Details

Time bar (total: 8.4s)

sample102.0ms

Algorithm
intervals
Results
78.0ms723×body80valid

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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)
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite63.0ms

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:
27.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
15.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series67.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
4.0ms
(* (* a a) (+ 1.0 a))
27.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify80.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
0564828
12826724
25001715

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
8.4b
(sqrt (+ (* a a) (* b b)))
8.4b
(sqrt (+ (* a a) (* b b)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×pow1
9×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×prod-diff sqrt-prod
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r/ flip-+ hypot-def
1×flip3-- associate-*l* *-commutative flip-- fma-udef unswap-sqr
Counts
4 → 79
Calls
4 calls:
0.0ms
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms
(sqrt (+ (* a a) (* b b)))
4.0ms
(sqrt (+ (* a a) (* b b)))

series57.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
6.0ms
(sqrt (+ (* a a) (* b b)))
6.0ms
(sqrt (+ (* a a) (* b b)))

simplify54.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0379738
11669640
25001616

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize21.0ms

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 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite78.0ms

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 distribute-lft-in
7×fma-def 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×+-commutative sum-log distribute-lft-out sqr-pow
Counts
4 → 109
Calls
4 calls:
40.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
8.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* a a) (+ 1.0 a))
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series58.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
29.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
4.0ms
(* (* a a) (+ 1.0 a))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify123.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
07401050
14178936
25001929

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* a a) (+ 1.0 a))
0.2b
(fma (pow (hypot a b) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
8.4b
(sqrt (+ (* a a) (* b b)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
11×*-un-lft-identity
9×add-cube-cbrt
7×associate-*r*
6×distribute-rgt-in distribute-lft-in prod-diff pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×sqrt-prod
2×sub-neg flip3-+ sqrt-div associate-*l* *-commutative flip-+ unswap-sqr
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- fma-udef hypot-def distribute-lft-out
Counts
4 → 87
Calls
4 calls:
14.0ms
(* (* a a) (+ 1.0 a))
0.0ms
(fma (pow (hypot a b) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms
(sqrt (+ (* a a) (* b b)))

series54.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (* a a) (+ 1.0 a))
36.0ms
(fma (pow (hypot a b) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
6.0ms
(sqrt (+ (* a a) (* b b)))

simplify71.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0497728
12424624
25003617

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes261.0ms

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
02914
12914

end0.0ms

sample2.5s

Algorithm
intervals
Results
2.2s20670×body80valid