Details

Time bar (total: 54.6s)

sample121.0ms

Algorithm
intervals
Results
56.0ms68×body1280valid
25.0ms54×body640valid
16.0ms24×body2560valid
7.0ms23×body320valid
7.0ms80×body80valid
1.0ms7×body160valid

simplify11.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
11.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.9b

localize18.0ms

Local error

Found 3 expressions with local error:

18.7b
(sqrt (+ (* x x) 1))
3.0b
(log (+ x (sqrt (+ (* x x) 1))))
0.0b
(+ x (sqrt (+ (* x x) 1)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×log-prod add-exp-log
3×flip3-+ add-cbrt-cube sqrt-prod flip-+ insert-posit16
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 45
Calls
3 calls:
Slowest
28.0ms
(log (+ x (sqrt (+ (* x x) 1))))
14.0ms
(sqrt (+ (* x x) 1))
13.0ms
(+ x (sqrt (+ (* x x) 1)))

series282.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
169.0ms
(log (+ x (sqrt (+ (* x x) 1))))
60.0ms
(+ x (sqrt (+ (* x x) 1)))
53.0ms
(sqrt (+ (* x x) 1))

simplify3.8s

Counts
25 → 54
Calls
25 calls:
Slowest
496.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
403.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
396.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
360.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
324.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))

prune545.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

21.6b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
0.1b
(* (* x x) -1/6)
0.1b
(* (* (* x x) -1/6) x)
0.0b
(* (pow x 5) 3/40)

rewrite368.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×add-cbrt-cube
18×pow1
15×add-sqr-sqrt
12×prod-exp
10×cbrt-unprod
9×*-un-lft-identity associate-*r* associate-*l* pow-prod-down add-cube-cbrt add-log-exp
4×unpow-prod-down insert-posit16 unswap-sqr
3×sum-log *-commutative
2×sqr-pow
1×pow-to-exp +-commutative associate-+l+ flip3-+ pow-exp flip-+
Counts
4 → 82
Calls
4 calls:
Slowest
274.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
64.0ms
(* (* (* x x) -1/6) x)
18.0ms
(* (* x x) -1/6)
9.0ms
(* (pow x 5) 3/40)

series256.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
78.0ms
(* (pow x 5) 3/40)
77.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
64.0ms
(* (* (* x x) -1/6) x)
36.0ms
(* (* x x) -1/6)

simplify4.4s

Counts
55 → 94
Calls
55 calls:
Slowest
684.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
405.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
397.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
359.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
226.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/6 -1/6) -1/6))

prune785.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 3 expressions with local error:

8.3b
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
0.1b
(/ -1/8 (* (* x x) x))
0.1b
(* (* x x) x)

rewrite794.0ms

Algorithm
rewrite-expression-head
Rules
23×pow1
18×add-exp-log
17×add-cbrt-cube
16×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
6×log-prod pow-plus prod-exp pow-prod-up cbrt-unprod distribute-lft-out
3×cbrt-undiv times-frac div-exp associate-*r* pow-prod-down insert-posit16 associate-/l* add-log-exp
2×pow2 log-div pow-sqr
1×clear-num associate-/r* frac-2neg flip3-+ rem-log-exp associate-*l* pow3 log-pow *-commutative flip-+ div-inv unswap-sqr
Counts
3 → 71
Calls
3 calls:
Slowest
740.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
27.0ms
(/ -1/8 (* (* x x) x))
26.0ms
(* (* x x) x)

series239.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
123.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
66.0ms
(* (* x x) x)
50.0ms
(/ -1/8 (* (* x x) x))

simplify3.9s

Counts
46 → 80
Calls
46 calls:
Slowest
530.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
477.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
423.0ms
(- (+ (log -2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ -1 x)) (* 3/32 (/ 1 (pow x 4)))))
401.0ms
(- (log -1/8) (+ (* 4 (pow x 2)) (+ (* 24 (pow x 4)) (* 3 (log x)))))
307.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x))

prune698.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

16.8b
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
10.9b
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
0.1b
(/ (/ 1/8 x) x)
0.1b
(/ (/ (/ 1/8 x) x) x)

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
253×*-un-lft-identity
251×add-sqr-sqrt
231×add-cube-cbrt
56×associate-/l*
22×div-inv
19×add-exp-log
18×add-cbrt-cube
10×log-prod
9×cbrt-undiv div-exp add-log-exp
8×difference-of-squares
6×associate-/r* frac-sub distribute-lft-out--
5×pow1 log-div
4×insert-posit16 distribute-lft-out
2×clear-num unpow-prod-down frac-2neg flip3-+ flip3-- diff-log frac-add flip-+ flip-- sqr-pow associate-/l/
1×sum-log sub-neg rem-log-exp associate--l+ log-pow
Counts
4 → 314
Calls
4 calls:
Slowest
166.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
91.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
11.0ms
(/ (/ (/ 1/8 x) x) x)
7.0ms
(/ (/ 1/8 x) x)

series302.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
75.0ms
(/ (/ (/ 1/8 x) x) x)
68.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
30.0ms
(/ (/ 1/8 x) x)

simplify30.0s

Counts
453 → 326
Calls
453 calls:
Slowest
628.0ms
(- (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (log -1/2))) (* 1/4 (/ 1 (pow x 2))))
449.0ms
(* (- (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (pow x 5))
423.0ms
(/ (* (* (/ (/ 1/8 x) x) (/ (/ 1/8 x) x)) (/ (/ 1/8 x) x)) (* (* x x) x))
393.0ms
(/ (exp (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
379.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))

prune2.7s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes214.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.3b

bsearch136.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.0s2320×body1280valid
1.3s1584×body640valid
564.0ms740×body2560valid
289.0ms798×body320valid
200.0ms2135×body80valid
84.0ms423×body160valid