Details

Time bar (total: 4.4s)

sample74.0ms

Algorithm
intervals
Results
51.0ms719×body80valid

simplify75.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05114
115514
243014
3119514
4252614
5500114

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize16.0ms

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)))))
0.0b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.4b
(* (* 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)
8.0ms
(* (* b b) (+ 3.0 a))

series61.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
5.0ms
(* (* a a) (- 1.0 a))
21.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) (+ 3.0 a))

simplify70.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0549670
12714602
25001598

prune142.0ms

Filtered
93 candidates to 63 candidates (32.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New90393
Fresh000
Picked011
Done000
Total90494

Merged error: 0.0b

Counts
94 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
8.8b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.8b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.8b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
16.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
8.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series191.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
44.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
45.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
45.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify62.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03863168
113142939
250012709

prune451.0ms

Filtered
99 candidates to 75 candidates (24.2%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New98199
Fresh022
Picked011
Done011
Total985103

Merged error: 0.0b

Counts
103 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

8.2b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.2b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.8b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.8b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
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))))))
8.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series144.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
31.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
43.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
41.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify132.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (118.0ms)

IterNodesCost
02961530
19491426
243671400
350011396

prune365.0ms

Filtered
68 candidates to 56 candidates (17.6%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New68068
Fresh022
Picked011
Done022
Total68573

Merged error: 0.0b

Counts
73 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
25×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×*-un-lft-identity associate-*l* add-cbrt-cube add-log-exp
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
2×+-commutative flip3-+ pow-prod-down *-commutative flip-+
1×associate-+r+ distribute-lft-out
Counts
4 → 101
Calls
4 calls:
8.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
5.0ms
(+ (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))

series43.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
10.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
9.0ms
(* 2 (* (pow a 2) (pow b 2)))
9.0ms
(* (pow a 2) (pow b 2))

simplify63.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0375699
11613621
25001616

prune184.0ms

Filtered
113 candidates to 60 candidates (46.9%)
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New1130113
Fresh011
Picked011
Done033
Total1135118

Merged error: 0.0b

Counts
118 → 5

regimes269.0ms

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 (1.0ms)

IterNodesCost
02514
12514

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.3s20447×body80valid

Profiling

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