Details

Time bar (total: 22.2s)

sample108.0ms

Algorithm
intervals
Results
74.0ms655×body80valid

simplify2.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
01931
15529
217928
359428
4238328
done500028

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

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

rewrite222.0ms

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:
89.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
65.0ms
(* (* a a) (+ 1.0 a))
12.0ms
(pow (+ (* a a) (* b b)) 2.0)
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series502.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
100.0ms
(* (* a a) (+ 1.0 a))
141.0ms
(pow (+ (* a a) (* b b)) 2.0)
74.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify3.7s

Counts
112 → 112
Iterations

Useful iterations: done (3.7s)

IterNodesCost
02011802
16181631
244291447
done50001446

prune602.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* b b) (- 1.0 (* 3.0 a)))
1.0b
(* (* b b) (- 1.0 (* 3.0 a)))
9.9b
(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)))
9.9b
(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)))

rewrite114.0ms

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:
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
61.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
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)))
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)))

series780.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
70.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
304.0ms
(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)))
301.0ms
(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)))

simplify2.0s

Counts
108 → 108
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01292220
13482078
220411844
done50011820

prune646.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 2 (* (pow a 2) (pow b 2)) (pow b 4))
0.0b
(+ (pow a 4) (fma 2 (* (pow a 2) (pow b 2)) (pow b 4)))
3.5b
(* (pow a 2) (pow b 2))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
17×unpow-prod-down
16×unswap-sqr
15×add-exp-log
11×*-un-lft-identity sqr-pow
10×unpow2
9×add-cube-cbrt prod-exp
8×associate-*r* associate-*l*
7×fma-def
6×pow-to-exp pow-exp
5×add-cbrt-cube add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×fma-udef
1×+-commutative associate-+r+ flip3-+ pow-prod-down sum-log *-commutative cbrt-unprod flip-+ distribute-lft-out
Counts
3 → 85
Calls
3 calls:
0.0ms
(fma 2 (* (pow a 2) (pow b 2)) (pow b 4))
23.0ms
(+ (pow a 4) (fma 2 (* (pow a 2) (pow b 2)) (pow b 4)))
38.0ms
(* (pow a 2) (pow b 2))

series248.0ms

Counts
3 → 9
Calls
3 calls:
116.0ms
(fma 2 (* (pow a 2) (pow b 2)) (pow b 4))
75.0ms
(+ (pow a 4) (fma 2 (* (pow a 2) (pow b 2)) (pow b 4)))
56.0ms
(* (pow a 2) (pow b 2))

simplify2.0s

Counts
94 → 94
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01191231
12801107
21759932
done5001907

prune362.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* b b) (- 1.0 (* 3.0 a)))
9.9b
(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)))
9.9b
(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)))
25.4b
(cbrt (pow (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))) 3))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
17×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×sqrt-prod
11×pow1
9×add-exp-log add-cbrt-cube
6×unpow-prod-down cube-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 cbrt-unprod
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/
1×cube-mult flip3-- pow1/3 unpow3 associate-*l* *-commutative flip-- rem-cbrt-cube unswap-sqr sqr-pow
Counts
4 → 92
Calls
4 calls:
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
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)))
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)))
4.0ms
(cbrt (pow (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))) 3))

series961.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
284.0ms
(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)))
322.0ms
(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)))
288.0ms
(cbrt (pow (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))) 3))

simplify2.7s

Counts
104 → 104
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01623283
14442616
228052508
done50012490

prune541.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes185.0ms

Accuracy

62.4% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 2.4b

bsearch218.0ms

Steps
ItersRangePoint
8
0.02325869037085268
8.505646244361715
2.006560387622814
8
-0.00047527308239176123
-6.160300464959826e-07
-0.0004706693102753827

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03671
15054
done5054

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.6s20583×body80valid