Details

Time bar (total: 5.8s)

sample88.0ms

Algorithm
intervals
Results
70.0ms636×body80valid

simplify73.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05114
115514
243014
3119514
4252614
5500114

prune3.0ms

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)))))
0.0b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (+ 3.0 a))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
9×associate-*r*
8×add-cube-cbrt
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×unpow-prod-down pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
23.0ms
(+ (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))

series302.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
56.0ms
(* (* a a) (- 1.0 a))
102.0ms
(pow (+ (* a a) (* b b)) 2.0)
32.0ms
(* (* b b) (+ 3.0 a))

simplify68.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
0506651
12520583
25001583

prune257.0ms

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 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)))))
2.5b
(* (pow a 2) (pow b 2))

rewrite49.0ms

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×*-un-lft-identity associate-*l* add-cbrt-cube add-log-exp
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
2×+-commutative flip3-+ pow-prod-down *-commutative flip-+
1×associate-+r+ distribute-lft-out
Counts
4 → 101
Calls
4 calls:
6.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
10.0ms
(* 2 (* (pow a 2) (pow b 2)))
18.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
12.0ms
(* (pow a 2) (pow b 2))

series178.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
36.0ms
(* 2 (* (pow a 2) (pow b 2)))
54.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
32.0ms
(* (pow a 2) (pow b 2))

simplify59.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0375699
11611622
25002616

prune255.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (+ 3.0 a))
28.2b
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
29×unpow-prod-down
20×cbrt-prod
19×*-un-lft-identity
18×add-sqr-sqrt
17×add-cube-cbrt
14×cube-prod
12×add-exp-log
10×pow1 add-cbrt-cube
7×sqr-pow
6×pow-unpow
5×pow-exp
4×associate-*r* add-log-exp
3×pow-to-exp pow-prod-down prod-exp cbrt-unprod
2×cube-mult pow-pow unpow3 associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ pow1/3 associate-*l* *-commutative rem-cbrt-cube flip-+ distribute-lft-out rem-cube-cbrt unswap-sqr
Counts
4 → 103
Calls
4 calls:
8.0ms
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
13.0ms
(* (* b b) (+ 3.0 a))
8.0ms
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

series425.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
114.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (+ 3.0 a))
153.0ms
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

simplify59.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0428776
11923748
25001740

prune304.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (+ 3.0 a))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
29.6b
(cbrt (* (pow (+ (* a a) (* b b)) 2.0) (pow (+ (* a a) (* b b)) 2.0)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×pow1 add-exp-log add-sqr-sqrt
9×add-cube-cbrt add-cbrt-cube
8×cbrt-prod
6×unpow-prod-down
4×associate-*r* add-log-exp
3×pow-unpow pow-prod-down prod-exp cbrt-unprod
2×pow1/3 associate-*r/ sqr-pow
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in flip3-+ associate-*l* pow-exp *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 65
Calls
4 calls:
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
14.0ms
(* (* b b) (+ 3.0 a))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
9.0ms
(cbrt (* (pow (+ (* a a) (* b b)) 2.0) (pow (+ (* a a) (* b b)) 2.0)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(pow (+ (* a a) (* b b)) 2.0)
38.0ms
(* (* b b) (+ 3.0 a))
148.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
155.0ms
(cbrt (* (pow (+ (* a a) (* b b)) 2.0) (pow (+ (* a a) (* b b)) 2.0)))

simplify47.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0347536
11480478
25002470

prune293.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes128.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02514
12514

end0.0ms

sample2.6s

Algorithm
intervals
Results
2.2s20502×body80valid