Details

Time bar (total: 6.9s)

sample108.0ms

Algorithm
intervals
Results
88.0ms697×body80valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff 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
Counts
4 → 100
Calls
4 calls:
26.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
13.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms
(* (* a a) (+ 1.0 a))
103.0ms
(pow (+ (* a a) (* b b)) 2.0)
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify75.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
0564828
12826724
25001715

prune345.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (pow (hypot a b) 2.0) (pow (hypot a 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
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×add-exp-log
18×unpow-prod-down *-un-lft-identity
16×add-cube-cbrt add-cbrt-cube
15×prod-exp
14×pow1 associate-*r*
11×unswap-sqr
10×sqr-pow
9×associate-*l*
7×distribute-rgt-in distribute-lft-in swap-sqr pow-prod-down cbrt-unprod
6×pow-to-exp prod-diff pow-exp add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×*-commutative
2×sub-neg associate-+r+ flip3-+ flip-+
1×+-commutative pow2 flip3-- fma-def sum-log pow-sqr pow-prod-up flip-- distribute-lft-out
Counts
4 → 129
Calls
4 calls:
4.0ms
(+ (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* a a) (+ 1.0 a))
8.0ms
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(+ (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
49.0ms
(* (* a a) (+ 1.0 a))
170.0ms
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify93.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
06331068
13219938
25001917

prune407.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
0.0b
(+ (pow (hypot a b) (+ 2.0 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
16×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
14×*-un-lft-identity
12×add-cube-cbrt
10×associate-*r*
8×distribute-rgt-in fma-def distribute-lft-in
7×pow-prod-down prod-exp cbrt-unprod
6×prod-diff add-log-exp
5×flip3-+ associate-*l* flip-+
4×expm1-log1p-u frac-add log1p-expm1-u
3×unpow-prod-down flip3-- *-commutative flip-- unswap-sqr
2×sub-neg associate-+r+
1×unpow-prod-up +-commutative sum-log distribute-lft-out sqr-pow
Counts
4 → 110
Calls
4 calls:
35.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
8.0ms
(+ (pow (hypot a b) (+ 2.0 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* a a) (+ 1.0 a))
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
130.0ms
(+ (pow (hypot a b) (+ 2.0 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms
(* (* a a) (+ 1.0 a))
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify113.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
07401050
14176936
25001929

prune421.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (sqrt (pow (hypot a b) (+ 2.0 2.0))) (sqrt (pow (hypot a b) (+ 2.0 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
12.8b
(sqrt (pow (hypot a b) (+ 2.0 2.0)))
12.8b
(sqrt (pow (hypot a b) (+ 2.0 2.0)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt sqrt-prod
11×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log add-cbrt-cube
8×unpow-prod-down rem-sqrt-square
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×unpow-prod-up expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg sqrt-pow1 pow1/2 associate-*r/
1×flip3-- associate-*l* *-commutative flip-- fma-udef unswap-sqr
Counts
4 → 89
Calls
4 calls:
0.0ms
(fma (sqrt (pow (hypot a b) (+ 2.0 2.0))) (sqrt (pow (hypot a b) (+ 2.0 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms
(sqrt (pow (hypot a b) (+ 2.0 2.0)))
2.0ms
(sqrt (pow (hypot a b) (+ 2.0 2.0)))

series574.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(fma (sqrt (pow (hypot a b) (+ 2.0 2.0))) (sqrt (pow (hypot a b) (+ 2.0 2.0))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
172.0ms
(sqrt (pow (hypot a b) (+ 2.0 2.0)))
166.0ms
(sqrt (pow (hypot a b) (+ 2.0 2.0)))

simplify48.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0368782
11427683
25001670

prune406.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes67.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
12714

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.5s20589×body80valid