Details

Time bar (total: 22.9s)

sample87.0ms

Algorithm
intervals
Results
55.0ms656×body80valid

simplify5.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
01829
15327
217226
350926
4149726
5357326
done500026

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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)
0.5b
(* (* b b) (+ 3.0 a))

rewrite220.0ms

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:
90.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
44.0ms
(* (* a a) (- 1.0 a))
13.0ms
(pow (+ (* a a) (* b b)) 2.0)
66.0ms
(* (* b b) (+ 3.0 a))

series470.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
92.0ms
(* (* a a) (- 1.0 a))
187.0ms
(pow (+ (* a a) (* b b)) 2.0)
44.0ms
(* (* b b) (+ 3.0 a))

simplify2.0s

Counts
126 → 126
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02352118
16051768
220891545
done50021519

prune502.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (+ 3.0 a) (pow b 2))
0.5b
(* (+ 3.0 a) (pow b 2))
8.9b
(sqrt (fma (fma (pow a 2) (- 1.0 a) (* (+ 3.0 a) (pow b 2))) 4.0 (pow (fma a a (* b b)) 2.0)))
8.9b
(sqrt (fma (fma (pow a 2) (- 1.0 a) (* (+ 3.0 a) (pow b 2))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
16×*-un-lft-identity associate-*r*
14×add-exp-log
12×add-cube-cbrt
8×unpow-prod-down associate-*l* add-cbrt-cube unswap-sqr
6×pow1 prod-exp sqrt-prod
4×expm1-log1p-u associate-*l/ log1p-expm1-u unpow2 add-log-exp sqr-pow
2×pow-to-exp rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-exp *-commutative cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 94
Calls
4 calls:
58.0ms
(* (+ 3.0 a) (pow b 2))
38.0ms
(* (+ 3.0 a) (pow b 2))
2.0ms
(sqrt (fma (fma (pow a 2) (- 1.0 a) (* (+ 3.0 a) (pow b 2))) 4.0 (pow (fma a a (* b b)) 2.0)))
2.0ms
(sqrt (fma (fma (pow a 2) (- 1.0 a) (* (+ 3.0 a) (pow b 2))) 4.0 (pow (fma a a (* b b)) 2.0)))

series709.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (+ 3.0 a) (pow b 2))
62.0ms
(* (+ 3.0 a) (pow b 2))
260.0ms
(sqrt (fma (fma (pow a 2) (- 1.0 a) (* (+ 3.0 a) (pow b 2))) 4.0 (pow (fma a a (* b b)) 2.0)))
307.0ms
(sqrt (fma (fma (pow a 2) (- 1.0 a) (* (+ 3.0 a) (pow b 2))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify3.5s

Counts
106 → 106
Iterations

Useful iterations: done (3.5s)

IterNodesCost
01201800
12681606
28401464
331121456
done50021450

prune735.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×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
1 → 10
Calls
1 calls:
0.0ms
(fma (* b b) (fma (* 2 a) a (* b b)) (pow a 4))

series89.0ms

Counts
1 → 3
Calls
1 calls:
89.0ms
(fma (* b b) (fma (* 2 a) a (* b b)) (pow a 4))

simplify2.4s

Counts
13 → 13
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
028255
160255
2146219
3479219
42645219
done5001219

prune78.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.1b
(* (* a a) (- 1.0 a))
0.5b
(* (* b b) (+ 3.0 a))
0.9b
(fma (* 2.0 (* a a)) (* b b) (pow b 4))

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×*-un-lft-identity
20×add-cube-cbrt
18×associate-*r/ prod-diff
16×pow1 add-exp-log add-cbrt-cube
13×distribute-rgt-in distribute-lft-in
12×associate-*r*
7×pow-prod-down prod-exp cbrt-unprod
5×associate-*l*
4×expm1-log1p-u flip3-+ frac-add flip-+ log1p-expm1-u add-log-exp
3×flip3-- *-commutative flip-- unswap-sqr
2×sub-neg
1×fma-udef distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 111
Calls
4 calls:
179.0ms
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
57.0ms
(* (* a a) (- 1.0 a))
41.0ms
(* (* b b) (+ 3.0 a))
0.0ms
(fma (* 2.0 (* a a)) (* b b) (pow b 4))

series357.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
70.0ms
(* (* a a) (- 1.0 a))
56.0ms
(* (* b b) (+ 3.0 a))
120.0ms
(fma (* 2.0 (* a a)) (* b b) (pow b 4))

simplify1.9s

Counts
123 → 123
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02482152
16961856
227521623
done50001597

prune470.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02053
12253
done2253

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.8s20728×body80valid