Details

Time bar (total: 6.1s)

sample101.0ms

Algorithm
intervals
Results
82.0ms697×body80valid

simplify79.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05314
117313
253212
3168112
4427812
5500112

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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)
0.9b
(* (* b b) (+ 3.0 a))

rewrite66.0ms

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:
29.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
16.0ms
(* (* a a) (- 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
14.0ms
(* (* b b) (+ 3.0 a))

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))
102.0ms
(pow (+ (* a a) (* b b)) 2.0)
33.0ms
(* (* b b) (+ 3.0 a))

simplify87.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
0646990
13454779
25001776

prune336.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (pow (hypot a b) (* 2 (/ 2.0 2))) (pow (hypot a b) (* 2 (/ 2.0 2)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(* (pow (hypot a b) (* 2 (/ 2.0 2))) (pow (hypot a b) (* 2 (/ 2.0 2))))
0.9b
(* (* b b) (+ 3.0 a))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
30×*-un-lft-identity
26×add-exp-log add-cube-cbrt
18×unpow-prod-down prod-diff
16×associate-*r* add-cbrt-cube
15×prod-exp
14×pow1
13×distribute-rgt-in distribute-lft-in
11×unswap-sqr
10×sqr-pow
9×associate-*l*
7×swap-sqr pow-prod-down cbrt-unprod
6×pow-to-exp 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 distribute-lft-out-- difference-of-squares
Counts
4 → 143
Calls
4 calls:
8.0ms
(+ (* (pow (hypot a b) (* 2 (/ 2.0 2))) (pow (hypot a b) (* 2 (/ 2.0 2)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
16.0ms
(* (* a a) (- 1.0 a))
10.0ms
(* (pow (hypot a b) (* 2 (/ 2.0 2))) (pow (hypot a b) (* 2 (/ 2.0 2))))
14.0ms
(* (* b b) (+ 3.0 a))

series386.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(+ (* (pow (hypot a b) (* 2 (/ 2.0 2))) (pow (hypot a b) (* 2 (/ 2.0 2)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
55.0ms
(* (* a a) (- 1.0 a))
169.0ms
(* (pow (hypot a b) (* 2 (/ 2.0 2))) (pow (hypot a b) (* 2 (/ 2.0 2))))
32.0ms
(* (* b b) (+ 3.0 a))

simplify101.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
07311506
139211214
250011198

prune398.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (hypot a b) (* 2 (* 2 (/ 2.0 2))))) (* (* (* b b) (+ 3.0 a)) 4.0))
0.0b
(fma (pow a 2) (* (- 1.0 a) 4.0) (pow (hypot a b) (* 2 (* 2 (/ 2.0 2)))))
0.0b
(* (* (* b b) (+ 3.0 a)) 4.0)
0.9b
(* (* b b) (+ 3.0 a))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-exp-log add-cbrt-cube
9×*-un-lft-identity pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt
7×add-cube-cbrt associate-*r*
6×add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×fma-def flip3-+ flip-+
2×associate-*l* associate-*l/ *-commutative fma-udef
1×+-commutative distribute-rgt-in associate-+l+ distribute-lft-in sum-log distribute-lft-out unswap-sqr
Counts
4 → 78
Calls
4 calls:
3.0ms
(+ (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (hypot a b) (* 2 (* 2 (/ 2.0 2))))) (* (* (* b b) (+ 3.0 a)) 4.0))
0.0ms
(fma (pow a 2) (* (- 1.0 a) 4.0) (pow (hypot a b) (* 2 (* 2 (/ 2.0 2)))))
33.0ms
(* (* (* b b) (+ 3.0 a)) 4.0)
14.0ms
(* (* b b) (+ 3.0 a))

series285.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(+ (fma (pow a 2) (* (- 1.0 a) 4.0) (pow (hypot a b) (* 2 (* 2 (/ 2.0 2))))) (* (* (* b b) (+ 3.0 a)) 4.0))
93.0ms
(fma (pow a 2) (* (- 1.0 a) 4.0) (pow (hypot a b) (* 2 (* 2 (/ 2.0 2)))))
50.0ms
(* (* (* b b) (+ 3.0 a)) 4.0)
32.0ms
(* (* b b) (+ 3.0 a))

simplify62.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0415754
12124664
25002657

prune315.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* b (* b (+ 3.0 a))) 4.0)
0.0b
(fma (pow a 2) (* (- 1.0 a) 4.0) (pow (hypot a b) (* 2 (* 2 (/ 2.0 2)))))
0.0b
(* b (+ 3.0 a))
0.2b
(* b (* b (+ 3.0 a)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity associate-*r/ pow-prod-down prod-exp cbrt-unprod
8×add-cube-cbrt associate-*r*
7×associate-*l*
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ *-commutative flip-+
2×associate-*l/
1×fma-udef distribute-lft-out unswap-sqr
Counts
4 → 86
Calls
4 calls:
40.0ms
(* (* b (* b (+ 3.0 a))) 4.0)
0.0ms
(fma (pow a 2) (* (- 1.0 a) 4.0) (pow (hypot a b) (* 2 (* 2 (/ 2.0 2)))))
9.0ms
(* b (+ 3.0 a))
11.0ms
(* b (* b (+ 3.0 a)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (* b (* b (+ 3.0 a))) 4.0)
94.0ms
(fma (pow a 2) (* (- 1.0 a) 4.0) (pow (hypot a b) (* 2 (* 2 (/ 2.0 2)))))
35.0ms
(* b (+ 3.0 a))
32.0ms
(* b (* b (+ 3.0 a)))

simplify58.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0377545
11976453
25003450

prune319.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03015
13015

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.4s20589×body80valid