Details

Time bar (total: 6.5s)

sample42.0ms

Algorithm
intervals
Results
18.0ms391×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: 3.1b

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))
3.1b
(/ (* 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))
23.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
32.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series205.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ 1.0 (* 10.0 k))
51.0ms
(* a (pow k m))
19.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
105.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify59.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0477629
12275544
25001524

prune265.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

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
(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
4.7b
(/ (fma k k (fma k 10.0 1.0)) a)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
172×times-frac
96×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
42×unpow-prod-down
19×add-exp-log
16×associate-/r*
14×sqr-pow
11×add-cbrt-cube
10×div-exp div-inv associate-/l*
4×pow1 cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-to-exp frac-2neg pow-exp clear-num fma-udef
1×associate-/r/
Counts
4 → 181
Calls
4 calls:
0.0ms
(fma k k (fma k 10.0 1.0))
0.0ms
(fma k 10.0 1.0)
15.0ms
(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
5.0ms
(/ (fma k k (fma k 10.0 1.0)) a)

series194.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(fma k k (fma k 10.0 1.0))
32.0ms
(fma k 10.0 1.0)
100.0ms
(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
41.0ms
(/ (fma k k (fma k 10.0 1.0)) a)

simplify90.0ms

Algorithm
egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
07151922
132801854
250021852

prune534.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (pow k (/ m 2)) (sqrt (fma k k (fma k 10.0 1.0)))) (/ (pow k (/ m 2)) (/ (sqrt (fma k k (fma k 10.0 1.0))) a)))
0.4b
(/ (pow k (/ m 2)) (/ (sqrt (fma k k (fma k 10.0 1.0))) a))
16.6b
(sqrt (fma k k (fma k 10.0 1.0)))
16.6b
(sqrt (fma k k (fma k 10.0 1.0)))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
785×times-frac
585×add-sqr-sqrt
319×add-cube-cbrt *-un-lft-identity
213×sqrt-prod
194×unpow-prod-down
159×associate-*r*
115×add-exp-log
92×sqr-pow
70×unswap-sqr
66×div-exp
46×associate-*l*
30×add-cbrt-cube
28×prod-exp
22×associate-/r*
18×div-inv
17×pow-to-exp pow-exp
12×cbrt-undiv
8×pow1
7×associate-/l*
6×cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 557
Calls
4 calls:
149.0ms
(* (/ (pow k (/ m 2)) (sqrt (fma k k (fma k 10.0 1.0)))) (/ (pow k (/ m 2)) (/ (sqrt (fma k k (fma k 10.0 1.0))) a)))
15.0ms
(/ (pow k (/ m 2)) (/ (sqrt (fma k k (fma k 10.0 1.0))) a))
1.0ms
(sqrt (fma k k (fma k 10.0 1.0)))
2.0ms
(sqrt (fma k k (fma k 10.0 1.0)))

series419.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(* (/ (pow k (/ m 2)) (sqrt (fma k k (fma k 10.0 1.0)))) (/ (pow k (/ m 2)) (/ (sqrt (fma k k (fma k 10.0 1.0))) a)))
194.0ms
(/ (pow k (/ m 2)) (/ (sqrt (fma k k (fma k 10.0 1.0))) a))
54.0ms
(sqrt (fma k k (fma k 10.0 1.0)))
48.0ms
(sqrt (fma k k (fma k 10.0 1.0)))

simplify136.0ms

Algorithm
egg-herbie
Counts
569 → 569
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0211310171
150029863

prune1.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

2.7b
(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)))))
6.9b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
8.2b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
9.6b
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

rewrite137.0ms

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))
32.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
67.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

series465.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(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)))))
76.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
67.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
158.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

simplify98.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06231864
131711567
250011493

prune556.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes111.0ms

Accuracy

97.6% (0.0b remaining)

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

bsearch53.0ms

Steps
ItersRangePoint
7
266562863.36314517
54925220648.27056
16862378543.897915

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05333
15933
25933

end0.0ms

sample1.1s

Algorithm
intervals
Results
473.0ms12045×body80valid
141.0ms4262×body80nan