Details

Time bar (total: 5.7s)

sample42.0ms

Algorithm
intervals
Results
16.0ms397×body80valid
4.0ms137×body80nan

simplify106.0ms

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: 3.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* a (pow k m))
3.3b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
14×add-sqr-sqrt
10×add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
8×add-log-exp
7×associate-*r*
6×prod-exp
4×unpow-prod-down div-exp
3×pow1 expm1-log1p-u fma-def times-frac associate-*l* associate-/r* sum-log log1p-expm1-u unswap-sqr
2×cbrt-undiv pow-to-exp flip3-+ pow-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×+-commutative associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
3 → 72
Calls
3 calls:
23.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
11.0ms
(* a (pow k m))
35.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series213.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
60.0ms
(* a (pow k m))
127.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify55.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0419575
12040495
25002476

prune225.0ms

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
(fma k k (fma k 10.0 1.0))
0.0b
(* a (pow k m))
0.0b
(fma k 10.0 1.0)
3.3b
(/ (* a (pow k m)) (fma k k (fma k 10.0 1.0)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
14×add-sqr-sqrt
11×add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
7×associate-*r*
6×prod-exp
4×pow1 expm1-log1p-u unpow-prod-down div-exp log1p-expm1-u add-log-exp
3×times-frac associate-*l* associate-/r* unswap-sqr
2×cbrt-undiv pow-to-exp pow-exp cbrt-unprod fma-udef sqr-pow
1×frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
4 → 72
Calls
4 calls:
0.0ms
(fma k k (fma k 10.0 1.0))
11.0ms
(* a (pow k m))
0.0ms
(fma k 10.0 1.0)
12.0ms
(/ (* a (pow k m)) (fma k k (fma k 10.0 1.0)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(fma k k (fma k 10.0 1.0))
69.0ms
(* a (pow k m))
33.0ms
(fma k 10.0 1.0)
133.0ms
(/ (* a (pow k m)) (fma k k (fma k 10.0 1.0)))

simplify48.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0339452
11565398
25001396

prune234.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma k k (fma k 10.0 1.0))
0.0b
(fma k 10.0 1.0)
0.3b
(/ 1 (/ (/ (fma k k (fma k 10.0 1.0)) a) (pow k m)))
6.3b
(/ (fma k k (fma k 10.0 1.0)) a)

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
910×times-frac
412×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
156×unpow-prod-down
98×associate-/r*
55×add-exp-log
52×sqr-pow
42×div-exp
34×div-inv
15×add-cbrt-cube
7×cbrt-undiv rec-exp 1-exp
6×pow-to-exp pow-exp associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef
1×pow-flip associate-/r/ inv-pow
Counts
4 → 471
Calls
4 calls:
0.0ms
(fma k k (fma k 10.0 1.0))
0.0ms
(fma k 10.0 1.0)
30.0ms
(/ 1 (/ (/ (fma k k (fma k 10.0 1.0)) a) (pow k m)))
5.0ms
(/ (fma k k (fma k 10.0 1.0)) a)

series433.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(fma k k (fma k 10.0 1.0))
32.0ms
(fma k 10.0 1.0)
329.0ms
(/ 1 (/ (/ (fma k k (fma k 10.0 1.0)) a) (pow k m)))
48.0ms
(/ (fma k k (fma k 10.0 1.0)) a)

simplify99.0ms

Algorithm
egg-herbie
Counts
483 → 483
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
019786582
150016184

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:

1.3b
(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)))))
6.2b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
6.8b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
10.5b
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

rewrite141.0ms

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 4))
33.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
70.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

series535.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(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)))))
85.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
81.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
179.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

simplify96.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
06231870
132191577
250011498

prune554.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes101.0ms

Accuracy

98.6% (0.0b remaining)

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

bsearch63.0ms

Steps
ItersRangePoint
9
5.098462060644642e+87
3.971023081162148e+94
4.152474476509974e+93

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04332
14932
24932

end0.0ms

sample1.1s

Algorithm
intervals
Results
465.0ms11815×body80valid
132.0ms4199×body80nan