Details

Time bar (total: 3.8s)

sample48.0ms

Algorithm
intervals
Results
32.0ms681×body80valid

simplify60.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0258
1418
2678
31198
43098
514948
650018

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

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
10×pow1 add-exp-log add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube
7×add-cube-cbrt
3×unpow-prod-down pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×diff-log sum-log
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow flip3-+ associate-*r* pow-exp associate--l+ *-commutative flip-- flip-+ distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
Counts
4 → 63
Calls
4 calls:
9.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
4.0ms
(+ (* a a) (* b b))
5.0ms
(* 4.0 (* b b))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series238.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
28.0ms
(+ (* a a) (* b b))
29.0ms
(* 4.0 (* b b))
104.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify41.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0338488
11360446
25001439

prune150.0ms

Filtered
75 candidates to 51 candidates (68.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New71475
Fresh000
Picked101
Done000
Total72476

Merged error: 0b

Counts
76 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* b b))
0.1b
(* (neg (pow b 3)) b)
0.3b
(pow (/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- (* a a) (* b b))) 2.0)
21.2b
(/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- (* a a) (* b b)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity associate-*l*
24×unpow-prod-down times-frac
16×add-exp-log
13×add-cbrt-cube
12×pow1 distribute-lft-neg-in distribute-rgt-neg-in
7×difference-of-squares
6×cube-prod
4×associate-*r* pow-prod-down prod-exp associate-/r* associate-/r/ cbrt-unprod add-log-exp
3×pow-unpow associate-/l* sqr-pow
2×cube-mult flip3-- unpow3 div-exp pow-exp *-commutative flip-- div-inv associate-/l/ unswap-sqr
1×cbrt-undiv distribute-lft-neg-out pow-to-exp neg-mul-1 pow-pow frac-2neg flip3-+ clear-num flip-+
Counts
4 → 131
Calls
4 calls:
5.0ms
(* 4.0 (* b b))
8.0ms
(* (neg (pow b 3)) b)
13.0ms
(pow (/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- (* a a) (* b b))) 2.0)
16.0ms
(/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- (* a a) (* b b)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 4.0 (* b b))
42.0ms
(* (neg (pow b 3)) b)
143.0ms
(pow (/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- (* a a) (* b b))) 2.0)
79.0ms
(/ (+ (* (neg (pow b 3)) b) (pow a 4)) (- (* a a) (* b b)))

simplify112.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
05811321
131091212
250021206

prune400.0ms

Filtered
143 candidates to 107 candidates (74.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1430143
Fresh033
Picked011
Done000
Total1434147

Merged error: 0b

Counts
147 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow a 4) (* 4.0 (pow b 2)))
0.0b
(- (+ (pow a 4) (* 4.0 (pow b 2))) 1.0)
0.0b
(* 4.0 (pow b 2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-log-exp
8×add-exp-log *-un-lft-identity associate-*r*
6×add-cube-cbrt
5×add-cbrt-cube
4×unpow-prod-down unswap-sqr
3×pow1 associate-*l* prod-exp
2×diff-log sum-log unpow2 sqr-pow
1×+-commutative pow-to-exp sub-neg flip3-- flip3-+ pow-exp associate--l+ *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out-- difference-of-squares
Counts
3 → 54
Calls
3 calls:
4.0ms
(+ (pow a 4) (* 4.0 (pow b 2)))
7.0ms
(- (+ (pow a 4) (* 4.0 (pow b 2))) 1.0)
5.0ms
(* 4.0 (pow b 2))

series128.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(+ (pow a 4) (* 4.0 (pow b 2)))
50.0ms
(- (+ (pow a 4) (* 4.0 (pow b 2))) 1.0)
30.0ms
(* 4.0 (pow b 2))

simplify189.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0231330
1877307
24451303
35001303

prune112.0ms

Filtered
63 candidates to 41 candidates (65.1%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New63063
Fresh022
Picked011
Done011
Total63467

Merged error: 0b

Counts
67 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b
(* 2.0 (* (pow a 2) (pow b 2)))
0.0b
(* 4.0 (* b b))
2.1b
(* (pow a 2) (pow b 2))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
44×add-exp-log
31×prod-exp
27×add-sqr-sqrt
17×unswap-sqr
16×add-cbrt-cube
14×unpow-prod-down associate-*l*
12×pow-to-exp pow-exp
11×pow1
10×add-cube-cbrt *-un-lft-identity associate-*r* unpow2 sqr-pow
9×add-log-exp
7×cbrt-unprod
5×pow-prod-down
3×sum-log *-commutative
1×+-commutative associate-+l+ flip3-+ flip-+
Counts
4 → 108
Calls
4 calls:
7.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
7.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
5.0ms
(* 4.0 (* b b))
7.0ms
(* (pow a 2) (pow b 2))

series170.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
37.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
30.0ms
(* 4.0 (* b b))
35.0ms
(* (pow a 2) (pow b 2))

simplify65.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0400683
11741575
25002568

prune195.0ms

Filtered
120 candidates to 61 candidates (50.8%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1200120
Fresh011
Picked011
Done022
Total1204124

Merged error: 0b

Counts
124 → 4

regimes172.0ms

Accuracy

98.4% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 9.3b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03620
14020
24120
34120

end0.0ms

sample1.2s

Algorithm
intervals
Results
917.0ms20481×body80valid

Profiling

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