Details

Time bar (total: 19.1s)

sample64.0ms

Algorithm
intervals
Results
38.0ms699×body80valid

simplify4.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
01931
15529
217828
354528
4167228
5479728
done500028

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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)
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite156.0ms

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:
69.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
36.0ms
(* (* a a) (+ 1.0 a))
11.0ms
(pow (+ (* a a) (* b b)) 2.0)
36.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
59.0ms
(* (* a a) (+ 1.0 a))
124.0ms
(pow (+ (* a a) (* b b)) 2.0)
57.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.2s

Counts
112 → 112
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02011802
15401621
220541446
done50001435

prune375.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
10.6b
(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)))
10.6b
(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)))

rewrite74.0ms

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:
32.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
35.0ms
(* (* 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)))

series584.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
233.0ms
(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)))
235.0ms
(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)))

simplify2.5s

Counts
108 → 108
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01292220
13212078
29551844
333491820
done50001748

prune432.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
10.6b
(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)))
11.2b
(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)))
11.2b
(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)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×add-exp-log add-cbrt-cube
6×cbrt-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 sqrt-prod cbrt-unprod
2×sub-neg pow1/3 associate-*r/
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 74
Calls
4 calls:
32.0ms
(* (* 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)))
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)))

series848.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
234.0ms
(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)))
277.0ms
(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)))
277.0ms
(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)))

simplify2.5s

Counts
86 → 86
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01802406
14352325
212662090
342831968
done50001966

prune462.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log unpow-prod-down 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 sqr-pow
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 84
Calls
4 calls:
31.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
9.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
11.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
10.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series565.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
169.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
167.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
175.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.3s

Counts
96 → 96
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01321508
13061389
28791248
330761230
done50001194

prune437.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes115.0ms

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
02057
12357
done2357

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.1s20523×body80valid