Details

Time bar (total: 4.7s)

sample38.0ms

Algorithm
intervals
Results
21.0ms603×body80valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0258
1418
2678
31198
43098
514948
650018

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
0.0b
(+ (* a a) (* b b))
0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
13×add-log-exp
8×add-sqr-sqrt *-un-lft-identity
6×add-cube-cbrt
5×pow1 add-exp-log
4×add-cbrt-cube
3×unpow-prod-down pow-unpow sum-log
2×+-commutative flip3-+ diff-log flip-+
1×pow-to-exp sub-neg flip3-- pow-pow pow-exp associate--l+ flip-- distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 55
Calls
4 calls:
278.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
7.0ms
(+ (* a a) (* b b))
53.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
9.0ms
(pow (+ (* a a) (* b b)) 2.0)

series281.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
28.0ms
(+ (* a a) (* b b))
69.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify42.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0330556
11404524
25001517

prune174.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
0.0b
(* 2 (* (pow a 2) (pow b 2)))
0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
1.9b
(* (pow a 2) (pow b 2))

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
27×add-sqr-sqrt
16×unswap-sqr
15×add-log-exp
14×unpow-prod-down *-un-lft-identity
12×pow-to-exp pow-exp
11×associate-*l* add-cbrt-cube
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
3×diff-log
2×pow-prod-down *-commutative distribute-lft-out--
1×+-commutative sub-neg flip3-- flip3-+ associate--l+ flip-- flip-+ distribute-lft-out difference-of-squares
Counts
4 → 105
Calls
4 calls:
230.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
23.0ms
(* 2 (* (pow a 2) (pow b 2)))
13.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
20.0ms
(* (pow a 2) (pow b 2))

series186.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
42.0ms
(* 2 (* (pow a 2) (pow b 2)))
54.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
36.0ms
(* (pow a 2) (pow b 2))

simplify56.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0382781
11592689
25001676

prune256.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2.0 (* (pow a 2) (pow b 2)))
0.0b
(+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2))))
0.0b
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
1.9b
(* (pow a 2) (pow b 2))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
25×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×associate-*l* add-cbrt-cube add-log-exp
10×unpow2 sqr-pow
9×add-cube-cbrt *-un-lft-identity associate-*r*
6×pow1
4×sum-log cbrt-unprod
2×+-commutative flip3-+ pow-prod-down *-commutative flip-+
1×associate-+l+
Counts
4 → 100
Calls
4 calls:
24.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
14.0ms
(+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2))))
52.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
16.0ms
(* (pow a 2) (pow b 2))

series190.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
56.0ms
(+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2))))
65.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
32.0ms
(* (pow a 2) (pow b 2))

simplify58.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0389729
11718632
25002624

prune239.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (pow a 2) (pow b 2))
1.9b
(* (pow a 2) (pow b 2))
22.7b
(sqrt (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))))
22.7b
(sqrt (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
32×unswap-sqr
28×add-exp-log unpow-prod-down
20×unpow2 sqr-pow
18×prod-exp
16×associate-*r* associate-*l*
14×add-cube-cbrt *-un-lft-identity
12×pow-to-exp pow-exp
8×add-cbrt-cube
6×pow1 sqrt-prod
4×sqrt-div add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-prod-down *-commutative cbrt-unprod flip-+
Counts
4 → 132
Calls
4 calls:
16.0ms
(* (pow a 2) (pow b 2))
18.0ms
(* (pow a 2) (pow b 2))
50.0ms
(sqrt (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))))
48.0ms
(sqrt (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))))

series331.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (pow a 2) (pow b 2))
35.0ms
(* (pow a 2) (pow b 2))
135.0ms
(sqrt (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))))
129.0ms
(sqrt (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))))

simplify48.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0294968
11213856
25002834

prune418.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes78.0ms

Accuracy

98.4% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 1.0b

bsearch108.0ms

Steps
ItersRangePoint
9
1.6312015655505496e-11
0.024130789021135513
9.00135537302134e-08
8
-21.084339142203387
-0.0006592480666379122
-0.0006735223120487487

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03919
13919

end0.0ms

sample1.2s

Algorithm
intervals
Results
715.0ms20441×body80valid