Details

Time bar (total: 17.1s)

sample126.0ms

Algorithm
intervals
Results
88.0ms693×body80valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
01829
15327
217226
355426
4211326
done500126

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

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)
1.5b
(* (* b b) (+ 3.0 a))

rewrite198.0ms

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:
80.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
38.0ms
(* (* a a) (- 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
64.0ms
(* (* b b) (+ 3.0 a))

series469.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
101.0ms
(* (* a a) (- 1.0 a))
169.0ms
(pow (+ (* a a) (* b b)) 2.0)
40.0ms
(* (* b b) (+ 3.0 a))

simplify493.0ms

Counts
126 → 126
Iterations

Useful iterations: done (487.0ms)

IterNodesCost
02352118
17461794
done50001553

prune471.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (* b b) (+ 3.0 a)) 4.0)
0.0b
(fma (* a a) (* (- 1.0 a) 4.0) (pow (fma a a (* b b)) 2.0))
0.3b
(pow (fma a a (* b b)) 2.0)
1.5b
(* (* b b) (+ 3.0 a))

rewrite129.0ms

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:
87.0ms
(* (* (* b b) (+ 3.0 a)) 4.0)
0.0ms
(fma (* a a) (* (- 1.0 a) 4.0) (pow (fma a a (* b b)) 2.0))
3.0ms
(pow (fma a a (* b b)) 2.0)
36.0ms
(* (* b b) (+ 3.0 a))

series398.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (* (* b b) (+ 3.0 a)) 4.0)
118.0ms
(fma (* a a) (* (- 1.0 a) 4.0) (pow (fma a a (* b b)) 2.0))
168.0ms
(pow (fma a a (* b b)) 2.0)
43.0ms
(* (* b b) (+ 3.0 a))

simplify3.2s

Counts
92 → 92
Iterations

Useful iterations: done (3.2s)

IterNodesCost
01551202
14381142
23099978
done5001972

prune411.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (* b b) (+ 3.0 a))
8.1b
(cbrt (fma a a (* b b)))
8.1b
(cbrt (fma a a (* b b)))
8.1b
(cbrt (fma a a (* b b)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ associate-*l* *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 65
Calls
4 calls:
40.0ms
(* (* b b) (+ 3.0 a))
1.0ms
(cbrt (fma a a (* b b)))
1.0ms
(cbrt (fma a a (* b b)))
1.0ms
(cbrt (fma a a (* b b)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* b b) (+ 3.0 a))
137.0ms
(cbrt (fma a a (* b b)))
136.0ms
(cbrt (fma a a (* b b)))
122.0ms
(cbrt (fma a a (* b b)))

simplify1.7s

Counts
77 → 77
Iterations

Useful iterations: done (1.7s)

IterNodesCost
088814
1244774
21679678
done5002669

prune563.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow a 4) (fma (* 2 (* a a)) (* b b) (pow b 4)))
0.0b
(* 2 (* a a))
1.8b
(fma (* 2 (* a a)) (* b b) (pow b 4))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
7×add-sqr-sqrt fma-def
6×add-cube-cbrt
5×add-log-exp
3×expm1-log1p-u unpow-prod-down associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
2×fma-udef
1×+-commutative associate-+r+ flip3-+ associate-*r* sum-log *-commutative flip-+ distribute-lft-out unswap-sqr sqr-pow
Counts
3 → 53
Calls
3 calls:
14.0ms
(+ (pow a 4) (fma (* 2 (* a a)) (* b b) (pow b 4)))
23.0ms
(* 2 (* a a))
0.0ms
(fma (* 2 (* a a)) (* b b) (pow b 4))

series179.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(+ (pow a 4) (fma (* 2 (* a a)) (* b b) (pow b 4)))
31.0ms
(* 2 (* a a))
85.0ms
(fma (* 2 (* a a)) (* b b) (pow b 4))

simplify1.5s

Counts
62 → 62
Iterations

Useful iterations: 2 (173.0ms)

IterNodesCost
081799
1212728
21446680
done5002680

prune209.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes152.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01829
12329
done2329

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.8s20552×body80valid