Details

Time bar (total: 4.7s)

sample66.0ms

Algorithm
intervals
Results
48.0ms683×body80valid

simplify66.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05114
115514
243014
3119514
4252614
5500114

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

localize14.0ms

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) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.6b
(* (* b b) (+ 3.0 a))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
9×associate-*r*
8×add-cube-cbrt
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 distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
7.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
8.0ms
(* (* a a) (- 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) (+ 3.0 a))

series294.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
49.0ms
(* (* a a) (- 1.0 a))
99.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (+ 3.0 a))

simplify70.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
0506651
12520583
25001583

prune206.0ms

Filtered
93 candidates to 63 candidates (67.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New88593
Fresh000
Picked011
Done000
Total88694

Merged error: 0b

Counts
94 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (+ 3.0 a))
12.5b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
12.5b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
12.5b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt
6×cbrt-div
4×flip3-+ associate-*r* flip-+ add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod
2×associate-*r/
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 63
Calls
4 calls:
8.0ms
(* (* b b) (+ 3.0 a))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series565.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* b b) (+ 3.0 a))
179.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
178.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
177.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify49.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03381282
114701156
250021120

prune274.0ms

Filtered
75 candidates to 61 candidates (81.3%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New75075
Fresh044
Picked011
Done011
Total75681

Merged error: 0b

Counts
81 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (+ 3.0 a))
21.6b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.6b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.6b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
13×*-un-lft-identity
12×add-sqr-sqrt
11×add-cube-cbrt
9×pow1 add-exp-log unpow-prod-down add-cbrt-cube
4×associate-*r* add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod sqr-pow
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ associate-*l* *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 69
Calls
4 calls:
8.0ms
(* (* b b) (+ 3.0 a))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series480.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* b b) (+ 3.0 a))
146.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
157.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
146.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0262598
11088544
25002538

prune265.0ms

Filtered
81 candidates to 64 candidates (79.0%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New81081
Fresh033
Picked011
Done022
Total81687

Merged error: 0b

Counts
87 → 6

localize13.0ms

Local error

Found 3 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)))
1.5b
(* (pow a 2) (pow b 2))

rewrite25.0ms

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×*-un-lft-identity add-cbrt-cube unpow2 sqr-pow
9×associate-*r*
8×add-cube-cbrt add-log-exp
5×pow1
4×cbrt-unprod
3×sum-log
2×pow-prod-down *-commutative
1×+-commutative associate-+r+ flip3-+ flip-+ distribute-lft-out
Counts
3 → 90
Calls
3 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)))
7.0ms
(* (pow a 2) (pow b 2))

series120.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
40.0ms
(* 2 (* (pow a 2) (pow b 2)))
31.0ms
(* (pow a 2) (pow b 2))

simplify50.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0330587
11424506
25001495

prune155.0ms

Filtered
99 candidates to 50 candidates (50.5%)
Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New99099
Fresh022
Picked011
Done033
Total996105

Merged error: 0b

Counts
105 → 6

regimes149.0ms

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
02514
12514

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.3s20368×body80valid