Details

Time bar (total: 4.7s)

sample61.0ms

Algorithm
intervals
Results
43.0ms671×body80valid

simplify94.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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

localize18.0ms

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)))

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)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
47.0ms
(* (* a a) (+ 1.0 a))
98.0ms
(pow (+ (* a a) (* b b)) 2.0)
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify65.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0504702
12520622
25003622

prune209.0ms

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)))
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))
7.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.5b
(sqrt (+ (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
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-div associate-*r/ add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-- flip-+ unswap-sqr
Counts
4 → 80
Calls
4 calls:
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms
(* (* 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)))))))
6.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series431.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
48.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
164.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
166.0ms
(sqrt (+ (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
92 → 92
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03331080
11424980
25002978

prune277.0ms

Filtered
92 candidates to 60 candidates (65.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New92092
Fresh044
Picked011
Done000
Total92597

Merged error: 0.0b

Counts
97 → 5

localize16.0ms

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)))
2.6b
(* (pow a 2) (pow b 2))

rewrite29.0ms

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)))))
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))

series169.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
49.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
37.0ms
(* 2 (* (pow a 2) (pow b 2)))
31.0ms
(* (pow a 2) (pow b 2))

simplify57.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0375699
11613621
25001616

prune194.0ms

Filtered
113 candidates to 60 candidates (53.1%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1130113
Fresh033
Picked011
Done011
Total1135118

Merged error: 0.0b

Counts
118 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
0.1b
(* (* a a) (+ 1.0 a))
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))
2.6b
(* (pow a 2) (pow b 2))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
28×add-exp-log
19×unswap-sqr
18×associate-*r/ associate-*r* add-cbrt-cube
16×pow1 prod-exp
14×unpow-prod-down *-un-lft-identity
13×associate-*l*
12×add-cube-cbrt
10×unpow2 sqr-pow
8×pow-prod-down cbrt-unprod
6×pow-to-exp pow-exp
4×distribute-rgt-in distribute-lft-in flip3-+ frac-add *-commutative flip-+ add-log-exp
3×flip3-- flip--
2×sub-neg
1×distribute-lft-out
Counts
4 → 126
Calls
4 calls:
11.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
10.0ms
(* (* a a) (+ 1.0 a))
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms
(* (pow a 2) (pow b 2))

series190.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
47.0ms
(* (* a a) (+ 1.0 a))
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
31.0ms
(* (pow a 2) (pow b 2))

simplify152.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (136.0ms)

IterNodesCost
0724912
14116774
25002770

prune382.0ms

Filtered
138 candidates to 80 candidates (58.0%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1380138
Fresh022
Picked011
Done022
Total1385143

Merged error: 0.0b

Counts
143 → 5

regimes112.0ms

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
02932
12932

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.3s20687×body80valid

Profiling

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