Details

Time bar (total: 5.2s)

sample43.0ms

Algorithm
intervals
Results
18.0ms399×body80valid
4.0ms134×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: 2.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(* a (pow k m))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
2.1b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
16×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
7×associate-*r*
6×fma-def prod-exp
4×pow1 expm1-log1p-u unpow-prod-down div-exp sum-log log1p-expm1-u
3×flip3-+ times-frac associate-*l* associate-/r* flip-+ unswap-sqr
2×cbrt-undiv +-commutative pow-to-exp pow-exp associate-/r/ cbrt-unprod sqr-pow
1×associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
4 → 88
Calls
4 calls:
5.0ms
(+ 1.0 (* 10.0 k))
11.0ms
(* a (pow k m))
25.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
31.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ 1.0 (* 10.0 k))
58.0ms
(* a (pow k m))
23.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
120.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify59.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0477629
12275544
25001524

prune267.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.3b
(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
1.8b
(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
45×times-frac
37×add-cube-cbrt *-un-lft-identity
27×associate-*r*
22×unpow-prod-down
19×add-exp-log
11×add-cbrt-cube add-log-exp
8×sqr-pow
7×associate-/l*
6×pow1 fma-def div-exp
4×expm1-log1p-u flip3-+ prod-exp sum-log associate-/r/ flip-+ log1p-expm1-u unswap-sqr
3×associate-*l* associate-/r*
2×cbrt-undiv +-commutative pow-to-exp pow-exp cbrt-unprod div-inv
1×associate-+l+ frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 135
Calls
4 calls:
5.0ms
(+ 1.0 (* 10.0 k))
23.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
28.0ms
(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
64.0ms
(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

series243.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(+ 1.0 (* 10.0 k))
19.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
64.0ms
(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
120.0ms
(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

simplify77.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06341353
129391224
250011204

prune401.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (* a (pow k m)))
0.3b
(cbrt (* a (pow k m)))
0.3b
(cbrt (* a (pow k m)))
2.1b
(/ (* (* (cbrt (* a (pow k m))) (cbrt (* a (pow k m)))) (cbrt (* a (pow k m)))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
9×add-cbrt-cube
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv cbrt-prod times-frac pow1/3 div-exp prod-exp associate-/r* cbrt-unprod
2×associate-/r/
1×frac-2neg flip3-+ clear-num flip-+ div-inv associate-/l*
Counts
4 → 60
Calls
4 calls:
4.0ms
(cbrt (* a (pow k m)))
5.0ms
(cbrt (* a (pow k m)))
4.0ms
(cbrt (* a (pow k m)))
64.0ms
(/ (* (* (cbrt (* a (pow k m))) (cbrt (* a (pow k m)))) (cbrt (* a (pow k m)))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series496.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(cbrt (* a (pow k m)))
119.0ms
(cbrt (* a (pow k m)))
119.0ms
(cbrt (* a (pow k m)))
137.0ms
(/ (* (* (cbrt (* a (pow k m))) (cbrt (* a (pow k m)))) (cbrt (* a (pow k m)))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify53.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0433889
11902690
25002624

prune237.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.8b
(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
6.4b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
6.7b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
9.8b
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
19×times-frac associate-/r*
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
12×unpow-prod-down div-exp
8×exp-neg distribute-rgt-neg-out associate-/l/
6×cube-prod associate-*r/ prod-exp add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u pow-to-exp mul-1-neg log-rec pow-exp un-div-inv log1p-expm1-u sqr-pow
2×cube-mult frac-2neg unpow3 clear-num cbrt-unprod div-inv associate-/l*
1×sub-neg flip3-- fma-neg diff-log prod-diff frac-sub flip-- fma-udef
Counts
4 → 115
Calls
4 calls:
0.0ms
(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
34.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
33.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
68.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

series534.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
82.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
84.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
172.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

simplify99.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
06231864
131711567
250011493

prune557.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes121.0ms

Accuracy

98.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.2b

bsearch52.0ms

Steps
ItersRangePoint
7
5.366729015293418e+103
4.473646891062652e+105
3.2595899677754594e+105

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04834
15434
25434

end0.0ms

sample1.1s

Algorithm
intervals
Results
470.0ms11973×body80valid
139.0ms4297×body80nan