Details

Time bar (total: 2.8s)

analyze136.0ms

Algorithm
search

sample26.0ms

Algorithm
intervals
Results
19.0ms256×body80valid

simplify92.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize15.0ms

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

rewrite27.0ms

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×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 sqr-pow
Counts
4 → 79
Calls
4 calls:
7.0ms
(+ (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)))

series58.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (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))
21.0ms
(pow (+ (* a a) (* b b)) 2.0)
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify69.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
0547721
12714641
25001637

prune151.0ms

Filtered
61 candidates to 91 candidates (-49.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New87491
Fresh000
Picked011
Done000
Total87592

Merged error: 0b

Counts
92 → 5

localize38.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* b b) (- 1.0 (* 3.0 a)))
18.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log unpow-prod-down add-cbrt-cube
4×add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 70
Calls
4 calls:
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
6.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
7.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series107.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
33.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
33.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
35.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify39.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0295702
11114636
25001618

prune228.0ms

Filtered
64 candidates to 82 candidates (-28.1%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New81182
Fresh123
Picked011
Done011
Total82587

Merged error: 0b

Counts
87 → 5

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
3.3b
(* (pow a 2) (pow b 2))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
28×prod-exp
24×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×associate-*l*
10×*-un-lft-identity add-cbrt-cube unpow2 sqr-pow
9×associate-*r*
8×add-cube-cbrt add-log-exp
5×pow1
4×cbrt-unprod
3×sum-log
2×pow-prod-down *-commutative
1×+-commutative associate-+r+ flip3-+ flip-+ distribute-lft-out
Counts
3 → 90
Calls
3 calls:
7.0ms
(+ (pow a 4) (+ (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))

series25.0ms

Counts
3 → 9
Calls
3 calls:
11.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
8.0ms
(* 2 (* (pow a 2) (pow b 2)))
7.0ms
(* (pow a 2) (pow b 2))

simplify49.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0330587
11424506
25001495

prune134.0ms

Filtered
50 candidates to 99 candidates (-98.0%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New99099
Fresh022
Picked011
Done022
Total995104

Merged error: 0b

Counts
104 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

4.8b
(exp (log (cbrt (pow (+ (* a a) (* b b)) 2.0))))
18.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
10×log-prod exp-sum
5×pow1 exp-prod
4×add-exp-log pow1/3 add-cbrt-cube add-log-exp sqr-pow
2×log-pow
1×rem-exp-log
Counts
4 → 68
Calls
4 calls:
6.0ms
(exp (log (cbrt (pow (+ (* a a) (* b b)) 2.0))))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series140.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(exp (log (cbrt (pow (+ (* a a) (* b b)) 2.0))))
34.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
34.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
37.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 3 (37.0ms)

IterNodesCost
0180761
1373717
21126673
35001635

prune232.0ms

Filtered
63 candidates to 80 candidates (-27.0%)
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New80080
Fresh011
Picked011
Done033
Total80585

Merged error: 0b

Counts
85 → 5

regimes247.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02715
12715

end0.0ms

analyze141.0ms

Algorithm
search

sample659.0ms

Algorithm
intervals
Results
534.0ms8000×body80valid
1.0ms7×body80invalid

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