Details

Time bar (total: 26.0s)

sample148.0ms

Algorithm
intervals
Results
103.0ms653×body80valid

simplify6.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
01931
15529
217828
354528
4167228
5479728
done500028

prune7.0ms

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)
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite156.0ms

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:
66.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
37.0ms
(* (* a a) (+ 1.0 a))
16.0ms
(pow (+ (* a a) (* b b)) 2.0)
31.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
63.0ms
(* (* a a) (+ 1.0 a))
125.0ms
(pow (+ (* a a) (* b b)) 2.0)
62.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.7s

Counts
112 → 112
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02011802
15401621
220541446
done50001435

prune565.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* b b) (- 1.0 (* 3.0 a)))
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))
11.9b
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))
11.9b
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity prod-diff
10×distribute-rgt-in distribute-lft-in
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u sub-neg associate-*r/ log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 96
Calls
4 calls:
61.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
48.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))
2.0ms
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))

series692.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
74.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
269.0ms
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))
276.0ms
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify3.3s

Counts
108 → 108
Iterations

Useful iterations: done (3.3s)

IterNodesCost
01292220
13212078
29551844
333491820
done50001748

prune595.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* b b) (- 1.0 (* 3.0 a)))
11.9b
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))
12.5b
(cbrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))
12.5b
(cbrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×add-exp-log add-cbrt-cube
6×cbrt-prod prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×sub-neg pow1/3 associate-*r/
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 74
Calls
4 calls:
63.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
286.0ms
(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))
437.0ms
(cbrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))
328.0ms
(cbrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify3.6s

Counts
86 → 86
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01802406
14352325
212662090
342831968
done50001966

prune668.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 2 (* a a) (* b b))
0.2b
(fma (* b b) (fma 2 (* a a) (* b b)) (pow a 4))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
0.0ms
(fma 2 (* a a) (* b b))
0.0ms
(fma (* b b) (fma 2 (* a a) (* b b)) (pow a 4))

series118.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(fma 2 (* a a) (* b b))
78.0ms
(fma (* b b) (fma 2 (* a a) (* b b)) (pow a 4))

simplify2.5s

Counts
26 → 26
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
040395
174392
2186340
3647340
43436340
done5000340

prune94.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes111.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02487
12987
done2987

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.9s20825×body80valid