Details

Time bar (total: 33.3s)

sample142.0ms

Algorithm
intervals
Results
56.0ms59×body1280valid
36.0ms61×body640valid
18.0ms25×body2560valid
10.0ms29×body320valid
6.0ms66×body80valid
4.0ms16×body160valid

simplify41.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
41.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 50.4b

localize27.0ms

Local error

Found 3 expressions with local error:

11.6b
(sqrt (+ (* x x) 1))
3.0b
(log (+ x (sqrt (+ (* x x) 1))))
0.7b
(+ x (sqrt (+ (* x x) 1)))

rewrite59.0ms

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
23.0ms
(+ x (sqrt (+ (* x x) 1)))
21.0ms
(log (+ x (sqrt (+ (* x x) 1))))
14.0ms
(sqrt (+ (* x x) 1))

series247.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
151.0ms
(log (+ x (sqrt (+ (* x x) 1))))
52.0ms
(+ x (sqrt (+ (* x x) 1)))
43.0ms
(sqrt (+ (* x x) 1))

simplify3.6s

Counts
25 → 54
Calls
25 calls:
Slowest
436.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
394.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
377.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
375.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
359.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))

prune537.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

17.9b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
0.5b
(* (* x x) -1/6)
0.1b
(* (* (* x x) -1/6) x)
0.1b
(* (pow x 5) 3/40)

rewrite459.0ms

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
364.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
55.0ms
(* (* (* x x) -1/6) x)
27.0ms
(* (* x x) -1/6)
12.0ms
(* (pow x 5) 3/40)

series268.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(* (pow x 5) 3/40)
77.0ms
(* (* (* x x) -1/6) x)
64.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
31.0ms
(* (* x x) -1/6)

simplify4.6s

Counts
55 → 94
Calls
55 calls:
Slowest
942.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
357.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
317.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
308.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
264.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* -1/6 -1/6) -1/6))

prune809.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

10.0b
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
0.4b
(/ -1/8 (* (* x x) x))
0.1b
(* (* x x) x)
0.0b
(+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))

rewrite754.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
22×*-un-lft-identity
19×add-exp-log
18×add-cbrt-cube
9×add-sqr-sqrt distribute-lft-out add-log-exp
8×add-cube-cbrt
6×log-prod pow-plus prod-exp pow-prod-up cbrt-unprod
4×insert-posit16
3×cbrt-undiv sum-log flip3-+ times-frac div-exp associate-*r* pow-prod-down flip-+ associate-/l*
2×pow2 log-div frac-add pow-sqr
1×+-commutative associate-+l+ 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
443.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
280.0ms
(+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))
15.0ms
(/ -1/8 (* (* x x) x))
14.0ms
(* (* x x) x)

series308.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
57.0ms
(/ -1/8 (* (* x x) x))
56.0ms
(* (* x x) x)
53.0ms
(+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))

simplify6.6s

Counts
58 → 101
Calls
58 calls:
Slowest
497.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
492.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
434.0ms
(- (log -1/8) (+ (* 4 (pow x 2)) (+ (* 24 (pow x 4)) (* 3 (log x)))))
425.0ms
(* (+ (* (/ -1/8 (* (* x x) x)) (/ -1/8 (* (* x x) x))) (- (* x x) (* (/ -1/8 (* (* x x) x)) x))) x)
420.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune789.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

5.0b
(- (/ -1/4 (* x x)) (- (log x) (/ 3/32 (* (* x x) (* x x)))))
0.4b
(/ -1/4 (* x x))
0.1b
(* (* x x) (* x x))
0.1b
(/ 3/32 (* (* x x) (* x x)))

rewrite163.0ms

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
99.0ms
(- (/ -1/4 (* x x)) (- (log x) (/ 3/32 (* (* x x) (* x x)))))
36.0ms
(* (* x x) (* x x))
20.0ms
(/ 3/32 (* (* x x) (* x x)))
6.0ms
(/ -1/4 (* x x))

series272.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(- (/ -1/4 (* x x)) (- (log x) (/ 3/32 (* (* x x) (* x x)))))
61.0ms
(/ 3/32 (* (* x x) (* x x)))
58.0ms
(* (* x x) (* x x))
31.0ms
(/ -1/4 (* x x))

simplify8.6s

Counts
129 → 153
Calls
129 calls:
Slowest
562.0ms
(* (* x x) (+ (log x) (/ 3/32 (* (* x x) (* x x)))))
392.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
358.0ms
(- (* -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))))
335.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
299.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes39.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.4b

bsearch107.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2280×body1280valid
791.0ms851×body2560valid
667.0ms1532×body640valid
262.0ms809×body320valid
204.0ms2112×body80valid
62.0ms416×body160valid