Details

Time bar (total: 26.5s)

sample120.0ms

Algorithm
intervals
Results
91.0ms642×body80valid

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
019696
155686
2179661
3588661
42195661
done5000661

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.1b
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b
(pow (fma a a (* b b)) 2.0)
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt pow1 add-exp-log
9×*-un-lft-identity add-cbrt-cube add-cube-cbrt
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow unpow-prod-down associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/ fma-udef
1×pow-to-exp pow-pow flip3-- associate-*l* pow-exp *-commutative flip-- unswap-sqr sqr-pow
Counts
4 → 72
Calls
4 calls:
0.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
2.0ms
(pow (fma a a (* b b)) 2.0)
32.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
72.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
145.0ms
(pow (fma a a (* b b)) 2.0)
74.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify3.2s

Counts
84 → 84
Iterations

Useful iterations: done (3.2s)

IterNodesCost
015833861
142429154
2254528272
done500028182

prune596.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize105.0ms

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)))
6.7b
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
6.7b
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt pow1
14×add-cbrt-cube add-exp-log
12×*-un-lft-identity prod-diff add-cube-cbrt
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 sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 96
Calls
4 calls:
31.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
30.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
2.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series716.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
72.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
280.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
289.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify2.2s

Counts
108 → 108
Iterations

Useful iterations: done (2.2s)

IterNodesCost
013144722
135041468
2205940080
done500039980

prune823.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize135.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
6.7b
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
7.2b
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
7.2b
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cube-cbrt
9×add-cbrt-cube add-exp-log
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 sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 74
Calls
4 calls:
45.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
266.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
360.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
334.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify2.7s

Counts
86 → 86
Iterations

Useful iterations: done (2.7s)

IterNodesCost
018249417
146746212
2237445450
done500144740

prune1.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

localize116.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
6.7b
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
6.7b
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
7.2b
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Counts
4 → 58
Calls
4 calls:
1.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
326.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
294.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
270.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
318.0ms
(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify2.6s

Counts
70 → 70
Iterations

Useful iterations: done (2.6s)

IterNodesCost
011748751
125546337
272646016
3300345415
done500045001

prune678.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.1b

regimes608.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
017661
120661
done20661

end0.0ms

sample4.1s

Algorithm
intervals
Results
3.6s20748×body80valid