Details

Time bar (total: 15.1s)

sample134.0ms

Algorithm
intervals
Results
58.0ms72×body1280valid
29.0ms57×body640valid
16.0ms28×body2560valid
8.0ms25×body320valid
4.0ms64×body80valid
2.0ms10×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.7b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.5b
(sqrt (+ (* x x) 1.0))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod flip3-+ add-cbrt-cube flip-+
3×sqrt-prod
2×+-commutative log-div sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
4 → 53
Calls
4 calls:
21.0ms
(+ (* x x) 1.0)
32.0ms
(+ x (sqrt (+ (* x x) 1.0)))
20.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
17.0ms
(sqrt (+ (* x x) 1.0))

series531.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(+ (* x x) 1.0)
91.0ms
(+ x (sqrt (+ (* x x) 1.0)))
305.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
73.0ms
(sqrt (+ (* x x) 1.0))

simplify1.0s

Counts
65 → 65
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0141885
1350804
21618719
done5001707

prune281.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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))))
0.3b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite371.0ms

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:
230.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
106.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series393.0ms

Counts
2 → 6
Calls
2 calls:
212.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
181.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify633.0ms

Counts
292 → 292
Iterations

Useful iterations: done (622.0ms)

IterNodesCost
03364436
19903368
done50003059

prune585.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.0625 (pow x 5))
0.4b
(/ 0.125 (pow x 3))
13.6b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.7b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite423.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
71×times-frac
68×*-un-lft-identity
46×add-cube-cbrt
26×unpow-prod-down
19×associate-/r*
15×add-exp-log
14×cube-prod
11×log-prod
10×difference-of-squares sqr-pow
9×add-log-exp
8×add-cbrt-cube
6×div-exp frac-sub associate-/l* distribute-lft-out--
5×pow1 log-div
4×cube-mult unpow3 distribute-lft-out
2×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ diff-log frac-add pow-exp clear-num flip-- flip-+ div-inv
1×sub-neg rem-log-exp sum-log log-pow associate--r+
Counts
4 → 160
Calls
4 calls:
7.0ms
(/ 0.0625 (pow x 5))
15.0ms
(/ 0.125 (pow x 3))
155.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
239.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series484.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ 0.0625 (pow x 5))
48.0ms
(/ 0.125 (pow x 3))
267.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
75.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.9s

Counts
172 → 172
Iterations

Useful iterations: 2 (688.0ms)

IterNodesCost
03182936
17262663
232512519
done50012519

prune691.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.0b
(+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x))
0.4b
(/ 0.125 (pow x 3))
10.2b
(log (+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x)))

rewrite1.6s

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×log-div flip3-+ diff-log flip-+
1×cbrt-undiv +-commutative pow-to-exp associate-+l- associate-+r- 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:
77.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
907.0ms
(+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x))
10.0ms
(/ 0.125 (pow x 3))
642.0ms
(log (+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
62.0ms
(+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x))
48.0ms
(/ 0.125 (pow x 3))
244.0ms
(log (+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x)))

simplify1.5s

Counts
137 → 137
Iterations

Useful iterations: 2 (526.0ms)

IterNodesCost
02242115
15241909
224951785
done50001785

prune347.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

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

bsearch130.0ms

Steps
ItersRangePoint
9
0.00015484893005477947
28918.939680702064
0.9042263775546854
10
-2676750800.736259
-2.9526231381329305e-09
-0.994187787075435

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03457
13957
done3957

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.5s2245×body1280valid
661.0ms1646×body640valid
393.0ms382×body160valid
372.0ms799×body2560valid
193.0ms762×body320valid
106.0ms2166×body80valid