Details

Time bar (total: 4.4s)

sample35.0ms

Algorithm
intervals
Results
15.0ms377×body80valid
5.0ms138×body80nan

simplify105.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0247
1535
21065
32695
49045
539765
650015

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
2.7b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
10×add-log-exp
8×add-cbrt-cube
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×fma-def
4×div-exp sum-log
3×pow1 expm1-log1p-u flip3-+ times-frac prod-exp associate-/r* flip-+ log1p-expm1-u
2×cbrt-undiv +-commutative associate-/r/
1×pow-to-exp associate-+l+ frac-2neg pow-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
3 → 61
Calls
3 calls:
2.0ms
(+ 1.0 (* 10.0 k))
10.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
13.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series164.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(+ 1.0 (* 10.0 k))
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
113.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify54.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0421510
11910434
25001411

prune201.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

4.4b
(/ a (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
16.6b
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.6b
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.6b
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
9×add-exp-log cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ flip-+
8×associate-/r/
7×add-cbrt-cube
4×pow1 expm1-log1p-u frac-times log1p-expm1-u add-log-exp
3×times-frac pow1/3 associate-/l*
2×cbrt-undiv associate-*r/ div-exp associate-*l/
1×frac-2neg prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 76
Calls
4 calls:
17.0ms
(/ a (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
5.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
6.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
6.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series528.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(/ a (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
108.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
114.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
107.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify140.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03871085
11299990
24786952
35001952

prune371.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (sqrt (+ 1.0 (* 10.0 k))) (sqrt (+ 1.0 (* 10.0 k))) (* k k))
0.1b
(sqrt (+ 1.0 (* 10.0 k)))
0.1b
(sqrt (+ 1.0 (* 10.0 k)))
2.7b
(/ (* a (pow k m)) (fma (sqrt (+ 1.0 (* 10.0 k))) (sqrt (+ 1.0 (* 10.0 k))) (* k k)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log
10×add-sqr-sqrt
9×add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×expm1-log1p-u sqrt-div div-exp log1p-expm1-u add-log-exp
3×times-frac prod-exp associate-/r*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×pow-to-exp frac-2neg pow-exp clear-num cbrt-unprod fma-udef div-inv associate-/l*
Counts
4 → 69
Calls
4 calls:
0.0ms
(fma (sqrt (+ 1.0 (* 10.0 k))) (sqrt (+ 1.0 (* 10.0 k))) (* k k))
3.0ms
(sqrt (+ 1.0 (* 10.0 k)))
3.0ms
(sqrt (+ 1.0 (* 10.0 k)))
4.0ms
(/ (* a (pow k m)) (fma (sqrt (+ 1.0 (* 10.0 k))) (sqrt (+ 1.0 (* 10.0 k))) (* k k)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(fma (sqrt (+ 1.0 (* 10.0 k))) (sqrt (+ 1.0 (* 10.0 k))) (* k k))
37.0ms
(sqrt (+ 1.0 (* 10.0 k)))
43.0ms
(sqrt (+ 1.0 (* 10.0 k)))
159.0ms
(/ (* a (pow k m)) (fma (sqrt (+ 1.0 (* 10.0 k))) (sqrt (+ 1.0 (* 10.0 k))) (* k k)))

simplify53.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0397830
11586664
25001590

prune253.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

16.6b
(cbrt (- (+ 1.0 (* 10.0 k)) (* k k)))
16.6b
(cbrt (- (+ 1.0 (* 10.0 k)) (* k k)))
17.3b
(- (* (+ 1.0 (* 10.0 k)) (+ 1.0 (* 10.0 k))) (* (* k k) (* k k)))
17.3b
(- (* (+ 1.0 (* 10.0 k)) (+ 1.0 (* 10.0 k))) (* (* k k) (* k k)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod add-sqr-sqrt add-log-exp
6×add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u cbrt-div flip3-- associate--l+ add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×distribute-rgt-in sub-neg distribute-lft-in fma-neg pow1/3 diff-log prod-diff
Counts
4 → 70
Calls
4 calls:
6.0ms
(cbrt (- (+ 1.0 (* 10.0 k)) (* k k)))
6.0ms
(cbrt (- (+ 1.0 (* 10.0 k)) (* k k)))
9.0ms
(- (* (+ 1.0 (* 10.0 k)) (+ 1.0 (* 10.0 k))) (* (* k k) (* k k)))
9.0ms
(- (* (+ 1.0 (* 10.0 k)) (+ 1.0 (* 10.0 k))) (* (* k k) (* k k)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(cbrt (- (+ 1.0 (* 10.0 k)) (* k k)))
121.0ms
(cbrt (- (+ 1.0 (* 10.0 k)) (* k k)))
38.0ms
(- (* (+ 1.0 (* 10.0 k)) (+ 1.0 (* 10.0 k))) (* (* k k) (* k k)))
33.0ms
(- (* (+ 1.0 (* 10.0 k)) (+ 1.0 (* 10.0 k))) (* (* k k) (* k k)))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0324944
11279802
25001760

prune477.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes86.0ms

Accuracy

97.7% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.1b

bsearch66.0ms

Steps
ItersRangePoint
8
166023.53156923671
2176177528.7908425
2657436.092148706

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05147
15747
25747

end0.0ms

sample994.0ms

Algorithm
intervals
Results
502.0ms11901×body80valid
153.0ms4227×body80nan