Details

Time bar (total: 4.7s)

sample60.0ms

Algorithm
intervals
Results
42.0ms682×body80valid

simplify72.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05114
115514
243014
3119514
4252614
5500114

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize17.0ms

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) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.4b
(pow (+ (* a a) (* b b)) 2.0)
1.0b
(* (* b b) (+ 3.0 a))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
9×associate-*r*
8×add-cube-cbrt
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×unpow-prod-down pow-unpow
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 distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
7.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
8.0ms
(* (* a a) (- 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
7.0ms
(* (* b b) (+ 3.0 a))

series291.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
49.0ms
(* (* a a) (- 1.0 a))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)
32.0ms
(* (* b b) (+ 3.0 a))

simplify68.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0506651
12520583
25001583

prune213.0ms

Filtered
93 candidates to 63 candidates (67.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New87693
Fresh000
Picked101
Done000
Total88694

Merged error: 0.0b

Counts
94 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* b b) (+ 3.0 a))
1.0b
(* (* b b) (+ 3.0 a))
9.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt associate-*r*
6×pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×flip3-+ sqrt-div associate-*r/ flip-+ add-log-exp
2×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 78
Calls
4 calls:
10.0ms
(* (* b b) (+ 3.0 a))
8.0ms
(* (* b b) (+ 3.0 a))
6.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
6.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series405.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* b b) (+ 3.0 a))
37.0ms
(* (* b b) (+ 3.0 a))
169.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
165.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify50.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0321932
11454858
25002856

prune265.0ms

Filtered
90 candidates to 60 candidates (66.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New89190
Fresh145
Picked011
Done000
Total90696

Merged error: 0b

Counts
96 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.7b
(* (pow a 2) (pow b 2))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
27×add-sqr-sqrt
16×unswap-sqr
15×add-log-exp
14×unpow-prod-down *-un-lft-identity
12×pow-to-exp pow-exp
11×associate-*l* add-cbrt-cube
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
3×diff-log
2×pow-prod-down *-commutative distribute-lft-out--
1×+-commutative sub-neg flip3-- flip3-+ associate--l+ flip-- flip-+ distribute-lft-out difference-of-squares
Counts
4 → 105
Calls
4 calls:
11.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
4.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
7.0ms
(* 2 (* (pow a 2) (pow b 2)))
7.0ms
(* (pow a 2) (pow b 2))

series179.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
51.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
41.0ms
(* 2 (* (pow a 2) (pow b 2)))
32.0ms
(* (pow a 2) (pow b 2))

simplify61.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0382781
11594688
25001675

prune201.0ms

Filtered
117 candidates to 61 candidates (52.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1170117
Fresh044
Picked011
Done011
Total1176123

Merged error: 0b

Counts
123 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* b b) (+ 3.0 a))
9.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
27.2b
(cbrt (pow (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) 3))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
15×add-sqr-sqrt
14×*-un-lft-identity
12×add-cube-cbrt sqrt-prod
11×pow1
9×add-exp-log add-cbrt-cube
6×unpow-prod-down sqrt-div cube-prod
4×flip3-+ associate-*r* flip-+ add-log-exp
3×pow-prod-down prod-exp cbrt-unprod
2×cube-div rem-sqrt-square cbrt-div sqrt-pow1 pow1/2 associate-*r/
1×distribute-rgt-in cube-mult distribute-lft-in pow1/3 unpow3 associate-*l* *-commutative rem-cbrt-cube distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 83
Calls
4 calls:
8.0ms
(* (* b b) (+ 3.0 a))
6.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
6.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
11.0ms
(cbrt (pow (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) 3))

series541.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (* b b) (+ 3.0 a))
170.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
168.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
171.0ms
(cbrt (pow (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) 3))

simplify62.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04191452
118051416
250021416

prune274.0ms

Filtered
95 candidates to 60 candidates (63.2%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New95095
Fresh033
Picked011
Done022
Total956101

Merged error: 0b

Counts
101 → 6

regimes124.0ms

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 (0.0ms)

IterNodesCost
02730
12730

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.3s20744×body80valid

Profiling

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