Details

Time bar (total: 13.8s)

sample97.0ms

Algorithm
intervals
Results
49.0ms69×body1280valid
20.0ms54×body640valid
5.0ms26×body320valid
4.0ms93×body80valid
2.0ms72×body80nan
2.0ms14×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044
154
done54

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize5.0ms

Local error

Found 1 expressions with local error:

4.0b
(log (+ 1.0 x))

rewrite6.0ms

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))

series73.0ms

Counts
1 → 3
Calls
1 calls:
73.0ms
(log (+ 1.0 x))

simplify793.0ms

Counts
18 → 18
Iterations

Useful iterations: done (792.0ms)

IterNodesCost
058178
1123171
2378151
31338151
done5000146

prune84.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
2×diff-log associate-*r/ frac-sub
1×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt sub-neg flip3-- *-un-lft-identity flip3-+ associate--l+ sum-log add-cbrt-cube flip-- flip-+
Counts
1 → 16
Calls
1 calls:
58.0ms
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

series47.0ms

Counts
1 → 3
Calls
1 calls:
47.0ms
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

simplify602.0ms

Counts
19 → 19
Iterations

Useful iterations: done (601.0ms)

IterNodesCost
060497
1186476
2777444
done5000426

prune111.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
11.5b
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
11.5b
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
11.5b
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite372.0ms

Algorithm
rewrite-expression-head
Rules
52×cbrt-div
30×associate-*r/
26×frac-sub
25×cbrt-prod
23×add-sqr-sqrt
16×frac-times
15×add-cube-cbrt *-un-lft-identity
13×flip3-- flip3-+ flip-- flip-+
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×associate-*l/ add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 109
Calls
4 calls:
264.0ms
(* (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
28.0ms
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
30.0ms
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
41.0ms
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
333.0ms
(* (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
286.0ms
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
318.0ms
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
315.0ms
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify1.8s

Counts
121 → 121
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02556502
16456058
226035818
done50015455

prune966.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (* 2 3))
11.5b
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
11.5b
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
31.0b
(pow (pow (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (* 2 3)) 1/3)

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
22×unpow-prod-down
12×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×cbrt-div
7×add-exp-log
5×pow1 pow-exp
4×pow-unpow associate-*r/ frac-sub add-cbrt-cube add-log-exp
3×pow-to-exp pow-pow pow1/3 sqr-pow
2×flip3-- flip3-+ flip-- flip-+
1×unpow1/3
Counts
4 → 76
Calls
4 calls:
58.0ms
(pow (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (* 2 3))
52.0ms
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
50.0ms
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
141.0ms
(pow (pow (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (* 2 3)) 1/3)

series1.8s

Counts
4 → 12
Calls
4 calls:
482.0ms
(pow (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (* 2 3))
289.0ms
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
329.0ms
(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
729.0ms
(pow (pow (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (* 2 3)) 1/3)

simplify1.6s

Counts
88 → 88
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02723590
18153135
233332997
done50002908

prune720.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes191.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.4b

bsearch3.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01726
12126
done2126

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.6s2298×body1280valid
607.0ms1679×body640valid
132.0ms828×body320valid
98.0ms2778×body80valid
92.0ms2672×body80nan
39.0ms417×body160valid