Details

Time bar (total: 25.4s)

sample135.0ms

Algorithm
intervals
Results
90.0ms680×body80valid

simplify6.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
01931
15529
217828
354528
4167228
5479728
done500028

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

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) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite206.0ms

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:
92.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
47.0ms
(* (* a a) (+ 1.0 a))
17.0ms
(pow (+ (* a a) (* b b)) 2.0)
44.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series470.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
78.0ms
(* (* a a) (+ 1.0 a))
161.0ms
(pow (+ (* a a) (* b b)) 2.0)
66.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.8s

Counts
112 → 112
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02011802
15401621
220541446
done50001435

prune471.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 3.0 a))
0.1b
(* (* a a) (+ 1.0 a))
0.2b
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-exp-log add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×prod-diff
7×associate-*r*
6×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×sub-neg fma-neg
2×flip3-- associate-*l* *-commutative flip-- unswap-sqr
1×flip3-+ diff-log flip-+ fma-udef distribute-lft-out
Counts
4 → 89
Calls
4 calls:
12.0ms
(- 1.0 (* 3.0 a))
63.0ms
(* (* a a) (+ 1.0 a))
1.0ms
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- 1.0 (* 3.0 a))
80.0ms
(* (* a a) (+ 1.0 a))
145.0ms
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
81.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.5s

Counts
101 → 101
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01601630
14241441
215711233
done50011210

prune476.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
9.6b
(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)))
9.6b
(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)))

rewrite107.0ms

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:
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
44.0ms
(* (* 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)))

series803.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
70.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
344.0ms
(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)))
317.0ms
(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)))

simplify3.4s

Counts
108 → 108
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01292220
13212078
29551844
333491820
done50001748

prune656.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
10.1b
(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)))
10.1b
(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)))
10.1b
(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)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 72
Calls
4 calls:
44.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
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)))
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:
64.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
339.0ms
(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)))
318.0ms
(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)))
413.0ms
(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)))

simplify2.7s

Counts
84 → 84
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01432483
13472463
210342202
336202028
done50001986

prune573.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes169.0ms

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
02144
12844
done2844

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.1s20632×body80valid