Details

Time bar (total: 5.0s)

sample39.0ms

Algorithm
intervals
Results
17.0ms388×body80valid
5.0ms146×body80nan

simplify101.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0247
1535
21065
32695
49045
539765
650015

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.8b

Counts
2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(* a (pow k m))
0.2b
(+ (+ 1.0 (* 10.0 k)) (* k k))
1.8b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite26.0ms

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))
12.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ 1.0 (* 10.0 k))
60.0ms
(* a (pow k m))
17.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
116.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify61.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0477629
12275544
25001524

prune259.0ms

Filtered
100 candidates to 79 candidates (79.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New973100
Fresh101
Picked101
Done000
Total993102

Merged error: 0.0b

Counts
102 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (pow k m))
0.1b
(fma 10.0 k 1.0)
0.3b
(fma k k (fma 10.0 k 1.0))
1.8b
(/ (* a (pow k m)) (fma k k (fma 10.0 k 1.0)))

rewrite13.0ms

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:
5.0ms
(* a (pow k m))
1.0ms
(fma 10.0 k 1.0)
1.0ms
(fma k k (fma 10.0 k 1.0))
5.0ms
(/ (* a (pow k m)) (fma k k (fma 10.0 k 1.0)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* a (pow k m))
31.0ms
(fma 10.0 k 1.0)
22.0ms
(fma k k (fma 10.0 k 1.0))
122.0ms
(/ (* a (pow k m)) (fma k k (fma 10.0 k 1.0)))

simplify49.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0337452
11558398
25002396

prune182.0ms

Filtered
84 candidates to 63 candidates (75.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New84084
Fresh022
Picked011
Done000
Total84387

Merged error: 0.0b

Counts
87 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt k)
0.6b
(cbrt k)
0.6b
(cbrt k)
1.8b
(/ (* (* 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)))

series932.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(cbrt k)
183.0ms
(cbrt k)
189.0ms
(cbrt k)
382.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify75.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
0514921
12446788
25001734

prune249.0ms

Filtered
91 candidates to 65 candidates (71.4%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New91091
Fresh011
Picked011
Done011
Total91394

Merged error: 0.0b

Counts
94 → 3

localize26.0ms

Local error

Found 4 expressions with local error:

2.3b
(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)))))
8.7b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
9.4b
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))
10.0b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))

rewrite55.0ms

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 3))
16.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))
20.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))

series517.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(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)))))
73.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
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))))
87.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))

simplify111.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
06231864
131711567
250011493

prune524.0ms

Filtered
127 candidates to 92 candidates (72.4%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1261127
Fresh000
Picked011
Done022
Total1264130

Merged error: 0.0b

Counts
130 → 4

regimes97.0ms

Accuracy

97.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.0b

bsearch64.0ms

Steps
ItersRangePoint
8
2961801.3515057173
792715797.106664
47938280.69878704

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04332
14932
24932

end0.0ms

sample1.1s

Algorithm
intervals
Results
573.0ms11890×body80valid
152.0ms4154×body80nan