Details

Time bar (total: 10.8s)

sample52.0ms

Algorithm
intervals
Results
34.0ms622×body80valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01931
15529
215828
344328
4120628
5344228
done500028

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

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)
1.3b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out
Counts
4 → 100
Calls
4 calls:
27.0ms
(+ (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)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(+ (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))
102.0ms
(pow (+ (* a a) (* b b)) 2.0)
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.1s

Counts
112 → 112
Iterations

Useful iterations: 2 (433.0ms)

IterNodesCost
02011802
15501621
222671446
done50001446

prune350.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
1.3b
(* (* b b) (- 1.0 (* 3.0 a)))
8.2b
(sqrt (+ (* a a) (* b b)))
8.2b
(sqrt (+ (* a a) (* b b)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×pow1
9×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×prod-diff sqrt-prod
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r/ flip-+ hypot-def
1×flip3-- associate-*l* *-commutative flip-- fma-udef unswap-sqr
Counts
4 → 79
Calls
4 calls:
0.0ms
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
3.0ms
(sqrt (+ (* a a) (* b b)))
4.0ms
(sqrt (+ (* a a) (* b b)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
35.0ms
(sqrt (+ (* a a) (* b b)))
39.0ms
(sqrt (+ (* a a) (* b b)))

simplify859.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (235.0ms)

IterNodesCost
01401569
13701164
21457995
done5000995

prune334.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))
0.0b
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
1.3b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-exp-log add-sqr-sqrt *-un-lft-identity add-cbrt-cube
13×distribute-rgt-in distribute-lft-in
12×add-cube-cbrt associate-+r+ associate-*r/ prod-diff
8×fma-def add-log-exp
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod
5×flip3-+ flip-+
4×expm1-log1p-u sub-neg frac-add log1p-expm1-u
3×unpow-prod-down flip3-- flip--
2×+-commutative associate-+l+ associate-*l* sum-log *-commutative unswap-sqr
1×distribute-lft-out sqr-pow
Counts
4 → 111
Calls
4 calls:
12.0ms
(+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))
8.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* a a) (+ 1.0 a))
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))
130.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
47.0ms
(* (* a a) (+ 1.0 a))
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.4s

Counts
123 → 123
Iterations

Useful iterations: 2 (595.0ms)

IterNodesCost
02252357
17062143
232741914
done50001914

prune421.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 (fma a a (* b b)) (pow a 3))
0.0b
(+ (fma 1.0 (fma a a (* b b)) (pow a 3)) (* (- (* 3.0 a)) (* b b)))
0.0b
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (fma 1.0 (fma a a (* b b)) (pow a 3)) (* (- (* 3.0 a)) (* b b)))))
1.4b
(* (- (* 3.0 a)) (* b b))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
10×fma-def
9×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity add-log-exp
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-out unpow-prod-down pow-prod-down prod-exp cbrt-unprod
2×+-commutative associate-+r+ flip3-+ sum-log flip-+ fma-udef
1×distribute-lft-neg-in distribute-rgt-in neg-mul-1 associate-+l+ distribute-rgt-neg-in distribute-lft-in associate-*r* unsub-neg *-commutative unswap-sqr sqr-pow
Counts
4 → 76
Calls
4 calls:
0.0ms
(fma 1.0 (fma a a (* b b)) (pow a 3))
3.0ms
(+ (fma 1.0 (fma a a (* b b)) (pow a 3)) (* (- (* 3.0 a)) (* b b)))
7.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (fma 1.0 (fma a a (* b b)) (pow a 3)) (* (- (* 3.0 a)) (* b b)))))
8.0ms
(* (- (* 3.0 a)) (* b b))

series271.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(fma 1.0 (fma a a (* b b)) (pow a 3))
62.0ms
(+ (fma 1.0 (fma a a (* b b)) (pow a 3)) (* (- (* 3.0 a)) (* b b)))
132.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (fma 1.0 (fma a a (* b b)) (pow a 3)) (* (- (* 3.0 a)) (* b b)))))
37.0ms
(* (- (* 3.0 a)) (* b b))

simplify720.0ms

Counts
88 → 88
Iterations

Useful iterations: done (718.0ms)

IterNodesCost
01331682
13641556
214751377
done50011376

prune348.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes77.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02232
13432
23932
34332
done4332

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s20276×body80valid