Details

Time bar (total: 11.2s)

sample54.0ms

Algorithm
intervals
Results
36.0ms622×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01931
15529
215828
344628
4122728
5353928
done500028

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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)))

rewrite65.0ms

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:
30.0ms
(+ (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)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
54.0ms
(* (* a a) (+ 1.0 a))
104.0ms
(pow (+ (* a a) (* b b)) 2.0)
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.1s

Counts
112 → 112
Iterations

Useful iterations: 2 (205.0ms)

IterNodesCost
02011802
15611635
225891447
done50011447

prune367.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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)))

rewrite23.0ms

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))))))
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms
(sqrt (+ (* a a) (* b b)))
4.0ms
(sqrt (+ (* a a) (* b b)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(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))))))
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
35.0ms
(sqrt (+ (* a a) (* b b)))
40.0ms
(sqrt (+ (* a a) (* b b)))

simplify695.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (140.0ms)

IterNodesCost
01401569
13811164
21612995
done5000995

prune365.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

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)))

rewrite55.0ms

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))))))
17.0ms
(* (* a a) (+ 1.0 a))
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))
137.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
48.0ms
(* (* a a) (+ 1.0 a))
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.5s

Counts
123 → 123
Iterations

Useful iterations: 2 (277.0ms)

IterNodesCost
02252357
17152159
236151917
done50011917

prune647.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* 1.0 (* a a)) (pow a 3)) (* (* b b) (- 1.0 (* 3.0 a))))
0.0b
(+ (* 1.0 (* a a)) (pow a 3))
0.0b
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (+ (* 1.0 (* a a)) (pow a 3)) (* (* b b) (- 1.0 (* 3.0 a))))))
1.3b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-log-exp
12×add-cube-cbrt associate-+r+ fma-def *-un-lft-identity prod-diff
11×distribute-rgt-in distribute-lft-in
9×pow1 add-exp-log add-cbrt-cube
6×associate-*r/
5×flip3-+ sum-log flip-+
4×expm1-log1p-u sub-neg frac-add log1p-expm1-u
3×+-commutative unpow-prod-down flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×cube-mult distribute-rgt-out
1×associate-+l+ associate-*l* *-commutative unswap-sqr sqr-pow
Counts
4 → 103
Calls
4 calls:
70.0ms
(+ (+ (* 1.0 (* a a)) (pow a 3)) (* (* b b) (- 1.0 (* 3.0 a))))
9.0ms
(+ (* 1.0 (* a a)) (pow a 3))
39.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (+ (* 1.0 (* a a)) (pow a 3)) (* (* b b) (- 1.0 (* 3.0 a))))))
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(+ (+ (* 1.0 (* a a)) (pow a 3)) (* (* b b) (- 1.0 (* 3.0 a))))
78.0ms
(+ (* 1.0 (* a a)) (pow a 3))
129.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (+ (* 1.0 (* a a)) (pow a 3)) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.3s

Counts
115 → 115
Iterations

Useful iterations: 2 (239.0ms)

IterNodesCost
02062521
16542294
231991918
done50011918

prune429.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02331
13131
done3131

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s20276×body80valid