Details

Time bar (total: 3.6s)

sample37.0ms

Algorithm
intervals
Results
23.0ms640×body80valid

simplify53.0ms

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

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log
8×add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity
5×add-log-exp
3×unpow-prod-down pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
1×+-commutative pow-to-exp pow-pow flip3-+ associate-*r* pow-exp sum-log *-commutative flip-+ unswap-sqr sqr-pow
Counts
3 → 47
Calls
3 calls:
9.0ms
(* 4.0 (* b b))
23.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series188.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(* 4.0 (* b b))
59.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
100.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify111.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0249342
1939315
23536315
35001315

prune127.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
3.0b
(* (pow a 2) (pow b 2))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
28×prod-exp
24×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×associate-*l*
10×*-un-lft-identity add-cbrt-cube unpow2 sqr-pow
9×associate-*r*
8×add-cube-cbrt add-log-exp
5×pow1
4×cbrt-unprod
3×sum-log
2×pow-prod-down *-commutative
1×+-commutative associate-+r+ flip3-+ flip-+ distribute-lft-out
Counts
3 → 90
Calls
3 calls:
18.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
10.0ms
(* 2 (* (pow a 2) (pow b 2)))
9.0ms
(* (pow a 2) (pow b 2))

series119.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
35.0ms
(* 2 (* (pow a 2) (pow b 2)))
36.0ms
(* (pow a 2) (pow b 2))

simplify53.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0330587
11424506
25001495

prune196.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* b b))
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)))
3.0b
(* (pow a 2) (pow b 2))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
44×add-exp-log
31×prod-exp
27×add-sqr-sqrt
17×unswap-sqr
16×add-cbrt-cube
14×unpow-prod-down associate-*l*
12×pow-to-exp pow-exp
11×pow1
10×add-cube-cbrt *-un-lft-identity associate-*r* unpow2 sqr-pow
9×add-log-exp
7×cbrt-unprod
5×pow-prod-down
3×sum-log *-commutative
1×+-commutative associate-+l+ flip3-+ flip-+
Counts
4 → 108
Calls
4 calls:
6.0ms
(* 4.0 (* b b))
10.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
26.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
9.0ms
(* (pow a 2) (pow b 2))

series159.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* 4.0 (* b b))
39.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
59.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
36.0ms
(* (pow a 2) (pow b 2))

simplify56.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0400683
11741575
25002568

prune234.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.3b
(pow (+ (* a a) (* b b)) (* 2 2.0))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
35.5b
(/ (+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
8×add-exp-log
6×pow1 unpow-prod-down add-cbrt-cube add-log-exp
4×pow-unpow
3×associate-/r* associate-/l*
2×pow-to-exp flip3-- pow-pow pow-exp associate-/r/ flip-- associate-/l/ sqr-pow
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp clear-num flip-+ div-inv
Counts
4 → 75
Calls
4 calls:
31.0ms
(- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
4.0ms
(pow (+ (* a a) (* b b)) (* 2 2.0))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
71.0ms
(/ (+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series447.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
114.0ms
(pow (+ (* a a) (* b b)) (* 2 2.0))
101.0ms
(pow (+ (* a a) (* b b)) 2.0)
169.0ms
(/ (+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify60.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
03981307
119641176
250021120

prune304.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes64.0ms

Accuracy

92.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.1b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03420
13420

end0.0ms

sample1.1s

Algorithm
intervals
Results
738.0ms20316×body80valid