Details

Time bar (total: 4.5s)

sample65.0ms

Algorithm
intervals
Results
48.0ms688×body80valid

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0258
1418
2678
31198
43098
514948
650018

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

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

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
10×pow1 add-exp-log add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube
7×add-cube-cbrt
3×unpow-prod-down pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×diff-log sum-log
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow flip3-+ associate-*r* pow-exp associate--l+ *-commutative flip-- flip-+ distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
Counts
4 → 63
Calls
4 calls:
138.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
23.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
6.0ms
(* 4.0 (* b b))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series271.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
66.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
25.0ms
(* 4.0 (* b b))
104.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify137.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0309549
11144520
24418513
35002513

prune175.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
10×pow1 add-exp-log
9×*-un-lft-identity add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
3×unpow-prod-down pow-unpow associate-*l* pow-prod-down prod-exp sum-log cbrt-unprod
2×+-commutative associate-+r+ flip3-+ flip-+
1×pow-to-exp associate-+r- sub-neg pow-pow diff-log associate-*r* pow-exp *-commutative distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 63
Calls
4 calls:
3.0ms
(+ (* a a) (* b b))
37.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (- (* 4.0 (* b b)) 1.0))
7.0ms
(* 4.0 (* b b))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series238.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* a a) (* b b))
77.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (- (* 4.0 (* b b)) 1.0))
29.0ms
(* 4.0 (* b b))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify41.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0337469
11337432
25001432

prune169.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
0.0b
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
1.2b
(* (pow a 2) (pow b 2))

rewrite173.0ms

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:
6.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
12.0ms
(* 2 (* (pow a 2) (pow b 2)))
142.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
9.0ms
(* (pow a 2) (pow b 2))

series183.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
37.0ms
(* 2 (* (pow a 2) (pow b 2)))
57.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
34.0ms
(* (pow a 2) (pow b 2))

simplify57.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0382781
11592689
25001676

prune244.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize19.0ms

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)))) (- (* 4.0 (* b b)) 1.0))
0.0b
(* 4.0 (* b b))
1.2b
(* (pow a 2) (pow b 2))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
44×add-exp-log
31×prod-exp
27×add-sqr-sqrt
17×unswap-sqr
16×add-cbrt-cube add-log-exp
14×unpow-prod-down associate-*l*
12×pow-to-exp *-un-lft-identity pow-exp
11×pow1
10×add-cube-cbrt associate-*r* unpow2 sqr-pow
7×cbrt-unprod
6×sum-log
5×pow-prod-down
4×frac-add
3×flip3-+ *-commutative flip-+
2×associate-+r+ flip3-- diff-log flip--
1×+-commutative associate-+r- sub-neg associate-+l+ distribute-lft-out
Counts
4 → 118
Calls
4 calls:
13.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
41.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (- (* 4.0 (* b b)) 1.0))
6.0ms
(* 4.0 (* b b))
9.0ms
(* (pow a 2) (pow b 2))

series162.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
67.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (- (* 4.0 (* b b)) 1.0))
25.0ms
(* 4.0 (* b b))
33.0ms
(* (pow a 2) (pow b 2))

simplify84.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
0573972
12569869
25001858

prune264.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes80.0ms

Accuracy

86.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.0b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03420
13420

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.4s20520×body80valid