Details

Time bar (total: 13.8s)

sample94.0ms

Algorithm
intervals
Results
46.0ms72×body1280valid
14.0ms40×body640valid
11.0ms28×body2560valid
6.0ms29×body320valid
4.0ms72×body80valid
2.0ms15×body160valid

simplify14.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.4b

localize8.0ms

Local error

Found 3 expressions with local error:

1.5b
(+ x (sqrt (+ (* x x) 1.0)))
3.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.0b
(sqrt (+ (* x x) 1.0))

rewrite76.0ms

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:
41.0ms
(+ x (sqrt (+ (* x x) 1.0)))
23.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms
(sqrt (+ (* x x) 1.0))

series403.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(+ x (sqrt (+ (* x x) 1.0)))
286.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
49.0ms
(sqrt (+ (* x x) 1.0))

simplify1.3s

Counts
51 → 51

prune218.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 270
Calls
1 calls:
134.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series214.0ms

Counts
1 → 3
Calls
1 calls:
214.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify1.5s

Counts
273 → 273

prune508.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.5b
(/ 0.125 (pow x 2))
10.0b
(log (+ (/ (- 0.0625) (pow x 5)) (* (/ 1 x) (- (/ 0.125 (pow x 2)) 0.5))))
17.9b
(+ (/ (- 0.0625) (pow x 5)) (* (/ 1 x) (- (/ 0.125 (pow x 2)) 0.5)))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
94×times-frac
68×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
45×unpow-prod-down
24×distribute-lft-neg-in distribute-rgt-neg-in
15×add-exp-log associate-/r* sqr-pow
13×associate-/l*
10×frac-add
8×neg-mul-1 add-cbrt-cube
7×log-div
6×div-exp add-log-exp
5×pow1
4×frac-times associate-+r+ flip3-- associate-*r/ flip-- unpow2
3×log-prod
2×cbrt-undiv neg-sub0 distribute-rgt-in pow-to-exp sub-neg frac-2neg distribute-lft-in flip3-+ div-sub associate-*l/ pow-exp clear-num flip-+ div-inv
1×+-commutative associate-+l- distribute-frac-neg rem-log-exp sum-log log-pow
Counts
4 → 192
Calls
4 calls:
15.0ms
(/ (- 0.0625) (pow x 5))
8.0ms
(/ 0.125 (pow x 2))
48.0ms
(log (+ (/ (- 0.0625) (pow x 5)) (* (/ 1 x) (- (/ 0.125 (pow x 2)) 0.5))))
112.0ms
(+ (/ (- 0.0625) (pow x 5)) (* (/ 1 x) (- (/ 0.125 (pow x 2)) 0.5)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ (- 0.0625) (pow x 5))
29.0ms
(/ 0.125 (pow x 2))
226.0ms
(log (+ (/ (- 0.0625) (pow x 5)) (* (/ 1 x) (- (/ 0.125 (pow x 2)) 0.5))))
78.0ms
(+ (/ (- 0.0625) (pow x 5)) (* (/ 1 x) (- (/ 0.125 (pow x 2)) 0.5)))

simplify1.4s

Counts
204 → 204

prune921.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x))
0.0b
(+ x (+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x)))
0.3b
(/ 1 (pow x 3))
8.3b
(log (+ x (+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x))))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
36×times-frac
30×add-sqr-sqrt add-cube-cbrt
18×add-log-exp
14×add-exp-log
12×unpow-prod-down cube-prod associate-/r*
7×sum-log distribute-lft-out
6×div-exp add-cbrt-cube
5×pow1 log-prod
4×cube-mult unpow3 sqr-pow
3×pow-to-exp rec-exp flip3-+ 1-exp pow-exp flip-+ associate-/l*
2×+-commutative associate-+l- log-div associate-+l+ diff-log frac-add
1×cbrt-undiv associate-+r- sub-neg associate-+r+ flip3-- pow-flip frac-2neg rem-log-exp clear-num log-pow flip-- div-inv inv-pow
Counts
4 → 124
Calls
4 calls:
29.0ms
(+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x))
68.0ms
(+ x (+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x)))
15.0ms
(/ 1 (pow x 3))
65.0ms
(log (+ x (+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x))))

series364.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x))
48.0ms
(+ x (+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x)))
50.0ms
(/ 1 (pow x 3))
197.0ms
(log (+ x (+ (- x (* 0.125 (/ 1 (pow x 3)))) (/ 0.5 x))))

simplify1.1s

Counts
136 → 136

prune333.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes153.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.0b

bsearch106.0ms

Steps
ItersRangePoint
9
0.0024368900564104884
555.6593536559827
0.882915536074428
10
-248837311.7084542
-0.0006576197608759923
-1.0077278576112656

simplify560.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.5s2325×body1280valid
940.0ms1577×body640valid
338.0ms804×body2560valid
264.0ms2112×body80valid
159.0ms782×body320valid
81.0ms400×body160valid