Details

Time bar (total: 4.5s)

sample51.0ms

Algorithm
intervals
Results
34.0ms619×body80valid

simplify92.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate-*r*
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 sqr-pow
Counts
4 → 79
Calls
4 calls:
17.0ms
(+ (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))
7.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
50.0ms
(* (* a a) (+ 1.0 a))
103.0ms
(pow (+ (* a a) (* b b)) 2.0)
63.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify65.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0504702
12520622
25002622

prune233.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

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

rewrite26.0ms

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:
8.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
7.0ms
(* 2 (* (pow a 2) (pow b 2)))
8.0ms
(* (pow a 2) (pow b 2))

series132.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
36.0ms
(* 2 (* (pow a 2) (pow b 2)))
37.0ms
(* (pow a 2) (pow b 2))

simplify50.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0330587
11424506
25001495

prune206.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (/ 1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.4b
(pow (/ 1 a) -4.0)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
16×pow1 add-sqr-sqrt *-un-lft-identity
14×add-cube-cbrt add-cbrt-cube
13×unpow-prod-down
9×times-frac
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/ pow-exp
3×pow-unpow pow-pow
2×sub-neg associate-+r+ flip3-+ div-exp associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp rec-exp flip3-- pow-flip 1-exp sum-log flip-- div-inv distribute-lft-out inv-pow sqr-pow
Counts
4 → 94
Calls
4 calls:
8.0ms
(+ (pow (/ 1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (/ 1 a) -4.0)
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (pow (/ 1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms
(* (* a a) (+ 1.0 a))
170.0ms
(pow (/ 1 a) -4.0)
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify71.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0603708
12815621
25002618

prune265.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
26.7b
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
29×unpow-prod-down
20×cbrt-prod
18×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity
14×cube-prod
12×add-exp-log
10×pow1 add-cbrt-cube
7×sqr-pow
6×pow-unpow
5×pow-exp
4×add-log-exp
3×pow-to-exp associate-*r* pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in cube-mult sub-neg pow-pow distribute-lft-in unpow3 associate-*r/
1×flip3-- pow1/3 associate-*l* *-commutative flip-- rem-cbrt-cube rem-cube-cbrt unswap-sqr
Counts
4 → 104
Calls
4 calls:
6.0ms
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
5.0ms
(pow (+ (* a a) (* b b)) 2.0)
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
6.0ms
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

series436.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
115.0ms
(pow (+ (* a a) (* b b)) 2.0)
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
151.0ms
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

simplify55.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0431825
11856787
25002781

prune305.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes134.0ms

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
02715
12715

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.2s20568×body80valid