Details

Time bar (total: 18.1s)

sample131.0ms

Algorithm
intervals
Results
60.0ms75×body1280valid
26.0ms48×body640valid
23.0ms34×body2560valid
8.0ms25×body320valid
5.0ms61×body80valid
3.0ms13×body160valid

simplify10.0ms

Calls
1 calls:
Slowest
10.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.8b

localize33.0ms

Local error

Found 3 expressions with local error:

17.5b
(sqrt (+ (* x x) 1))
3.0b
(log (+ x (sqrt (+ (* x x) 1))))
0.8b
(+ x (sqrt (+ (* x x) 1)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×pow1 add-exp-log
3×log-prod flip3-+ add-cbrt-cube sqrt-prod flip-+ insert-posit16 add-log-exp
2×log-div sqrt-div
1×+-commutative rem-sqrt-square pow1/2 rem-log-exp log-pow
Calls
3 calls:
Slowest
2.0ms
(sqrt (+ (* x x) 1))
2.0ms
(log (+ x (sqrt (+ (* x x) 1))))
2.0ms
(+ x (sqrt (+ (* x x) 1)))

series144.0ms

Calls
3 calls:
Slowest
104.0ms
(log (+ x (sqrt (+ (* x x) 1))))
23.0ms
(+ x (sqrt (+ (* x x) 1)))
17.0ms
(sqrt (+ (* x x) 1))

simplify2.1s

Calls
21 calls:
Slowest
480.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
205.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
174.0ms
(sqrt (- (* (* x x) (* x x)) (* 1 1)))
169.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
147.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune443.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

22.4b
(+ (* (pow x 5) 3/40) (* x (* (* x x) -1/6)))
0.2b
(* (* x x) -1/6)
0.1b
(* x (* (* x x) -1/6))
0.1b
(* (pow x 5) 3/40)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube associate-*l* add-exp-log insert-posit16
3×*-commutative
1×+-commutative sum-log flip3-+ associate-*r* flip-+
Calls
4 calls:
Slowest
8.0ms
(* x (* (* x x) -1/6))
5.0ms
(+ (* (pow x 5) 3/40) (* x (* (* x x) -1/6)))
5.0ms
(* (pow x 5) 3/40)
4.0ms
(* (* x x) -1/6)

series122.0ms

Calls
4 calls:
Slowest
64.0ms
(+ (* (pow x 5) 3/40) (* x (* (* x x) -1/6)))
29.0ms
(* (pow x 5) 3/40)
18.0ms
(* x (* (* x x) -1/6))
11.0ms
(* (* x x) -1/6)

simplify401.0ms

Calls
15 calls:
Slowest
85.0ms
(- (* 3/40 (pow x 5)) (* 1/6 (pow x 3)))
74.0ms
(* (exp (* (pow x 5) 3/40)) (exp (* x (* (* x x) -1/6))))
59.0ms
(- (* 3/40 (pow x 5)) (* 1/6 (pow x 3)))
56.0ms
(- (* 3/40 (pow x 5)) (* 1/6 (pow x 3)))
23.0ms
(* -1/6 (pow x 3))

prune498.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

19.2b
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
13.9b
(log (- (/ -1/2 x) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))
0.3b
(/ -1/8 (* (* x x) x))
0.2b
(/ 1/16 (pow x 5))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
8×add-sqr-sqrt
6×log-prod add-cube-cbrt add-log-exp
5×pow1 log-div add-exp-log
4×associate-/r* add-cbrt-cube insert-posit16
3×frac-sub
2×clear-num frac-2neg flip3-+ frac-add flip-+ div-inv distribute-lft-out distribute-lft-out--
1×+-commutative sum-log flip3-- rem-log-exp log-pow flip-- difference-of-squares
Calls
4 calls:
Slowest
30.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))
10.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
1.0ms
(/ -1/8 (* (* x x) x))
1.0ms
(/ 1/16 (pow x 5))

series214.0ms

Calls
4 calls:
Slowest
110.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))
64.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
25.0ms
(/ 1/16 (pow x 5))
14.0ms
(/ -1/8 (* (* x x) x))

simplify3.3s

Calls
31 calls:
Slowest
410.0ms
(log (- (pow (/ -1/2 x) 3) (pow (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5))) 3)))
349.0ms
(log (- (* (/ -1/2 x) (/ -1/2 x)) (* (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5))) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5))))))
336.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))
328.0ms
(log (- (* -1/2 (+ (* (/ -1/8 (* (* x x) x)) (/ -1/8 (* (* x x) x))) (- (* (/ 1/16 (pow x 5)) (/ 1/16 (pow x 5))) (* (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))) (* x (+ (pow (/ -1/8 (* (* x x) x)) 3) (pow (/ 1/16 (pow x 5)) 3)))))
295.0ms
(- (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (log -1/2))) (* 1/4 (/ 1 (pow x 2))))

prune687.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

12.4b
(log (+ x (+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x)))))
0.3b
(/ -1/8 (* (* x x) x))
0.0b
(* (* x x) x)
0.0b
(+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
6×add-log-exp
5×add-sqr-sqrt pow1 add-exp-log add-cube-cbrt
4×add-cbrt-cube insert-posit16
3×log-prod flip3-+ flip-+
2×log-div frac-add
1×pow2 +-commutative associate-+l+ clear-num associate-/r* sum-log frac-2neg pow-plus rem-log-exp associate-*l* pow3 log-pow *-commutative div-inv distribute-lft-out
Calls
4 calls:
Slowest
15.0ms
(+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x)))
12.0ms
(log (+ x (+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x)))))
5.0ms
(* (* x x) x)
2.0ms
(/ -1/8 (* (* x x) x))

series153.0ms

Calls
4 calls:
Slowest
96.0ms
(log (+ x (+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x)))))
26.0ms
(+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x)))
17.0ms
(/ -1/8 (* (* x x) x))
13.0ms
(* (* x x) x)

simplify4.4s

Calls
24 calls:
Slowest
1.2s
(log (+ (pow x 3) (pow (+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x))) 3)))
475.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
450.0ms
(- (+ (log -2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ -1 x)) (* 3/32 (/ 1 (pow x 4)))))
348.0ms
(- (log -1/8) (+ (* 4 (pow x 2)) (+ (* 24 (pow x 4)) (* 3 (log x)))))
308.0ms
(+ (* (- (* x x) (* (/ 1/2 x) (/ 1/2 x))) (* (* x x) x)) (* (- x (/ 1/2 x)) -1/8))

prune483.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes119.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 30.7b

bsearch159.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.1s2388×body1280valid
847.0ms1613×body640valid
679.0ms768×body320valid
563.0ms787×body2560valid
245.0ms2047×body80valid
74.0ms397×body160valid