Details

Time bar (total: 4.1s)

sample66.0ms

Algorithm
intervals
Results
42.0ms635×body80valid

simplify93.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (91.0ms)

IterNodesCost
0494631
1494631

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

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) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite28.0ms

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)))

series59.0ms

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))))))
5.0ms
(* (* a a) (+ 1.0 a))
21.0ms
(pow (+ (* a a) (* b b)) 2.0)
9.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify27.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
056931297

prune153.0ms

Filtered
63 candidates to 91 candidates (-44.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New86591
Fresh000
Picked101
Done000
Total87592

Merged error: 0.0b

Counts
92 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* b b) (* a a)) 2.0)
0.3b
(pow (+ (* b b) (* a a)) 2.0)
9.7b
(sqrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
9.7b
(sqrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×add-exp-log unpow-prod-down pow-unpow sqrt-prod
4×sqrt-div add-cbrt-cube add-log-exp
2×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 flip3-+ pow1/2 pow-exp flip-+ sqr-pow
Counts
4 → 64
Calls
4 calls:
4.0ms
(pow (+ (* b b) (* a a)) 2.0)
4.0ms
(pow (+ (* b b) (* a a)) 2.0)
6.0ms
(sqrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
6.0ms
(sqrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))

series98.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(pow (+ (* b b) (* a a)) 2.0)
21.0ms
(pow (+ (* b b) (* a a)) 2.0)
29.0ms
(sqrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
27.0ms
(sqrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))

simplify63.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
052751744

prune233.0ms

Filtered
58 candidates to 76 candidates (-31.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New74276
Fresh044
Picked101
Done000
Total75681

Merged error: 0.0b

Counts
81 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))) (cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))))
10.2b
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
10.2b
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
10.2b
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))

rewrite38.0ms

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:
18.0ms
(* (cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))) (cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))))
6.0ms
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
6.0ms
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
6.0ms
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))

series207.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))) (cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a))))))))
48.0ms
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
51.0ms
(cbrt (+ (pow (+ (* b b) (* a a)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* 3.0 a)))) (* a (* a (+ 1.0 a)))))))
48.0ms
(cbrt (+ (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
99 → 99
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049134777
149134777

prune473.0ms

Filtered
78 candidates to 99 candidates (-26.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New99099
Fresh055
Picked011
Done000
Total996105

Merged error: 0.0b

Counts
105 → 6

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
5×add-sqr-sqrt add-log-exp
4×add-cube-cbrt *-un-lft-identity associate-*r*
2×associate-*l* *-commutative
1×+-commutative flip3-+ sum-log flip-+ unswap-sqr
Counts
3 → 58
Calls
3 calls:
10.0ms
(+ (* (* b b) (* (* a a) 2)) (pow a 4))
5.0ms
(* (* a a) 2)
10.0ms
(* (* b b) (* (* a a) 2))

series27.0ms

Counts
3 → 9
Calls
3 calls:
14.0ms
(+ (* (* b b) (* (* a a) 2)) (pow a 4))
3.0ms
(* (* a a) 2)
10.0ms
(* (* b b) (* (* a a) 2))

simplify57.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
04984619
14984619

prune66.0ms

Filtered
34 candidates to 67 candidates (-97.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New67067
Fresh044
Picked011
Done011
Total67673

Merged error: 0.0b

Counts
73 → 6

regimes117.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03594
13594

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.5s20472×body80valid

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