Details

Time bar (total: 5.3s)

sample64.0ms

Algorithm
intervals
Results
45.0ms678×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

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

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

series298.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(+ (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))
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
98.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify68.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0504702
12520622
25003622

prune227.0ms

Filtered
91 candidates to 61 candidates (67.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New87491
Fresh000
Picked011
Done000
Total87592

Merged error: 0.0b

Counts
92 → 5

localize13.0ms

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 a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
1.5b
(* (pow a 2) (pow b 2))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
20×add-log-exp
16×add-exp-log unswap-sqr
15×*-un-lft-identity
14×unpow-prod-down
10×unpow2 sqr-pow
9×prod-exp
8×add-cube-cbrt associate-*r* associate-*l*
7×sum-log
6×pow-to-exp pow-exp add-cbrt-cube
4×pow1
3×diff-log
2×+-commutative flip3-+ flip-+ distribute-lft-out distribute-lft-out--
1×sub-neg associate-+r+ flip3-- pow-prod-down associate--l+ *-commutative flip-- cbrt-unprod difference-of-squares
Counts
4 → 94
Calls
4 calls:
7.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
10.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
4.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
7.0ms
(* (pow a 2) (pow b 2))

series182.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
52.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
49.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
31.0ms
(* (pow a 2) (pow b 2))

simplify56.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0387802
11681732
25002728

prune205.0ms

Filtered
106 candidates to 63 candidates (59.4%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1060106
Fresh033
Picked011
Done011
Total1065111

Merged error: 0.0b

Counts
111 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 3.0 a))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
1.5b
(* (pow a 2) (pow b 2))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×add-exp-log
18×unswap-sqr
16×add-cbrt-cube
15×associate-*r* prod-exp
14×pow1 unpow-prod-down
12×*-un-lft-identity
10×add-cube-cbrt associate-*l* unpow2 sqr-pow
7×pow-prod-down cbrt-unprod
6×pow-to-exp pow-exp add-log-exp
4×associate-*r/
3×distribute-rgt-in sub-neg distribute-lft-in *-commutative
2×flip3-- flip--
1×flip3-+ diff-log flip-+ distribute-lft-out
Counts
4 → 112
Calls
4 calls:
3.0ms
(- 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))

series167.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- 1.0 (* 3.0 a))
47.0ms
(* (* a a) (+ 1.0 a))
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
31.0ms
(* (pow a 2) (pow b 2))

simplify72.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0474593
12437482
25003478

prune283.0ms

Filtered
124 candidates to 68 candidates (54.8%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1240124
Fresh022
Picked011
Done022
Total1245129

Merged error: 0.0b

Counts
129 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) (* 2 2.0))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
3.4b
(+ (pow (+ (* a a) (* b b)) (* 2 2.0)) (neg (* (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))))
30.8b
(/ (+ (pow (+ (* a a) (* b b)) (* 2 2.0)) (neg (* (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
16×add-sqr-sqrt add-cube-cbrt
12×times-frac
8×add-exp-log add-log-exp
6×pow1 unpow-prod-down add-cbrt-cube
5×distribute-lft-out
4×distribute-rgt-in pow-unpow associate-+r+ distribute-neg-in distribute-lft-in associate-/l*
3×div-sub associate-/r*
2×neg-sub0 pow-to-exp associate-+r- pow-pow flip3-+ unsub-neg pow-exp sum-log associate-/r/ flip-+ associate-/l/ sqr-pow
1×cbrt-undiv +-commutative flip3-- frac-2neg div-exp neg-log clear-num flip-- div-inv
Counts
4 → 90
Calls
4 calls:
4.0ms
(pow (+ (* a a) (* b b)) (* 2 2.0))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
9.0ms
(+ (pow (+ (* a a) (* b b)) (* 2 2.0)) (neg (* (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))))
18.0ms
(/ (+ (pow (+ (* a a) (* b b)) (* 2 2.0)) (neg (* (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
102.0ms
(pow (+ (* a a) (* b b)) (* 2 2.0))
103.0ms
(pow (+ (* a a) (* b b)) 2.0)
472.0ms
(+ (pow (+ (* a a) (* b b)) (* 2 2.0)) (neg (* (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))))
389.0ms
(/ (+ (pow (+ (* a a) (* b b)) (* 2 2.0)) (neg (* (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify86.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05203173
126152859
250012842

prune341.0ms

Filtered
102 candidates to 76 candidates (74.5%)
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New1020102
Fresh011
Picked011
Done033
Total1025107

Merged error: 0.0b

Counts
107 → 5

regimes157.0ms

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

sample1.8s

Algorithm
intervals
Results
1.4s20550×body80valid

Profiling

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