Details

Time bar (total: 5.3s)

sample60.0ms

Algorithm
intervals
Results
42.0ms679×body80valid

simplify79.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05314
117313
253212
3168112
4427812
5500112

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.2b

Counts
2 → 1

localize19.0ms

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))
0.4b
(pow (+ (* a a) (* b b)) 2.0)
0.9b
(* (* b b) (+ 3.0 a))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
18×prod-diff
15×pow1 add-exp-log
14×add-cbrt-cube
13×distribute-rgt-in distribute-lft-in
9×associate-*r*
7×fma-def
6×unpow-prod-down pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 114
Calls
4 calls:
8.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
9.0ms
(* (* a a) (- 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) (+ 3.0 a))

series301.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(+ (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))
109.0ms
(pow (+ (* a a) (* b b)) 2.0)
33.0ms
(* (* b b) (+ 3.0 a))

simplify95.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
0646990
13454779
25001776

prune298.0ms

Filtered
126 candidates to 80 candidates (63.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1215126
Fresh000
Picked101
Done000
Total1225127

Merged error: 0.0b

Counts
127 → 5

localize22.0ms

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))
0.1b
(* b (* b (+ 3.0 a)))
0.4b
(pow (+ (* a a) (* b b)) 2.0)

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
24×*-un-lft-identity
22×add-cube-cbrt
18×prod-diff
16×distribute-rgt-in distribute-lft-in
15×pow1 add-exp-log
14×add-cbrt-cube
7×fma-def
6×unpow-prod-down associate-*r/ associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*l* log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ *-commutative flip-+ sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 114
Calls
4 calls:
8.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a))))))
9.0ms
(* (* a a) (- 1.0 a))
7.0ms
(* b (* b (+ 3.0 a)))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)

series297.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a))))))
55.0ms
(* (* a a) (- 1.0 a))
32.0ms
(* b (* b (+ 3.0 a)))
103.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify85.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
0637989
13290778
25001775

prune292.0ms

Filtered
126 candidates to 80 candidates (63.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1260126
Fresh044
Picked011
Done000
Total1265131

Merged error: 0.0b

Counts
131 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* b b) (+ 3.0 a))
9.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite28.0ms

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×expm1-log1p-u flip3-+ associate-*r* flip-+ log1p-expm1-u 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 → 71
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))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series591.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (* b b) (+ 3.0 a))
186.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
184.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
183.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify52.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03511377
115581248
250011230

prune543.0ms

Filtered
83 candidates to 72 candidates (86.7%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New83083
Fresh033
Picked011
Done011
Total83588

Merged error: 0.0b

Counts
88 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
0.0b
(* 2 (pow a 2))
0.1b
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
1.5b
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
9×add-exp-log prod-diff
8×associate-*r*
6×add-cbrt-cube add-log-exp
4×pow1 expm1-log1p-u unpow-prod-down log1p-expm1-u unswap-sqr
3×fma-neg associate-*l* prod-exp fma-udef
2×unpow2 sqr-pow
1×pow-to-exp sub-neg flip3-- diff-log pow-exp associate--l+ *-commutative flip-- cbrt-unprod distribute-lft-out-- difference-of-squares
Counts
4 → 78
Calls
4 calls:
4.0ms
(- (fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
6.0ms
(* 2 (pow a 2))
1.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
1.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series221.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
24.0ms
(* 2 (pow a 2))
63.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
70.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify48.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0276764
11144636
25001628

prune226.0ms

Filtered
90 candidates to 61 candidates (67.8%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New89190
Fresh022
Picked101
Done022
Total90595

Merged error: 0b

Counts
95 → 5

regimes144.0ms

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
02714
12714

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.4s20618×body80valid