Details

Time bar (total: 34.7s)

sample174.0ms

Algorithm
intervals
Results
84.0ms77×body1280valid
36.0ms52×body640valid
19.0ms22×body2560valid
11.0ms24×body320valid
8.0ms74×body80valid
2.0ms7×body160valid

simplify22.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
22.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.6b

localize26.0ms

Local error

Found 3 expressions with local error:

15.9b
(sqrt (+ (* x x) 1))
2.9b
(log (+ x (sqrt (+ (* x x) 1))))
0.6b
(+ x (sqrt (+ (* x x) 1)))

rewrite33.0ms

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
15.0ms
(+ x (sqrt (+ (* x x) 1)))
11.0ms
(log (+ x (sqrt (+ (* x x) 1))))
7.0ms
(sqrt (+ (* x x) 1))

series242.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
128.0ms
(log (+ x (sqrt (+ (* x x) 1))))
63.0ms
(+ x (sqrt (+ (* x x) 1)))
50.0ms
(sqrt (+ (* x x) 1))

simplify4.1s

Counts
25 → 54
Calls
25 calls:
Slowest
471.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
455.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
446.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
438.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))
370.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))

prune521.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

19.8b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
0.2b
(* (* x x) -1/6)
0.1b
(* (pow x 5) 3/40)
0.1b
(* (* (* x x) -1/6) x)

rewrite418.0ms

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
337.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
41.0ms
(* (* (* x x) -1/6) x)
27.0ms
(* (* x x) -1/6)
11.0ms
(* (pow x 5) 3/40)

series218.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
73.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
66.0ms
(* (pow x 5) 3/40)
48.0ms
(* (* (* x x) -1/6) x)
30.0ms
(* (* x x) -1/6)

simplify4.7s

Counts
55 → 94
Calls
55 calls:
Slowest
681.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
359.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
354.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
324.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
276.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/6 -1/6) -1/6))

prune764.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

8.6b
(- (/ -1/4 (* x x)) (- (log x) (/ 3/32 (* (* x x) (* x x)))))
0.2b
(/ -1/4 (* x x))
0.2b
(/ 3/32 (* (* x x) (* x x)))
0.1b
(* (* x x) (* x x))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
116×pow1
39×add-cbrt-cube add-exp-log
36×pow-prod-up
23×pow-prod-down
22×pow-sqr
18×pow-plus
17×prod-exp cbrt-unprod
16×*-un-lft-identity
13×pow2 add-sqr-sqrt
9×add-cube-cbrt
8×add-log-exp
7×cbrt-undiv times-frac div-exp
6×associate-/l*
5×associate--r+ distribute-lft-out--
4×insert-posit16
3×log-prod diff-log associate--l+
2×clear-num associate-/r* sub-neg frac-2neg flip3-- frac-sub div-inv flip-- difference-of-squares
1×swap-sqr associate-*r* associate-*l* log-pow *-commutative associate--r- unswap-sqr
Counts
4 → 141
Calls
4 calls:
Slowest
126.0ms
(- (/ -1/4 (* x x)) (- (log x) (/ 3/32 (* (* x x) (* x x)))))
27.0ms
(* (* x x) (* x x))
21.0ms
(/ 3/32 (* (* x x) (* x x)))
6.0ms
(/ -1/4 (* x x))

series262.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
88.0ms
(- (/ -1/4 (* x x)) (- (log x) (/ 3/32 (* (* x x) (* x x)))))
70.0ms
(/ 3/32 (* (* x x) (* x x)))
57.0ms
(* (* x x) (* x x))
46.0ms
(/ -1/4 (* x x))

simplify8.9s

Counts
129 → 153
Calls
129 calls:
Slowest
577.0ms
(* (* x x) (+ (log x) (/ 3/32 (* (* x x) (* x x)))))
384.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
354.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
332.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
326.0ms
(- (* -1/4 (+ (* (log x) (log x)) (+ (* (/ 3/32 (* (* x x) (* x x))) (/ 3/32 (* (* x x) (* x x)))) (* (log x) (/ 3/32 (* (* x x) (* x x))))))) (* (* x x) (- (pow (log x) 3) (pow (/ 3/32 (* (* x x) (* x x))) 3))))

prune1.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

10.2b
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
0.2b
(/ -1/8 (* (* x x) x))
0.1b
(* (* x x) x)
0.0b
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
24×pow1
19×add-exp-log
18×add-cbrt-cube
13×add-log-exp
12×distribute-lft-out
9×add-sqr-sqrt
8×add-cube-cbrt
6×log-prod sum-log pow-plus prod-exp pow-prod-up cbrt-unprod
4×insert-posit16
3×cbrt-undiv times-frac div-exp associate-*r* pow-prod-down associate-/l*
2×pow2 log-div flip3-+ pow-sqr flip-+
1×+-commutative associate-+r+ clear-num associate-/r* frac-2neg rem-log-exp associate-*l* pow3 log-pow *-commutative div-inv unswap-sqr
Counts
4 → 89
Calls
4 calls:
Slowest
590.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
459.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
25.0ms
(* (* x x) x)
24.0ms
(/ -1/8 (* (* x x) x))

series268.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
49.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
47.0ms
(/ -1/8 (* (* x x) x))
47.0ms
(* (* x x) x)

simplify5.5s

Counts
56 → 101
Calls
56 calls:
Slowest
575.0ms
(- (+ (log -2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ -1 x)) (* 3/32 (/ 1 (pow x 4)))))
472.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
463.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
443.0ms
(- (log -1/8) (+ (* 4 (pow x 2)) (+ (* 24 (pow x 4)) (* 3 (log x)))))
339.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x))

prune765.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

99.3% (0.2b remaining)

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

bsearch133.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.0s2374×body1280valid
1.2s1535×body640valid
665.0ms808×body2560valid
268.0ms749×body320valid
208.0ms2125×body80valid
80.0ms409×body160valid