Details

Time bar (total: 19.1s)

sample81.0ms

Algorithm
intervals
Results
44.0ms72×body1280valid
16.0ms50×body640valid
4.0ms29×body320valid
3.0ms98×body80valid
2.0ms93×body80nan
1.0ms7×body160valid

simplify1.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044
154
done54

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize4.0ms

Local error

Found 1 expressions with local error:

2.1b
(log (+ 1.0 x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×log-prod *-un-lft-identity
2×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt log-div
1×flip3-+ rem-log-exp log-pow add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
1 → 15
Calls
1 calls:
5.0ms
(log (+ 1.0 x))

series64.0ms

Counts
1 → 3
Calls
1 calls:
64.0ms
(log (+ 1.0 x))

simplify3.7s

Counts
18 → 18
Iterations

Useful iterations: 5 (1.9s)

IterNodesCost
058178
1123171
2260151
3528151
41197146
53028140
done5000140

prune54.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b
(* x (+ 1.0 (/ -1/2 (/ (* 1.0 1.0) x))))
0.2b
(/ -1/2 (/ (* 1.0 1.0) x))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
22×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
13×add-exp-log add-cbrt-cube
7×associate-/r*
5×cbrt-undiv div-exp div-inv
4×pow1 associate-*r*
3×associate-*l* associate-/l*
2×associate-*r/ prod-exp cbrt-unprod add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in flip3-+ pow-prod-down clear-num associate-/r/ *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
2 → 71
Calls
2 calls:
61.0ms
(* x (+ 1.0 (/ -1/2 (/ (* 1.0 1.0) x))))
15.0ms
(/ -1/2 (/ (* 1.0 1.0) x))

series127.0ms

Counts
2 → 6
Calls
2 calls:
109.0ms
(* x (+ 1.0 (/ -1/2 (/ (* 1.0 1.0) x))))
18.0ms
(/ -1/2 (/ (* 1.0 1.0) x))

simplify3.5s

Counts
77 → 77
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
0146994
1354928
21127852
34629842
done5001842

prune299.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ -1/2 (/ (* 1.0 1.0) x))
0.2b
(/ -1/2 (/ (* 1.0 1.0) x))
0.2b
(/ -1/2 (/ (* 1.0 1.0) x))
16.8b
(/ (* x (+ (pow 1.0 3) (pow (/ -1/2 (/ (* 1.0 1.0) x)) 3))) (+ (* 1.0 1.0) (- (* (/ -1/2 (/ (* 1.0 1.0) x)) (/ -1/2 (/ (* 1.0 1.0) x))) (* 1.0 (/ -1/2 (/ (* 1.0 1.0) x))))))

rewrite448.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
36×add-exp-log add-cbrt-cube
24×associate-/r*
17×cbrt-undiv div-exp
16×div-inv
10×associate-/l*
5×associate-/r/
4×pow1 frac-2neg prod-exp clear-num cbrt-unprod add-log-exp
2×flip3-+ associate-*r/ flip-+ associate-/l/
Counts
4 → 169
Calls
4 calls:
11.0ms
(/ -1/2 (/ (* 1.0 1.0) x))
11.0ms
(/ -1/2 (/ (* 1.0 1.0) x))
21.0ms
(/ -1/2 (/ (* 1.0 1.0) x))
398.0ms
(/ (* x (+ (pow 1.0 3) (pow (/ -1/2 (/ (* 1.0 1.0) x)) 3))) (+ (* 1.0 1.0) (- (* (/ -1/2 (/ (* 1.0 1.0) x)) (/ -1/2 (/ (* 1.0 1.0) x))) (* 1.0 (/ -1/2 (/ (* 1.0 1.0) x))))))

series438.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(/ -1/2 (/ (* 1.0 1.0) x))
17.0ms
(/ -1/2 (/ (* 1.0 1.0) x))
25.0ms
(/ -1/2 (/ (* 1.0 1.0) x))
378.0ms
(/ (* x (+ (pow 1.0 3) (pow (/ -1/2 (/ (* 1.0 1.0) x)) 3))) (+ (* 1.0 1.0) (- (* (/ -1/2 (/ (* 1.0 1.0) x)) (/ -1/2 (/ (* 1.0 1.0) x))) (* 1.0 (/ -1/2 (/ (* 1.0 1.0) x))))))

simplify1.6s

Counts
181 → 181
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01763506
14553004
219272708
done50022690

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

9.4b
(/ (* x (+ (pow 1.0 3) (pow (/ -1/2 (/ (* 1.0 1.0) x)) 3))) (* (cbrt (+ (* (/ -1/2 (/ (* 1.0 1.0) x)) (- (/ -1/2 (/ (* 1.0 1.0) x)) 1.0)) (* 1.0 1.0))) (cbrt (+ (* (/ -1/2 (/ (* 1.0 1.0) x)) (- (/ -1/2 (/ (* 1.0 1.0) x)) 1.0)) (* 1.0 1.0)))))
12.3b
(cbrt (+ (* (/ -1/2 (/ (* 1.0 1.0) x)) (- (/ -1/2 (/ (* 1.0 1.0) x)) 1.0)) (* 1.0 1.0)))
12.3b
(cbrt (+ (* (/ -1/2 (/ (* 1.0 1.0) x)) (- (/ -1/2 (/ (* 1.0 1.0) x)) 1.0)) (* 1.0 1.0)))
12.3b
(cbrt (+ (* 1.0 1.0) (- (* (/ -1/2 (/ (* 1.0 1.0) x)) (/ -1/2 (/ (* 1.0 1.0) x))) (* 1.0 (/ -1/2 (/ (* 1.0 1.0) x))))))

rewrite513.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
16×add-exp-log
12×add-cbrt-cube
10×flip3-+ flip-+
9×cbrt-prod
8×associate-/r/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 cbrt-undiv frac-times associate-*r/ div-exp prod-exp cbrt-unprod add-log-exp
3×pow1/3
2×associate-*l/ associate-/l/
1×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
232.0ms
(/ (* x (+ (pow 1.0 3) (pow (/ -1/2 (/ (* 1.0 1.0) x)) 3))) (* (cbrt (+ (* (/ -1/2 (/ (* 1.0 1.0) x)) (- (/ -1/2 (/ (* 1.0 1.0) x)) 1.0)) (* 1.0 1.0))) (cbrt (+ (* (/ -1/2 (/ (* 1.0 1.0) x)) (- (/ -1/2 (/ (* 1.0 1.0) x)) 1.0)) (* 1.0 1.0)))))
68.0ms
(cbrt (+ (* (/ -1/2 (/ (* 1.0 1.0) x)) (- (/ -1/2 (/ (* 1.0 1.0) x)) 1.0)) (* 1.0 1.0)))
78.0ms
(cbrt (+ (* (/ -1/2 (/ (* 1.0 1.0) x)) (- (/ -1/2 (/ (* 1.0 1.0) x)) 1.0)) (* 1.0 1.0)))
132.0ms
(cbrt (+ (* 1.0 1.0) (- (* (/ -1/2 (/ (* 1.0 1.0) x)) (/ -1/2 (/ (* 1.0 1.0) x))) (* 1.0 (/ -1/2 (/ (* 1.0 1.0) x))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
470.0ms
(/ (* x (+ (pow 1.0 3) (pow (/ -1/2 (/ (* 1.0 1.0) x)) 3))) (* (cbrt (+ (* (/ -1/2 (/ (* 1.0 1.0) x)) (- (/ -1/2 (/ (* 1.0 1.0) x)) 1.0)) (* 1.0 1.0))) (cbrt (+ (* (/ -1/2 (/ (* 1.0 1.0) x)) (- (/ -1/2 (/ (* 1.0 1.0) x)) 1.0)) (* 1.0 1.0)))))
265.0ms
(cbrt (+ (* (/ -1/2 (/ (* 1.0 1.0) x)) (- (/ -1/2 (/ (* 1.0 1.0) x)) 1.0)) (* 1.0 1.0)))
185.0ms
(cbrt (+ (* (/ -1/2 (/ (* 1.0 1.0) x)) (- (/ -1/2 (/ (* 1.0 1.0) x)) 1.0)) (* 1.0 1.0)))
238.0ms
(cbrt (+ (* 1.0 1.0) (- (* (/ -1/2 (/ (* 1.0 1.0) x)) (/ -1/2 (/ (* 1.0 1.0) x))) (* 1.0 (/ -1/2 (/ (* 1.0 1.0) x))))))

simplify1.8s

Counts
82 → 82
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02395040
16924631
227123979
done50003910

prune673.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes142.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.7b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02358
12958
done2958

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.6s2271×body1280valid
605.0ms1664×body640valid
552.0ms2742×body80nan
179.0ms839×body320valid
125.0ms2821×body80valid
75.0ms405×body160valid