Details

Time bar (total: 3.1s)

analyze132.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%68.7%6.3%6
25%56.2%18.8%7
25%48.4%26.6%8
25%35.1%39.9%9
28.1%18.3%53.6%10
31.6%12.3%56.1%11
33.4%5.9%60.8%12
35.2%3.8%61%13
36.1%2.9%61%14

sample24.0ms

Algorithm
intervals
Results
16.0ms256×body80valid

simplify81.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
0490631
1490631

prune6.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.2b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×associate-*r/
3×distribute-rgt-in unpow-prod-down pow-unpow distribute-lft-in
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out sqr-pow
Counts
4 → 77
Calls
4 calls:
8.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
7.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series59.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
5.0ms
(* (* a a) (+ 1.0 a))
21.0ms
(pow (+ (* a a) (* b b)) 2.0)
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify27.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
058811271

prune140.0ms

Filtered
63 candidates to 89 candidates (-41.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New87289
Fresh000
Picked011
Done000
Total87390

Merged error: 0.0b

Counts
90 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* a a) 2)
0.0b
(+ (pow b 4) (+ (* (* b b) (* (* a a) 2)) (pow a 4)))
0.0b
(+ (* (* b b) (* (* a a) 2)) (pow a 4))
2.2b
(* (* b b) (* (* a a) 2))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
11×add-log-exp
7×*-un-lft-identity
6×add-sqr-sqrt
5×add-cube-cbrt
4×associate-*r* sum-log
2×+-commutative flip3-+ associate-*l* *-commutative flip-+
1×associate-+r+ distribute-lft-out unswap-sqr
Counts
4 → 72
Calls
4 calls:
5.0ms
(* (* a a) 2)
13.0ms
(+ (pow b 4) (+ (* (* b b) (* (* a a) 2)) (pow a 4)))
11.0ms
(+ (* (* b b) (* (* a a) 2)) (pow a 4))
9.0ms
(* (* b b) (* (* a a) 2))

series37.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (* a a) 2)
13.0ms
(+ (pow b 4) (+ (* (* b b) (* (* a a) 2)) (pow a 4)))
14.0ms
(+ (* (* b b) (* (* a a) 2)) (pow a 4))
7.0ms
(* (* b b) (* (* a a) 2))

simplify36.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
05557980

prune104.0ms

Filtered
47 candidates to 84 candidates (-78.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New83184
Fresh011
Picked101
Done011
Total84387

Merged error: 0.0b

Counts
87 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* b (* b (* a (+ a a)))) (pow b 4))
0.0b
(+ (+ (* b (* b (* a (+ a a)))) (pow b 4)) (pow a 4))
0.5b
(* b (* b (* a (+ a a))))
0.6b
(* b (* a (+ a a)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
28×distribute-rgt-in distribute-lft-in
18×pow1 add-exp-log add-cbrt-cube
11×add-log-exp
10×associate-*r/
9×associate-+l+ pow-prod-down prod-exp cbrt-unprod
8×*-un-lft-identity
6×add-sqr-sqrt add-cube-cbrt associate-*l*
4×flip3-+ sum-log flip-+
2×+-commutative associate-*r* *-commutative
1×distribute-lft-out
Counts
4 → 88
Calls
4 calls:
12.0ms
(+ (* b (* b (* a (+ a a)))) (pow b 4))
14.0ms
(+ (+ (* b (* b (* a (+ a a)))) (pow b 4)) (pow a 4))
9.0ms
(* b (* b (* a (+ a a))))
7.0ms
(* b (* a (+ a a)))

series37.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (* b (* b (* a (+ a a)))) (pow b 4))
13.0ms
(+ (+ (* b (* b (* a (+ a a)))) (pow b 4)) (pow a 4))
7.0ms
(* b (* b (* a (+ a a))))
7.0ms
(* b (* a (+ a a)))

simplify50.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
049231227
149231227

prune104.0ms

Filtered
54 candidates to 100 candidates (-85.2%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1000100
Fresh011
Picked011
Done011
Total1003103

Merged error: 0.0b

Counts
103 → 3

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))
0.3b
(pow (+ (* b b) (* a a)) 2.0)
4.2b
(- (pow (+ (* b b) (* a a)) (* 2.0 2)) (* 4.0 (* (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))))
31.0b
(/ (- (pow (+ (* b b) (* a a)) (* 2.0 2)) (* 4.0 (* (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))) (- (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
272×associate-*r/
56×frac-add
42×flip3-+ flip-+
36×frac-times
31×flip3-- flip--
16×distribute-rgt-in distribute-lft-in
15×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×add-exp-log
11×add-cbrt-cube
10×pow1
9×times-frac
8×associate--r+
6×associate-*l/ add-log-exp
3×unpow-prod-down pow-unpow associate-*l* pow-prod-down prod-exp associate-/r* cbrt-unprod associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub div-exp associate-*r* pow-exp clear-num *-commutative div-inv sqr-pow
Counts
4 → 138
Calls
4 calls:
27.0ms
(* (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))
5.0ms
(pow (+ (* b b) (* a a)) 2.0)
8.0ms
(- (pow (+ (* b b) (* a a)) (* 2.0 2)) (* 4.0 (* (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))))
14.0ms
(/ (- (pow (+ (* b b) (* a a)) (* 2.0 2)) (* 4.0 (* (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))) (- (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))

series247.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))
22.0ms
(pow (+ (* b b) (* a a)) 2.0)
91.0ms
(- (pow (+ (* b b) (* a a)) (* 2.0 2)) (* 4.0 (* (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))))
103.0ms
(/ (- (pow (+ (* b b) (* a a)) (* 2.0 2)) (* 4.0 (* (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))) (- (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))

simplify83.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
0503310732

prune756.0ms

Filtered
109 candidates to 150 candidates (-37.6%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1491150
Fresh000
Picked011
Done022
Total1494153

Merged error: 0b

Counts
153 → 4

regimes278.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06131
16131

end0.0ms

sample646.0ms

Algorithm
intervals
Results
513.0ms8000×body80valid
0.0ms2×body80invalid

Profiling

Loading profile data...