Details

Time bar (total: 10.1s)

analyze5.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%74.9%25.1%0
0%74.9%25.1%1
37.5%37.5%25.1%2
37.5%18.7%43.8%3
46.8%9.4%43.8%4
51.5%4.7%43.8%5
51.5%2.3%46.1%6
52.7%1.2%46.1%7
53.3%0.6%46.1%8
53.3%0.3%46.4%9
53.4%0.1%46.4%10
53.5%0.1%46.4%11
53.5%0%46.5%12
53.5%0%46.5%13
53.5%0%46.5%14

sample33.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
3.0ms256×pre80true

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0502233

prune15.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.1b

Counts
2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow (fabs x) 5) 5.0)
0.1b
(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
0.1b
(/ (pow (fabs x) 3) 3.0)
1.0b
(sqrt PI)

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
77×times-frac
69×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity
32×associate-*r/
24×unpow-prod-down
22×associate-*l*
19×add-exp-log associate-/l*
16×frac-add
13×sqrt-prod add-cbrt-cube
12×flip3-+ cube-prod flip-+
8×frac-times sqr-pow
7×pow1 div-exp
6×associate-/r*
4×cube-mult unpow3 add-log-exp
3×cbrt-undiv associate-*r* div-inv unswap-sqr
2×pow-to-exp frac-2neg pow-exp prod-exp clear-num cbrt-unprod
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative
Counts
4 → 183
Calls
4 calls:
5.0ms
(/ (pow (fabs x) 5) 5.0)
22.0ms
(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
5.0ms
(/ (pow (fabs x) 3) 3.0)
1.0ms
(sqrt PI)

series76.0ms

Counts
4 → 10
Calls
4 calls:
10.0ms
(/ (pow (fabs x) 5) 5.0)
55.0ms
(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
11.0ms
(/ (pow (fabs x) 3) 3.0)
0.0ms
(sqrt PI)

simplify63.0ms

Algorithm
egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
052304238

prune532.0ms

Filtered
133 candidates to 193 candidates (-45.1%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1903193
Fresh101
Picked011
Done000
Total1914195

Merged error: 0b

Counts
195 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow (fabs x) 7) 0.047619047619047616)
0.1b
(* (pow (fabs x) 5) 0.2)
0.1b
(* (sqrt (/ 1 PI)) (+ (* (pow (fabs x) 3) 0.6666666666666666) (+ (* (pow (fabs x) 5) 0.2) (+ (* (fabs x) 2.0) (* (pow (fabs x) 7) 0.047619047619047616)))))
0.1b
(* (pow (fabs x) 3) 0.6666666666666666)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
42×associate-*l*
24×*-un-lft-identity
23×add-cube-cbrt
21×add-exp-log
16×sqrt-prod
14×unswap-sqr
12×unpow-prod-down associate-*r* add-cbrt-cube
11×times-frac
10×prod-exp
6×pow1 sqr-pow
4×cube-prod *-commutative cbrt-unprod add-log-exp
3×pow-to-exp sqrt-div pow-exp
2×frac-times flip3-+ associate-*r/ flip-+
1×distribute-rgt-in cube-mult distribute-lft-in unpow3 pow-prod-down associate-*l/ div-inv
Counts
4 → 122
Calls
4 calls:
5.0ms
(* (pow (fabs x) 7) 0.047619047619047616)
5.0ms
(* (pow (fabs x) 5) 0.2)
15.0ms
(* (sqrt (/ 1 PI)) (+ (* (pow (fabs x) 3) 0.6666666666666666) (+ (* (pow (fabs x) 5) 0.2) (+ (* (fabs x) 2.0) (* (pow (fabs x) 7) 0.047619047619047616)))))
6.0ms
(* (pow (fabs x) 3) 0.6666666666666666)

series76.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* (pow (fabs x) 7) 0.047619047619047616)
10.0ms
(* (pow (fabs x) 5) 0.2)
46.0ms
(* (sqrt (/ 1 PI)) (+ (* (pow (fabs x) 3) 0.6666666666666666) (+ (* (pow (fabs x) 5) 0.2) (+ (* (fabs x) 2.0) (* (pow (fabs x) 7) 0.047619047619047616)))))
7.0ms
(* (pow (fabs x) 3) 0.6666666666666666)

simplify76.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
050142303

prune338.0ms

Filtered
93 candidates to 134 candidates (-44.1%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1340134
Fresh022
Picked011
Done011
Total1344138

Merged error: 0b

Counts
138 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI))))
0.4b
(* (sqrt (/ 1.0 (sqrt PI))) (* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI)))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
92×associate-*r/
72×sqrt-prod
48×frac-add
47×add-sqr-sqrt
45×sqrt-div
41×frac-times
38×times-frac
36×flip3-+ flip-+
35×add-cube-cbrt *-un-lft-identity
28×associate-*l*
26×associate-*r*
25×associate-*l/
13×pow1
11×add-exp-log add-cbrt-cube
4×pow-prod-down prod-exp cbrt-unprod add-log-exp unswap-sqr
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative div-inv
Counts
4 → 161
Calls
4 calls:
24.0ms
(* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI))))
30.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI)))))
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series140.0ms

Counts
4 → 8
Calls
4 calls:
77.0ms
(* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI))))
63.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (* (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt (/ 1.0 (sqrt PI)))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify71.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
050887602

prune845.0ms

Filtered
133 candidates to 169 candidates (-27.1%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1690169
Fresh011
Picked011
Done022
Total1694173

Merged error: 0b

Counts
173 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ 1.0 (sqrt PI))) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0))))))
0.5b
(* (* (sqrt (/ 1.0 (sqrt PI))) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))) (* (sqrt (/ 1.0 (sqrt PI))) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
1201×associate-*r/
925×sqrt-div
592×frac-add
585×frac-times
444×flip3-+ flip-+
65×pow1
54×associate-*l/
52×sqrt-prod
44×add-sqr-sqrt
38×pow-prod-down
26×associate-*l*
22×add-cube-cbrt *-un-lft-identity times-frac
20×sqrt-pow1 pow1/2
18×add-exp-log add-cbrt-cube
9×prod-exp cbrt-unprod
8×pow-prod-up unswap-sqr
7×associate-*r*
6×sqrt-unprod pow-sqr
4×add-log-exp
2×rem-sqrt-square pow-plus *-commutative
1×pow2 swap-sqr rem-square-sqrt div-inv
Counts
4 → 463
Calls
4 calls:
30.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0))))))
56.0ms
(* (* (sqrt (/ 1.0 (sqrt PI))) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))) (* (sqrt (/ 1.0 (sqrt PI))) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))))
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series159.0ms

Counts
4 → 8
Calls
4 calls:
93.0ms
(* (sqrt (/ 1.0 (sqrt PI))) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0))))))
66.0ms
(* (* (sqrt (/ 1.0 (sqrt PI))) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))) (* (sqrt (/ 1.0 (sqrt PI))) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify361.0ms

Algorithm
egg-herbie
Counts
471 → 471
Iterations

Useful iterations: 0 (98.0ms)

IterNodesCost
0557163716

prune5.9s

Filtered
259 candidates to 471 candidates (-81.9%)
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New4710471
Fresh000
Picked011
Done033
Total4714475

Merged error: 0b

Counts
475 → 4

regimes83.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03233
13233

end0.0ms

analyze5.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%74.9%25.1%0
0%74.9%25.1%1
37.5%37.5%25.1%2
37.5%18.7%43.8%3
46.8%9.4%43.8%4
51.5%4.7%43.8%5
51.5%2.3%46.1%6
52.7%1.2%46.1%7
53.3%0.6%46.1%8
53.3%0.3%46.4%9
53.4%0.1%46.4%10
53.5%0.1%46.4%11
53.5%0%46.5%12
53.5%0%46.5%13
53.5%0%46.5%14

sample924.0ms

Algorithm
intervals
Results
747.0ms8000×body80valid
80.0ms8002×pre80true
0.0ms2×body80invalid

Profiling

Loading profile data...