Details

Time bar (total: 19.3s)

sample51.0ms

Algorithm
intervals
Results
25.0ms388×body80valid
6.0ms134×body80nan

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
done5001
51406
4257
396
248
124
012

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ (* k (+ k 10.0)) 1.0) (pow k m))
0.0b
(* k (+ k 10.0))
2.2b
(/ a (/ (+ (* k (+ k 10.0)) 1.0) (pow k m)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
105×add-sqr-sqrt *-un-lft-identity
103×add-cube-cbrt
48×unpow-prod-down
32×associate-/r*
20×add-exp-log
16×sqr-pow
12×add-cbrt-cube
10×div-exp
6×div-inv associate-/l*
5×pow1
4×cbrt-undiv associate-*r*
3×associate-*l* add-log-exp
2×pow-to-exp clear-num frac-2neg flip3-+ pow-exp associate-*r/ flip-+ associate-/l/
1×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
3 → 190
Calls
3 calls:
31.0ms
(/ (+ (* k (+ k 10.0)) 1.0) (pow k m))
15.0ms
(* k (+ k 10.0))
22.0ms
(/ a (/ (+ (* k (+ k 10.0)) 1.0) (pow k m)))

series274.0ms

Counts
3 → 9
Calls
3 calls:
101.0ms
(/ (+ (* k (+ k 10.0)) 1.0) (pow k m))
48.0ms
(* k (+ k 10.0))
125.0ms
(/ a (/ (+ (* k (+ k 10.0)) 1.0) (pow k m)))

simplify1.3s

Counts
199 → 199
Iterations
IterNodes
done5000
11026
0366

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (pow k m))
0.0b
(* k (+ k 10.0))
0.6b
(/ 1 (+ (* k (+ k 10.0)) 1.0))
1.9b
(* (/ 1 (+ (* k (+ k 10.0)) 1.0)) (* a (pow k m)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
32×prod-exp
31×add-sqr-sqrt
26×*-un-lft-identity
24×add-cube-cbrt
22×add-cbrt-cube
21×associate-*l*
18×times-frac
12×associate-*r*
10×div-exp
9×pow1
8×cbrt-unprod
5×pow-to-exp rec-exp 1-exp pow-exp
4×unpow-prod-down associate-/r/ add-log-exp unswap-sqr
3×cbrt-undiv associate-/r* flip3-+ *-commutative flip-+ associate-/l*
2×pow-prod-down associate-*r/ div-inv sqr-pow
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in associate-*l/ pow-flip distribute-lft-out inv-pow
Counts
4 → 127
Calls
4 calls:
13.0ms
(* a (pow k m))
17.0ms
(* k (+ k 10.0))
22.0ms
(/ 1 (+ (* k (+ k 10.0)) 1.0))
69.0ms
(* (/ 1 (+ (* k (+ k 10.0)) 1.0)) (* a (pow k m)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* a (pow k m))
50.0ms
(* k (+ k 10.0))
36.0ms
(/ 1 (+ (* k (+ k 10.0)) 1.0))
137.0ms
(* (/ 1 (+ (* k (+ k 10.0)) 1.0)) (* a (pow k m)))

simplify2.6s

Counts
139 → 139
Iterations
IterNodes
done5001
23956
1679
0234

prune747.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt k)
0.6b
(cbrt k)
15.0b
(sqrt (+ (* k (+ k 10.0)) 1.0))
15.0b
(sqrt (+ (* k (+ k 10.0)) 1.0))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×add-cbrt-cube sqrt-div add-exp-log add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow1/3 flip-+
Counts
4 → 52
Calls
4 calls:
1.0ms
(cbrt k)
1.0ms
(cbrt k)
24.0ms
(sqrt (+ (* k (+ k 10.0)) 1.0))
21.0ms
(sqrt (+ (* k (+ k 10.0)) 1.0))

series596.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(cbrt k)
231.0ms
(cbrt k)
70.0ms
(sqrt (+ (* k (+ k 10.0)) 1.0))
63.0ms
(sqrt (+ (* k (+ k 10.0)) 1.0))

simplify703.0ms

Counts
64 → 64
Iterations
IterNodes
done5000
2681
1180
079

prune519.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize124.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (* (exp (- (- (* m (log k))))) 10.0) (/ (* (* k k) k) a))
6.3b
(- (* (/ (exp (- (- (* m (log k))))) k) (/ a k)) (/ (* (exp (- (- (* m (log k))))) 10.0) (/ (* (* k k) k) a)))
8.1b
(/ (* (exp (- (- (* m (log k))))) a) (* k k))
8.9b
(+ (* (/ 99.0 (* k k)) (/ (* (exp (- (- (* m (log k))))) a) (* k k))) (- (* (/ (exp (- (- (* m (log k))))) k) (/ a k)) (/ (* (exp (- (- (* m (log k))))) 10.0) (/ (* (* k k) k) a))))

rewrite394.0ms

Algorithm
rewrite-expression-head
Rules
48×add-cbrt-cube
42×add-exp-log
18×cbrt-undiv div-exp
15×frac-add
14×times-frac prod-exp cbrt-unprod
13×associate-*l/
12×frac-sub
11×add-log-exp
9×frac-times associate-*r/
8×add-sqr-sqrt associate-/r* *-un-lft-identity add-cube-cbrt
4×pow1 flip3-- div-inv flip-- associate-/l/
2×neg-sub0 exp-neg associate-+r+ clear-num sum-log sub-neg frac-2neg exp-diff diff-log associate-/l*
1×+-commutative associate-+r- flip3-+ associate-/r/ flip-+
Counts
4 → 112
Calls
4 calls:
47.0ms
(/ (* (exp (- (- (* m (log k))))) 10.0) (/ (* (* k k) k) a))
32.0ms
(- (* (/ (exp (- (- (* m (log k))))) k) (/ a k)) (/ (* (exp (- (- (* m (log k))))) 10.0) (/ (* (* k k) k) a)))
44.0ms
(/ (* (exp (- (- (* m (log k))))) a) (* k k))
267.0ms
(+ (* (/ 99.0 (* k k)) (/ (* (exp (- (- (* m (log k))))) a) (* k k))) (- (* (/ (exp (- (- (* m (log k))))) k) (/ a k)) (/ (* (exp (- (- (* m (log k))))) 10.0) (/ (* (* k k) k) a))))

series770.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (* (exp (- (- (* m (log k))))) 10.0) (/ (* (* k k) k) a))
239.0ms
(- (* (/ (exp (- (- (* m (log k))))) k) (/ a k)) (/ (* (exp (- (- (* m (log k))))) 10.0) (/ (* (* k k) k) a)))
168.0ms
(/ (* (exp (- (- (* m (log k))))) a) (* k k))
219.0ms
(+ (* (/ 99.0 (* k k)) (/ (* (exp (- (- (* m (log k))))) a) (* k k))) (- (* (/ (exp (- (- (* m (log k))))) k) (/ a k)) (/ (* (exp (- (- (* m (log k))))) 10.0) (/ (* (* k k) k) a))))

simplify1.6s

Counts
124 → 124
Iterations
IterNodes
done5001
11070
0311

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes205.0ms

Accuracy

97.2% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.9b

bsearch87.0ms

Steps
ItersRangePoint
8
4.703882389530098e+116
1.702292392859228e+121
5.127945408381113e+118

simplify2.7s

Iterations
IterNodes
done5000
61937
5714
4280
3112
261
154
036

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.0s11997×body80valid
296.0ms4180×body80nan