Details

Time bar (total: 24.8s)

sample54.0ms

Algorithm
intervals
Results
28.0ms256×body80valid
6.0ms256×pre80true

simplify3.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01435
13335
211931
358631
4438731
done500031

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
0.0b
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
3.4b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
736×times-frac
551×*-un-lft-identity
321×add-sqr-sqrt add-cube-cbrt
115×distribute-lft-out
72×associate-/l*
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
6×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×fma-def frac-2neg flip3-+ clear-num flip-+
2×associate-/r/
1×+-commutative associate-+l+ sum-log fma-udef
Counts
4 → 422
Calls
4 calls:
6.0ms
(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
28.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
49.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
42.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series563.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
207.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
211.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
125.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify2.3s

Counts
434 → 434
Iterations

Useful iterations: done (2.3s)

IterNodesCost
051620618
1117520002
2327719166
done500018557

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ alpha (+ beta 3.0)))
3.4b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
872×times-frac
765×*-un-lft-identity
360×add-sqr-sqrt add-cube-cbrt
229×distribute-lft-out
72×associate-/l*
31×div-inv
19×add-exp-log add-cbrt-cube
11×associate-/r*
10×cbrt-undiv div-exp
4×associate-/l/
3×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×flip3-+ associate-/r/ flip-+
Counts
3 → 457
Calls
3 calls:
51.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
117.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ alpha (+ beta 3.0)))
38.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series562.0ms

Counts
3 → 9
Calls
3 calls:
216.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
245.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ alpha (+ beta 3.0)))
102.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify2.3s

Counts
466 → 466
Iterations

Useful iterations: done (2.3s)

IterNodesCost
050421948
1115821258
2329920333
done500019605

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ alpha (+ beta 3.0))))
0.1b
(/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ alpha (+ beta 3.0)))
3.4b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
3.4b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite722.0ms

Algorithm
rewrite-expression-head
Rules
1625×times-frac
1425×*-un-lft-identity
721×add-sqr-sqrt
651×sqrt-prod
638×add-cube-cbrt
449×distribute-lft-out
281×associate-*r*
63×associate-/l*
55×associate-*l*
52×div-inv
20×unswap-sqr
15×add-exp-log add-cbrt-cube
11×associate-/r*
6×pow1
5×associate-/l/
4×cbrt-undiv expm1-log1p-u flip3-+ div-exp associate-/r/ flip-+ log1p-expm1-u add-log-exp
3×frac-2neg sqrt-div clear-num
2×prod-exp cbrt-unprod
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 796
Calls
4 calls:
519.0ms
(* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ alpha (+ beta 3.0))))
77.0ms
(/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ alpha (+ beta 3.0)))
19.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
19.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series682.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ alpha (+ beta 3.0))))
196.0ms
(/ (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (+ alpha (+ beta 3.0)))
128.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
136.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify2.5s

Counts
808 → 808
Iterations

Useful iterations: done (2.5s)

IterNodesCost
078542812
1151740452
2421338080
done500036696

prune3.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.3b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (fma 1.0 2.0 (+ alpha beta)) (+ 3.0 (+ alpha beta)))
1.8b
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (* (fma 1.0 2.0 (+ alpha beta)) (+ 3.0 (+ alpha beta))))
3.4b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
52×times-frac
32×add-sqr-sqrt
30×add-cube-cbrt
20×associate-/l*
19×add-exp-log add-cbrt-cube
13×distribute-lft-out
7×cbrt-undiv div-exp
5×pow1 associate-*r*
4×associate-*r/ associate-/r* div-inv
3×expm1-log1p-u flip3-+ associate-*l* prod-exp cbrt-unprod flip-+ log1p-expm1-u associate-/l/ add-log-exp
2×frac-2neg clear-num associate-/r/
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
3 → 117
Calls
3 calls:
111.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ 3.0 (+ alpha beta)))
72.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (* (fma 1.0 2.0 (+ alpha beta)) (+ 3.0 (+ alpha beta))))
34.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series399.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (+ 3.0 (+ alpha beta)))
235.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (* (fma 1.0 2.0 (+ alpha beta)) (+ 3.0 (+ alpha beta))))
113.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.9s

Counts
126 → 126
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01963501
15013451
220613049
done50023042

prune483.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.3b

regimes131.0ms

Accuracy

59.1% (1.0b remaining)

Error of 2.3b against oracle of 1.3b and baseline of 3.8b

bsearch103.0ms

Steps
ItersRangePoint
8
1.7519304510016456e+160
7.027642810475786e+162
6.375269332570683e+160

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02452
13052
done3052

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.2s8000×body80valid
187.0ms8000×pre80true