Details

Time bar (total: 6.1s)

sample56.0ms

Algorithm
intervals
Results
29.0ms381×body80valid
11.0ms134×body80nan

simplify107.0ms

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: 1.9b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

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:
13.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
2.0ms
(+ 1.0 (* 10.0 k))
14.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series164.0ms

Counts
3 → 9
Calls
3 calls:
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
31.0ms
(+ 1.0 (* 10.0 k))
115.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify58.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0421510
11910434
25001411

prune198.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(+ 1.0 (* 10.0 k))
0.4b
(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
1.5b
(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

rewrite66.0ms

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:
10.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
2.0ms
(+ 1.0 (* 10.0 k))
14.0ms
(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
34.0ms
(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

series242.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
39.0ms
(+ 1.0 (* 10.0 k))
63.0ms
(/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k)))
118.0ms
(* a (/ (pow k m) (+ (+ 1.0 (* 10.0 k)) (* k k))))

simplify78.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06341353
129391224
250011204

prune440.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 10.0 k 1.0)
0.1b
(/ 1 (/ (/ (fma k k (fma 10.0 k 1.0)) a) (pow k m)))
3.1b
(/ (fma k k (fma 10.0 k 1.0)) a)

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
910×times-frac
411×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
156×unpow-prod-down
98×associate-/r*
54×add-exp-log
52×sqr-pow
42×div-exp
34×div-inv
14×add-cbrt-cube
7×cbrt-undiv rec-exp 1-exp
6×pow-to-exp pow-exp associate-/l*
4×pow1
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×pow-flip associate-/r/ fma-udef inv-pow
Counts
3 → 461
Calls
3 calls:
0.0ms
(fma 10.0 k 1.0)
24.0ms
(/ 1 (/ (/ (fma k k (fma 10.0 k 1.0)) a) (pow k m)))
2.0ms
(/ (fma k k (fma 10.0 k 1.0)) a)

series195.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(fma 10.0 k 1.0)
119.0ms
(/ 1 (/ (/ (fma k k (fma 10.0 k 1.0)) a) (pow k m)))
46.0ms
(/ (fma k k (fma 10.0 k 1.0)) a)

simplify105.0ms

Algorithm
egg-herbie
Counts
470 → 470
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
019806536
150016146

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.5b
(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)))))
7.0b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
7.2b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
8.9b
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

rewrite96.0ms

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)))))
19.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
20.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
53.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

series682.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(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)))))
268.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
77.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
165.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

simplify101.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
06231864
131711567
250011493

prune538.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes82.0ms

Accuracy

96.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.8b

bsearch47.0ms

Steps
ItersRangePoint
6
2.5067473576404643e+51
1.7561373841210664e+52
1.1763946994143888e+52

simplify6.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04834
15434
25434

end0.0ms

sample1.6s

Algorithm
intervals
Results
936.0ms11950×body80valid
248.0ms4351×body80nan