Details

Time bar (total: 8.8s)

sample98.0ms

Algorithm
intervals
Results
75.0ms723×body80valid

simplify93.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115

prune9.0ms

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)
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite57.0ms

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:
24.0ms
(+ (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))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series62.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
4.0ms
(* (* a a) (+ 1.0 a))
23.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify66.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
0504702
12520622
25002622

prune788.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
8.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-div associate-*r/ add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-- flip-+ unswap-sqr
Counts
4 → 80
Calls
4 calls:
11.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
29.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
28.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series83.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
35.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
33.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify48.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03331080
11424980
25002978

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
16.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log unpow-prod-down add-cbrt-cube
4×add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 70
Calls
4 calls:
11.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series123.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
40.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
38.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
38.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0266651
11020585
25001579

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

16.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down *-un-lft-identity
4×pow1 add-exp-log pow1/3 add-cbrt-cube add-log-exp sqr-pow
Counts
4 → 60
Calls
4 calls:
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series154.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
37.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
41.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
38.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify98.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (22.0ms)

IterNodesCost
0102632
1220588
2765580
33241572
45001572

prune1.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes626.0ms

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
02932
12932

end0.0ms

sample2.5s

Algorithm
intervals
Results
2.1s20670×body80valid