Details

Time bar (total: 5.2s)

sample60.0ms

Algorithm
intervals
Results
39.0ms618×body80valid

simplify96.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115

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

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)))

rewrite32.0ms

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:
10.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
50.0ms
(* (* a a) (+ 1.0 a))
100.0ms
(pow (+ (* a a) (* b b)) 2.0)
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify70.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
0504702
12520622
25002622

prune217.0ms

Filtered
91 candidates to 61 candidates (67.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New86591
Fresh000
Picked101
Done000
Total87592

Merged error: 0.0b

Counts
92 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* b b) (- 1.0 (* 3.0 a)))
10.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite27.0ms

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

series586.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
176.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
180.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
180.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify53.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03481404
114381278
250011257

prune295.0ms

Filtered
76 candidates to 61 candidates (80.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New75176
Fresh134
Picked011
Done000
Total76581

Merged error: 0.0b

Counts
81 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

10.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series692.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
172.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
173.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
174.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify109.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02021636
16821512
234211460
350011460

prune326.0ms

Filtered
64 candidates to 60 candidates (93.8%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New64064
Fresh033
Picked011
Done011
Total64569

Merged error: 0.0b

Counts
69 → 5

localize15.0ms

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
(* 2 (* (pow a 2) (pow b 2)))
0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
2.4b
(* (pow a 2) (pow b 2))

rewrite30.0ms

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)))))
7.0ms
(* 2 (* (pow a 2) (pow b 2)))
5.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
8.0ms
(* (pow a 2) (pow b 2))

series169.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
34.0ms
(* 2 (* (pow a 2) (pow b 2)))
53.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
32.0ms
(* (pow a 2) (pow b 2))

simplify55.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0375699
11611622
25002616

prune178.0ms

Filtered
113 candidates to 60 candidates (53.1%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1130113
Fresh022
Picked011
Done022
Total1135118

Merged error: 0.0b

Counts
118 → 5

regimes122.0ms

Accuracy

0% (0.5b 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
03148
13148

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.3s20562×body80valid