Details

Time bar (total: 15.2s)

sample106.0ms

Algorithm
intervals
Results
36.0ms506×body80nan
27.0ms259×body160nan
16.0ms256×body80valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1109
2119
done119

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.5b
(log (+ x (sqrt (- (* x x) 1.0))))
30.0b
(sqrt (- (* x x) 1.0))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod sqrt-prod
3×add-cbrt-cube
2×log-div flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow flip-- difference-of-squares
Counts
3 → 43
Calls
3 calls:
55.0ms
(+ x (sqrt (- (* x x) 1.0)))
31.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
18.0ms
(sqrt (- (* x x) 1.0))

series463.0ms

Counts
3 → 9
Calls
3 calls:
96.0ms
(+ x (sqrt (- (* x x) 1.0)))
284.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
83.0ms
(sqrt (- (* x x) 1.0))

simplify1.6s

Counts
52 → 52
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0140780
1315710
2860637
32835619
done5001613

prune189.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))
0.2b
(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
0.6b
(/ 0.09375 (pow x 4))
0.7b
(/ 0.25 (* x x))

rewrite553.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
25×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
18×distribute-lft-out--
14×add-exp-log
13×pow1
12×unpow-prod-down
11×add-cbrt-cube
10×add-log-exp
9×log-pow
8×associate-/r*
6×associate-/l*
5×diff-log div-exp distribute-lft-out
4×associate--l+ sqr-pow
3×cbrt-undiv log-prod associate--r+
2×sub-neg frac-2neg clear-num sum-log div-inv
1×+-commutative pow-to-exp flip3-- flip3-+ frac-add pow-exp prod-exp flip-- cbrt-unprod flip-+ associate--r- difference-of-squares
Counts
4 → 111
Calls
4 calls:
41.0ms
(+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))
484.0ms
(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
12.0ms
(/ 0.09375 (pow x 4))
12.0ms
(/ 0.25 (* x x))

series354.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))
167.0ms
(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
41.0ms
(/ 0.09375 (pow x 4))
39.0ms
(/ 0.25 (* x x))

simplify1.1s

Counts
123 → 123
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02031749
14411649
213271529
done50011512

prune456.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.0b
(+ x (- (- x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.4b
(/ 0.125 (pow x 3))
0.5b
(log (+ x (- (- x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite669.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
43×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt
18×add-log-exp
13×unpow-prod-down cube-prod
12×associate-/r*
10×add-exp-log
9×distribute-lft-out--
6×log-prod diff-log add-cbrt-cube distribute-lft-out
5×pow1 difference-of-squares sqr-pow
4×cube-mult sub-neg associate-+r+ unpow3 associate--l+
3×div-exp sum-log associate-/l*
2×log-div flip3-- flip3-+ frac-sub flip-- flip-+
1×cbrt-undiv +-commutative associate--l- pow-to-exp associate-+r- frac-2neg rem-log-exp pow-exp clear-num log-pow div-inv
Counts
4 → 128
Calls
4 calls:
165.0ms
(- (- x (/ 0.5 x)) (/ 0.125 (pow x 3)))
286.0ms
(+ x (- (- x (/ 0.5 x)) (/ 0.125 (pow x 3))))
9.0ms
(/ 0.125 (pow x 3))
204.0ms
(log (+ x (- (- x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (- x (/ 0.5 x)) (/ 0.125 (pow x 3)))
49.0ms
(+ x (- (- x (/ 0.5 x)) (/ 0.125 (pow x 3))))
45.0ms
(/ 0.125 (pow x 3))
176.0ms
(log (+ x (- (- x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify941.0ms

Counts
140 → 140
Iterations

Useful iterations: done (936.0ms)

IterNodesCost
02282177
14841943
214451833
done50011813

prune448.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (pow (+ (log x) (- (log 2) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))) 3))
0.6b
(/ 0.09375 (pow x 4))
0.7b
(/ 0.25 (* x x))
0.7b
(pow (+ (log x) (- (log 2) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))) 3)

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
120×*-un-lft-identity
56×distribute-lft-out
41×pow1
38×unpow-prod-down
36×log-pow
32×cbrt-prod distribute-lft-out--
28×add-sqr-sqrt add-cube-cbrt
26×cube-prod
24×times-frac
15×add-exp-log
12×add-cbrt-cube
8×associate-/r*
6×associate-/l* sqr-pow
5×div-exp
4×cube-div add-log-exp
3×cbrt-undiv pow-unpow
2×cube-mult pow-to-exp cbrt-div frac-2neg flip3-+ unpow3 pow-exp clear-num flip-+ div-inv
1×pow-pow pow1/3 prod-exp rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 154
Calls
4 calls:
678.0ms
(cbrt (pow (+ (log x) (- (log 2) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))) 3))
8.0ms
(/ 0.09375 (pow x 4))
13.0ms
(/ 0.25 (* x x))
796.0ms
(pow (+ (log x) (- (log 2) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))) 3)

series457.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(cbrt (pow (+ (log x) (- (log 2) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))) 3))
45.0ms
(/ 0.09375 (pow x 4))
29.0ms
(/ 0.25 (* x x))
264.0ms
(pow (+ (log x) (- (log 2) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))) 3)

simplify1.9s

Counts
166 → 166
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03423803
18573357
229543095
done50013087

prune506.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes13.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01114
11214
done1214

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.3s7613×body160nan
1.0s16245×body80nan
486.0ms8000×body80valid