Details

Time bar (total: 6.5s)

sample58.0ms

Algorithm
intervals
Results
40.0ms668×body80valid

simplify88.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
05314
117313
253212
3168112
4427812
5500112

prune7.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

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)
0.5b
(* (* b b) (+ 3.0 a))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
88×*-un-lft-identity
82×add-sqr-sqrt
67×distribute-rgt-in distribute-lft-in
64×associate-+r+
56×add-cube-cbrt
54×prod-diff
45×associate-*l*
44×associate-+l+
16×unpow-prod-down
15×pow1 add-exp-log associate-*r*
14×add-cbrt-cube unswap-sqr
13×distribute-lft-out
12×fma-def swap-sqr
9×+-commutative
6×sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×flip3-+ flip-+ sqr-pow
1×pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 218
Calls
4 calls:
84.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
18.0ms
(* (* a a) (- 1.0 a))
15.0ms
(pow (+ (* a a) (* b b)) 2.0)
11.0ms
(* (* b b) (+ 3.0 a))

series339.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
63.0ms
(* (* a a) (- 1.0 a))
112.0ms
(pow (+ (* a a) (* b b)) 2.0)
43.0ms
(* (* b b) (+ 3.0 a))

simplify126.0ms

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
010031880
145201480
250011480

prune533.0ms

Filtered
230 candidates to 143 candidates (37.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2255230
Fresh000
Picked101
Done000
Total2265231

Merged error: 0.0b

Counts
231 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* a a) (- 1.0 a) (* 3.0 (* b b)))
0.2b
(* 3.0 (* b b))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) a)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
30×*-un-lft-identity
28×associate-*l*
24×associate-*r*
18×add-cube-cbrt
15×pow1 add-exp-log
14×add-cbrt-cube unswap-sqr
10×swap-sqr
8×unpow-prod-down
6×pow-prod-down prod-exp *-commutative cbrt-unprod
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
1×pow-to-exp pow-pow pow-exp fma-udef sqr-pow
Counts
4 → 112
Calls
4 calls:
1.0ms
(fma (* a a) (- 1.0 a) (* 3.0 (* b b)))
9.0ms
(* 3.0 (* b b))
15.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) a)

series206.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(fma (* a a) (- 1.0 a) (* 3.0 (* b b)))
25.0ms
(* 3.0 (* b b))
112.0ms
(pow (+ (* a a) (* b b)) 2.0)
24.0ms
(* (* b b) a)

simplify55.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0372506
11589447
25001435

prune299.0ms

Filtered
124 candidates to 78 candidates (37.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1240124
Fresh044
Picked011
Done000
Total1245129

Merged error: 0.0b

Counts
129 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (+ 3.0 a))
0.5b
(* (* b b) (+ 3.0 a))
8.7b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
38×associate-*l*
30×*-un-lft-identity
20×unswap-sqr
18×add-cube-cbrt
16×pow1
14×add-exp-log associate-*r* add-cbrt-cube
12×hypot-def
10×sqrt-prod
8×swap-sqr
6×pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out
4×+-commutative distribute-rgt-in expm1-log1p-u unpow-prod-down distribute-lft-in flip3-+ sqrt-div associate-*r/ flip-+ log1p-expm1-u add-log-exp sqr-pow
2×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 142
Calls
4 calls:
11.0ms
(* (* b b) (+ 3.0 a))
11.0ms
(* (* b b) (+ 3.0 a))
87.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
88.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series462.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (* b b) (+ 3.0 a))
35.0ms
(* (* b b) (+ 3.0 a))
194.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
190.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify63.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04121220
118291138
250021130

prune493.0ms

Filtered
154 candidates to 104 candidates (32.5%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1522154
Fresh123
Picked011
Done011
Total1536159

Merged error: 0.0b

Counts
159 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite358.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
24×*-un-lft-identity hypot-def
20×sqrt-prod
12×unswap-sqr
8×pow1 add-cube-cbrt unpow-prod-down sqrt-div distribute-lft-out sqr-pow
4×add-exp-log expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*l* add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
Counts
4 → 100
Calls
4 calls:
88.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
88.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
88.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
90.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series761.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
190.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
188.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
188.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify121.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 3 (105.0ms)

IterNodesCost
01841604
16971524
235991520
350011512

prune483.0ms

Filtered
112 candidates to 92 candidates (17.9%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1120112
Fresh033
Picked011
Done022
Total1126118

Merged error: 0.0b

Counts
118 → 6

regimes186.0ms

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
02315
12315

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s20764×body80valid