Details

Time bar (total: 18.7s)

sample135.0ms

Algorithm
intervals
Results
62.0ms73×body1280valid
31.0ms59×body640valid
18.0ms26×body2560valid
6.0ms20×body320valid
6.0ms62×body80valid
3.0ms16×body160valid

simplify11.0ms

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.3b

localize16.0ms

Local error

Found 3 expressions with local error:

15.2b
(sqrt (+ (* x x) 1))
3.2b
(log (+ x (sqrt (+ (* x x) 1))))
1.1b
(+ x (sqrt (+ (* x x) 1)))

rewrite6.0ms

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)))

series140.0ms

Calls
3 calls:
Slowest
89.0ms
(log (+ x (sqrt (+ (* x x) 1))))
34.0ms
(+ x (sqrt (+ (* x x) 1)))
16.0ms
(sqrt (+ (* x x) 1))

simplify2.1s

Calls
21 calls:
Slowest
553.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
197.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
177.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
149.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
137.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))

prune423.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

20.3b
(+ (* (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)

rewrite20.0ms

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
(+ (* (pow x 5) 3/40) (* x (* (* x x) -1/6)))
5.0ms
(* (* x x) -1/6)
3.0ms
(* x (* (* x x) -1/6))
2.0ms
(* (pow x 5) 3/40)

series125.0ms

Calls
4 calls:
Slowest
74.0ms
(+ (* (pow x 5) 3/40) (* x (* (* x x) -1/6)))
19.0ms
(* (pow x 5) 3/40)
17.0ms
(* (* x x) -1/6)
15.0ms
(* x (* (* x x) -1/6))

simplify443.0ms

Calls
15 calls:
Slowest
94.0ms
(- (* 3/40 (pow x 5)) (* 1/6 (pow x 3)))
94.0ms
(- (* 3/40 (pow x 5)) (* 1/6 (pow x 3)))
74.0ms
(* (exp (* (pow x 5) 3/40)) (exp (* x (* (* x x) -1/6))))
72.0ms
(- (* 3/40 (pow x 5)) (* 1/6 (pow x 3)))
19.0ms
(* -1/6 (pow x 3))

prune530.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

19.5b
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
12.6b
(log (- (/ -1/2 x) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))
0.5b
(/ -1/8 (* (* x x) x))
0.2b
(/ 1/16 (pow x 5))

rewrite68.0ms

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
40.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))
20.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
5.0ms
(/ 1/16 (pow x 5))
2.0ms
(/ -1/8 (* (* x x) x))

series226.0ms

Calls
4 calls:
Slowest
91.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))
78.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
33.0ms
(/ 1/16 (pow x 5))
24.0ms
(/ -1/8 (* (* x x) x))

simplify3.3s

Calls
31 calls:
Slowest
383.0ms
(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))))))
381.0ms
(log (- (pow (/ -1/2 x) 3) (pow (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5))) 3)))
312.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))
312.0ms
(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)))))
275.0ms
(- (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (log -1/2))) (* 1/4 (/ 1 (pow x 2))))

prune778.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

19.5b
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
19.5b
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
19.5b
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
12.6b
(log (- (/ -1/2 x) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
10×add-log-exp
7×add-sqr-sqrt
6×log-prod
5×pow1 log-div add-exp-log add-cube-cbrt
4×flip3-+ add-cbrt-cube frac-add flip-+ insert-posit16 distribute-lft-out
3×+-commutative sum-log frac-sub
2×distribute-lft-out--
1×flip3-- rem-log-exp log-pow flip-- difference-of-squares
Calls
4 calls:
Slowest
37.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))
20.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
15.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
12.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))

series315.0ms

Calls
4 calls:
Slowest
95.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))
80.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
79.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))
61.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))

simplify4.3s

Calls
36 calls:
Slowest
354.0ms
(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))))))
352.0ms
(log (- (pow (/ -1/2 x) 3) (pow (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5))) 3)))
351.0ms
(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)))))
349.0ms
(- (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (log -1/2))) (* 1/4 (/ 1 (pow x 2))))
310.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))

prune902.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.2b

bsearch137.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.1s2383×body1280valid
858.0ms1561×body640valid
597.0ms761×body320valid
562.0ms785×body2560valid
205.0ms2126×body80valid
95.0ms384×body160valid