Details

Time bar (total: 19.0s)

sample133.0ms

Algorithm
intervals
Results
59.0ms68×body1280valid
31.0ms57×body640valid
16.0ms24×body2560valid
9.0ms26×body320valid
6.0ms63×body80valid
4.0ms18×body160valid

simplify42.0ms

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: 52.7b

localize22.0ms

Local error

Found 4 expressions with local error:

13.3b
(sqrt (+ (* x x) 1))
3.3b
(log (+ x (sqrt (+ (* x x) 1))))
1.1b
(+ x (sqrt (+ (* x x) 1)))
0.0b
(+ (* x x) 1)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
5×pow1 add-exp-log
4×flip3-+ add-cbrt-cube flip-+ insert-posit16 add-log-exp
3×log-prod sqrt-prod
2×+-commutative log-div sqrt-div
1×rem-sqrt-square pow1/2 rem-log-exp log-pow
Calls
4 calls:
Slowest
4.0ms
(sqrt (+ (* x x) 1))
3.0ms
(log (+ x (sqrt (+ (* x x) 1))))
3.0ms
(+ x (sqrt (+ (* x x) 1)))
3.0ms
(+ (* x x) 1)

series170.0ms

Calls
4 calls:
Slowest
109.0ms
(log (+ x (sqrt (+ (* x x) 1))))
24.0ms
(sqrt (+ (* x x) 1))
21.0ms
(+ x (sqrt (+ (* x x) 1)))
16.0ms
(+ (* x x) 1)

simplify2.2s

Calls
24 calls:
Slowest
517.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
204.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
194.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
173.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
158.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))

prune617.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

16.5b
(+ (* (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)

rewrite27.0ms

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
9.0ms
(+ (* (pow x 5) 3/40) (* x (* (* x x) -1/6)))
7.0ms
(* x (* (* x x) -1/6))
5.0ms
(* (* x x) -1/6)
5.0ms
(* (pow x 5) 3/40)

series134.0ms

Calls
4 calls:
Slowest
87.0ms
(+ (* (pow x 5) 3/40) (* x (* (* x x) -1/6)))
20.0ms
(* (pow x 5) 3/40)
16.0ms
(* x (* (* x x) -1/6))
11.0ms
(* (* x x) -1/6)

simplify387.0ms

Calls
15 calls:
Slowest
105.0ms
(* (exp (* (pow x 5) 3/40)) (exp (* x (* (* x x) -1/6))))
68.0ms
(- (* 3/40 (pow x 5)) (* 1/6 (pow x 3)))
63.0ms
(- (* 3/40 (pow x 5)) (* 1/6 (pow x 3)))
49.0ms
(- (* 3/40 (pow x 5)) (* 1/6 (pow x 3)))
16.0ms
(* -1/6 (pow x 3))

prune543.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

20.2b
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
12.4b
(log (- (/ -1/2 x) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))
0.3b
(/ 1/16 (pow x 5))
0.1b
(/ -1/8 (* (* x x) x))

rewrite39.0ms

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
27.0ms
(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))

series600.0ms

Calls
4 calls:
Slowest
492.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))
65.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
23.0ms
(/ -1/8 (* (* x x) x))
21.0ms
(/ 1/16 (pow x 5))

simplify3.3s

Calls
31 calls:
Slowest
422.0ms
(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)))))
406.0ms
(log (- (pow (/ -1/2 x) 3) (pow (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5))) 3)))
333.0ms
(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))))))
284.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))
273.0ms
(- (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (log -1/2))) (* 1/4 (/ 1 (pow x 2))))

prune752.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

9.7b
(log (+ x (+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x)))))
0.1b
(/ -1/8 (* (* x x) x))
0.1b
(* (* x x) x)
0.0b
(+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x)))

rewrite20.0ms

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
10.0ms
(+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x)))
6.0ms
(log (+ x (+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x)))))
2.0ms
(* (* x x) x)
1.0ms
(/ -1/8 (* (* x x) x))

series139.0ms

Calls
4 calls:
Slowest
84.0ms
(log (+ x (+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x)))))
21.0ms
(+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x)))
20.0ms
(/ -1/8 (* (* x x) x))
13.0ms
(* (* x x) x)

simplify4.3s

Calls
24 calls:
Slowest
1.1s
(log (+ (pow x 3) (pow (+ (+ x (/ 1/2 x)) (/ -1/8 (* (* x x) x))) 3)))
535.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
465.0ms
(- (+ (log -2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ -1 x)) (* 3/32 (/ 1 (pow x 4)))))
358.0ms
(- (log -1/8) (+ (* 4 (pow x 2)) (+ (* 24 (pow x 4)) (* 3 (log x)))))
268.0ms
(+ (* (- (* x x) (* (/ 1/2 x) (/ 1/2 x))) (* (* x x) x)) (* (- x (/ 1/2 x)) -1/8))

prune523.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes202.0ms

Accuracy

99.4% (0.2b remaining)

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

bsearch147.0ms

end0.0ms

sample4.7s

Algorithm
intervals
Results
2.4s2315×body1280valid
938.0ms1579×body640valid
664.0ms819×body2560valid
290.0ms774×body320valid
208.0ms2072×body80valid
87.0ms441×body160valid