Details

Time bar (total: 4.2s)

sample67.0ms

Algorithm
intervals
Results
47.0ms634×body80valid

simplify94.0ms

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

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)
0.5b
(* (* 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:
9.0ms
(+ (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)))

series55.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ (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))
20.0ms
(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 (61.0ms)

IterNodesCost
0547721
12714641
25001637

prune147.0ms

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

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New86591
Fresh000
Picked011
Done000
Total86692

Merged error: 0.0b

Counts
92 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
10.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×add-log-exp
3×flip3-+ pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 64
Calls
4 calls:
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
5.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
5.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series123.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
38.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
40.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
38.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify52.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03741512
115221386
250021359

prune360.0ms

Filtered
61 candidates to 76 candidates (-24.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New74276
Fresh044
Picked101
Done011
Total75782

Merged error: 0b

Counts
82 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

9.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite23.0ms

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) (- 1.0 (* 3.0 a)))))))
6.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
5.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
5.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series137.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
30.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
38.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
40.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify129.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (115.0ms)

IterNodesCost
03021616
19921520
245101476
350011472

prune429.0ms

Filtered
56 candidates to 68 candidates (-21.4%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New68068
Fresh055
Picked011
Done011
Total68775

Merged error: 0b

Counts
75 → 7

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
3.6b
(* (pow a 2) (pow b 2))

rewrite20.0ms

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×add-cbrt-cube unpow2 sqr-pow
9×associate-*r*
8×add-cube-cbrt *-un-lft-identity
5×pow1 add-log-exp
4×cbrt-unprod
2×pow-prod-down *-commutative
1×+-commutative flip3-+ sum-log flip-+
Counts
3 → 87
Calls
3 calls:
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))

series24.0ms

Counts
3 → 9
Calls
3 calls:
9.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
7.0ms
(* 2 (* (pow a 2) (pow b 2)))
8.0ms
(* (pow a 2) (pow b 2))

simplify46.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0297518
11270444
25001432

prune118.0ms

Filtered
47 candidates to 96 candidates (-104.3%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New96096
Fresh044
Picked011
Done022
Total967103

Merged error: 0b

Counts
103 → 7

regimes325.0ms

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
02715
12715

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.4s20208×body80valid

Profiling

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