Details

Time bar (total: 4.8s)

sample61.0ms

Algorithm
intervals
Results
38.0ms708×body80valid

simplify79.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05314
117313
253212
3168112
4427812
5500112
done500112

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(* (* b b) (+ 3.0 a))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
18×prod-diff
15×pow1 add-exp-log
14×add-cbrt-cube
13×distribute-rgt-in distribute-lft-in
9×associate-*r*
7×fma-def
6×unpow-prod-down 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 distribute-lft-out-- difference-of-squares
Counts
4 → 114
Calls
4 calls:
60.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
32.0ms
(* (* a a) (- 1.0 a))
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
31.0ms
(* (* b b) (+ 3.0 a))

series320.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
52.0ms
(* (* a a) (- 1.0 a))
110.0ms
(pow (+ (* a a) (* b b)) 2.0)
38.0ms
(* (* b b) (+ 3.0 a))

simplify87.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
0646990
13454779
25001776
done5001776

prune326.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0))
0.0b
(* (* (* b b) (+ 3.0 a)) 4.0)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(* (* b b) (+ 3.0 a))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 add-exp-log
18×add-cbrt-cube
10×*-un-lft-identity
9×add-sqr-sqrt pow-prod-down prod-exp cbrt-unprod
8×add-cube-cbrt
7×associate-*r*
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow
2×flip3-+ associate-*l* associate-*l/ *-commutative flip-+
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in pow-exp fma-udef distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 80
Calls
4 calls:
0.0ms
(fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0))
67.0ms
(* (* (* b b) (+ 3.0 a)) 4.0)
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
32.0ms
(* (* b b) (+ 3.0 a))

series271.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(fma (pow a 2) (* (- 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0))
53.0ms
(* (* (* b b) (+ 3.0 a)) 4.0)
107.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (+ 3.0 a))

simplify58.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0398569
12053480
25001472
done5001472

prune305.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 2 (pow a 2))
0.1b
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
1.1b
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×add-exp-log associate-*r*
6×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down unswap-sqr
3×pow1 expm1-log1p-u associate-*l* prod-exp log1p-expm1-u add-log-exp
2×fma-udef unpow2 sqr-pow
1×pow-to-exp pow-exp *-commutative cbrt-unprod
Counts
3 → 49
Calls
3 calls:
12.0ms
(* 2 (pow a 2))
0.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
1.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series161.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(* 2 (pow a 2))
61.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
75.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify179.0ms

Counts
58 → 58
Iterations

Useful iterations: 3 (169.0ms)

IterNodesCost
0175324
1799276
24170274
35001267
done5001267

prune184.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (pow a 4) 1.0 (* 4.0 (- (pow a 2) (pow a 3))))
0.0b
(- (pow a 2) (pow a 3))
0.0b
(* (* (* b b) (+ 3.0 a)) 4.0)
0.3b
(* (* b b) (+ 3.0 a))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
96×prod-diff
77×add-sqr-sqrt
71×unpow-prod-down
60×*-un-lft-identity
56×add-cube-cbrt
29×sqr-pow
28×cube-prod
19×unpow2
18×pow1 add-exp-log add-cbrt-cube
16×difference-of-squares
9×cube-mult unpow3 pow-prod-down prod-exp cbrt-unprod
8×fma-neg
7×associate-*r*
6×add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
2×flip3-+ associate-*l* associate-*l/ *-commutative flip-+ distribute-lft-out--
1×distribute-rgt-in sub-neg flip3-- distribute-rgt-out-- distribute-lft-in diff-log flip-- fma-udef distribute-lft-out unswap-sqr
Counts
4 → 198
Calls
4 calls:
0.0ms
(fma (pow a 4) 1.0 (* 4.0 (- (pow a 2) (pow a 3))))
25.0ms
(- (pow a 2) (pow a 3))
68.0ms
(* (* (* b b) (+ 3.0 a)) 4.0)
32.0ms
(* (* b b) (+ 3.0 a))

series197.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(fma (pow a 4) 1.0 (* 4.0 (- (pow a 2) (pow a 3))))
73.0ms
(- (pow a 2) (pow a 3))
49.0ms
(* (* (* b b) (+ 3.0 a)) 4.0)
34.0ms
(* (* b b) (+ 3.0 a))

simplify115.0ms

Counts
210 → 210
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
06781826
131081209
250021189
done50021189

prune314.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes127.0ms

Accuracy

65.6% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 2.4b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03521
13521
done3521

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.0s20783×body80valid