Details

Time bar (total: 5.7s)

sample65.0ms

Algorithm
intervals
Results
44.0ms679×body80valid

simplify92.0ms

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

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))
0.4b
(pow (+ (* a a) (* b b)) 2.0)
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite31.0ms

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))))))
11.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series306.0ms

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))))))
50.0ms
(* (* a a) (+ 1.0 a))
101.0ms
(pow (+ (* a a) (* b b)) 2.0)
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify67.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0504702
12520622
25002622

prune213.0ms

Filtered
91 candidates to 61 candidates (67.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New86591
Fresh000
Picked011
Done000
Total86692

Merged error: 0.0b

Counts
92 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
8.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite29.0ms

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)))))))

series453.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
172.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
171.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify49.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03331080
11424980
25002978

prune277.0ms

Filtered
92 candidates to 60 candidates (65.2%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New90292
Fresh314
Picked101
Done011
Total94498

Merged error: 0b

Counts
98 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
8.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
4×cbrt-div add-log-exp
3×flip3-+ associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod flip-+
2×distribute-rgt-in sub-neg distribute-lft-in pow1/3 sqrt-div associate-*r/
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 66
Calls
4 calls:
10.0ms
(* (* 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
(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)))))))

series596.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
173.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
186.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
188.0ms
(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
78 → 78
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04221358
116691246
250021231

prune335.0ms

Filtered
78 candidates to 60 candidates (76.9%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New78078
Fresh022
Picked011
Done011
Total78482

Merged error: 0b

Counts
82 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

8.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
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)))))))
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)))))))

series693.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
174.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
176.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
171.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify110.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
01851456
16871384
235271384
350011380

prune285.0ms

Filtered
72 candidates to 56 candidates (77.8%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New72072
Fresh011
Picked011
Done022
Total72476

Merged error: 0b

Counts
76 → 4

regimes140.0ms

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

sample1.7s

Algorithm
intervals
Results
1.4s20618×body80valid