 0.125 (pow x 3))
214.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

simplify1.2s

Counts
137 → 137
Iterations

Useful iterations: 2 (409.0ms)

IterNodesCost
02252109
15251903
224841771
done50011771

prune358.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.3b
(/ 0.125 (pow x 3))
12.9b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
18.3b
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite800.0ms

Algorithm
rewrite-expression-head
Rules
69×times-frac
68×*-un-lft-identity
66×add-sqr-sqrt
46×add-cube-cbrt
26×unpow-prod-down
19×associate-/r*
15×add-exp-log
12×cube-prod
10×log-prod distribute-lft-out-- sqr-pow
9×add-log-exp
8×frac-sub add-cbrt-cube difference-of-squares
6×div-exp associate-/l*
5×pow1 log-div
4×cube-mult flip3-- unpow3 flip--
3×diff-log
2×cbrt-undiv pow-to-exp sub-neg frac-2neg pow-exp associate--l+ clear-num div-inv
1×associate--l- rem-log-exp log-pow
Counts
4 → 160
Calls
4 calls:
9.0ms
(/ 0.0625 (pow x 5))
14.0ms
(/ 0.125 (pow x 3))
305.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
462.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ 0.0625 (pow x 5))
56.0ms
(/ 0.125 (pow x 3))
198.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
72.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify1.8s

Counts
172 → 172
Iterations

Useful iterations: 2 (773.0ms)

IterNodesCost
03202874
17022609
231272481
done50022481

prune535.0ms

Pruning

6 alts after pruning (3 fresh and 3 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 31.7b

bsearch86.0ms

Steps
ItersRangePoint
9
5.2366538615162886e-09
1.4124627081995123
0.8917023207783242
7
-3.309911606533295
-0.03117879455470207
-1.016091287793054

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03457
13857
done3857

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.9s2340×body1280valid
529.0ms1585×body640valid
382.0ms763×body2560valid
157.0ms783×body320valid
138.0ms2109×body80valid
88.0ms420×body160valid