Details

Time bar (total: 5.6s)

sample51.0ms

Algorithm
intervals
Results
26.0ms380×body80valid
7.0ms156×body80nan

simplify109.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0247
1535
21065
32695
49045
539765
650015

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 1.7b

Counts
2 → 1

localize15.0ms

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))
1.7b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite24.0ms

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:
3.0ms
(+ 1.0 (* 10.0 k))
5.0ms
(* a (pow k m))
5.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
9.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ 1.0 (* 10.0 k))
61.0ms
(* a (pow k m))
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
115.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify67.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0477629
12275544
25001524

prune239.0ms

Filtered
100 candidates to 79 candidates (79.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New964100
Fresh000
Picked101
Done000
Total974101

Merged error: 0.0b

Counts
101 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt k)
0.6b
(cbrt k)
0.6b
(cbrt k)
1.7b
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
30×prod-exp
16×div-exp
13×add-cbrt-cube
11×pow-exp
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×pow-to-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac pow1/3 associate-/r* cbrt-unprod
2×associate-/r/
1×frac-2neg flip3-+ clear-num flip-+ div-inv associate-/l*
Counts
4 → 79
Calls
4 calls:
1.0ms
(cbrt k)
1.0ms
(cbrt k)
1.0ms
(cbrt k)
12.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series907.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(cbrt k)
182.0ms
(cbrt k)
177.0ms
(cbrt k)
374.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify65.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0514921
12446788
25001734

prune247.0ms

Filtered
91 candidates to 65 candidates (71.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New91091
Fresh033
Picked011
Done000
Total91495

Merged error: 0.0b

Counts
95 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma 10.0 k 1.0)
0.1b
(pow (fma k k (fma 10.0 k 1.0)) 3)
1.7b
(/ (* a (pow k m)) (cbrt (pow (fma k k (fma 10.0 k 1.0)) 3)))
10.0b
(cbrt (pow (fma k k (fma 10.0 k 1.0)) 3))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×add-exp-log times-frac associate-/r*
12×unpow-prod-down cube-prod
8×add-cbrt-cube
5×pow1
4×expm1-log1p-u cube-mult unpow3 div-exp log1p-expm1-u add-log-exp sqr-pow
3×pow-unpow prod-exp
2×cbrt-undiv pow-to-exp pow-exp
1×pow-pow frac-2neg pow1/3 clear-num rem-cbrt-cube cbrt-unprod fma-udef div-inv associate-/l* rem-cube-cbrt
Counts
4 → 107
Calls
4 calls:
1.0ms
(fma 10.0 k 1.0)
2.0ms
(pow (fma k k (fma 10.0 k 1.0)) 3)
8.0ms
(/ (* a (pow k m)) (cbrt (pow (fma k k (fma 10.0 k 1.0)) 3)))
2.0ms
(cbrt (pow (fma k k (fma 10.0 k 1.0)) 3))

series222.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma 10.0 k 1.0)
43.0ms
(pow (fma k k (fma 10.0 k 1.0)) 3)
120.0ms
(/ (* a (pow k m)) (cbrt (pow (fma k k (fma 10.0 k 1.0)) 3)))
22.0ms
(cbrt (pow (fma k k (fma 10.0 k 1.0)) 3))

simplify60.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0425769
11906700
25001683

prune225.0ms

Filtered
119 candidates to 67 candidates (56.3%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1190119
Fresh022
Picked011
Done011
Total1194123

Merged error: 0.0b

Counts
123 → 4

localize32.0ms

Local error

Found 4 expressions with local error:

2.5b
(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)))))
7.7b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
9.4b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
9.5b
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

rewrite50.0ms

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:
1.0ms
(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)))))
15.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
16.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
15.0ms
(- (* 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:
169.0ms
(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)))))
272.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
76.0ms
(/ (* 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))))

simplify105.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
06231864
131711567
250011493

prune503.0ms

Filtered
127 candidates to 92 candidates (72.4%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1252127
Fresh011
Picked011
Done022
Total1256131

Merged error: 0.0b

Counts
131 → 6

regimes120.0ms

Accuracy

97% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch75.0ms

Steps
ItersRangePoint
9
15146.518640101762
1580762020.1433036
3884199.03848918

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05340
15940
25940

end0.0ms

sample1.5s

Algorithm
intervals
Results
855.0ms11927×body80valid
194.0ms4128×body80nan