Details

Time bar (total: 16.2s)

sample101.0ms

Algorithm
intervals
Results
44.0ms63×body1280valid
23.0ms64×body640valid
10.0ms23×body2560valid
6.0ms24×body320valid
4.0ms69×body80valid
2.0ms13×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize37.0ms

Local error

Found 3 expressions with local error:

0.6b
(+ x (sqrt (+ (* x x) 1.0)))
3.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.1b
(sqrt (+ (* x x) 1.0))

rewrite87.0ms

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)))
32.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
19.0ms
(sqrt (+ (* x x) 1.0))

series464.0ms

Counts
3 → 9
Calls
3 calls:
105.0ms
(+ x (sqrt (+ (* x x) 1.0)))
274.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
85.0ms
(sqrt (+ (* x x) 1.0))

simplify1.5s

Counts
51 → 51
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0133761
1767687
done5000612

prune223.0ms

Pruning

4 alts after pruning (4 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))))
0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite423.0ms

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:
259.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
118.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series494.0ms

Counts
2 → 6
Calls
2 calls:
265.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
230.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify871.0ms

Counts
292 → 292
Iterations

Useful iterations: done (858.0ms)

IterNodesCost
03364436
done50013513

prune715.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x))
0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.2b
(/ 0.125 (pow x 3))
14.1b
(log (+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x)))

rewrite1.7s

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:
917.0ms
(+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x))
83.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
12.0ms
(/ 0.125 (pow x 3))
729.0ms
(log (+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x)))

series634.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x))
180.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
77.0ms
(/ 0.125 (pow x 3))
291.0ms
(log (+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x)))

simplify1.5s

Counts
137 → 137
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02242115
done50001910

prune464.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.125 (pow x 3))
0.5b
(/ 0.0625 (pow x 5))
15.1b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
19.6b
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

rewrite580.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
94×times-frac
63×*-un-lft-identity
46×add-cube-cbrt
33×unpow-prod-down
22×difference-of-squares
19×associate-/r*
17×sqr-pow
16×cube-prod
15×add-exp-log
8×log-prod add-cbrt-cube
7×distribute-lft-out--
6×div-exp associate-/l* add-log-exp
5×pow1 log-div frac-sub
4×cube-mult unpow3
3×flip3-- flip--
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
1×sub-neg diff-log rem-log-exp log-pow
Counts
4 → 167
Calls
4 calls:
11.0ms
(/ 0.125 (pow x 3))
8.0ms
(/ 0.0625 (pow x 5))
430.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
117.0ms
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

series719.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ 0.125 (pow x 3))
101.0ms
(/ 0.0625 (pow x 5))
337.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
205.0ms
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

simplify937.0ms

Counts
179 → 179
Iterations

Useful iterations: done (926.0ms)

IterNodesCost
03382966
done50012708

prune701.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.3b

bsearch99.0ms

Steps
ItersRangePoint
10
1.0194597579740466e-06
20796729.49276672
0.9017023301953626
8
-11.923248480236845
-0.0008047768791668974
-1.002814715336328

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03457
13857
done3857

end0.0ms

sample3.8s

Algorithm
intervals
Results
2.0s2305×body1280valid
672.0ms1572×body640valid
405.0ms828×body2560valid
216.0ms771×body320valid
182.0ms2130×body80valid
96.0ms394×body160valid