Details

Time bar (total: 25.5s)

sample24.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01435
13335
211931
358631
4438731
done500031

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize12.0ms

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))
3.1b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite124.0ms

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:
5.0ms
(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
26.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
47.0ms
(/ (/ (/ (+ 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))
17.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series421.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (fma 1.0 2.0 (+ alpha beta)) 1.0)
145.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
165.0ms
(/ (/ (/ (+ 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))
90.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.4s

Counts
434 → 434
Iterations

Useful iterations: done (1.4s)

IterNodesCost
051620618
1117520002
2327719166
done500018557

prune905.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
1.7b
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
2.1b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))

rewrite805.0ms

Algorithm
rewrite-expression-head
Rules
11464×times-frac
7044×*-un-lft-identity
4536×add-sqr-sqrt add-cube-cbrt
3150×sqrt-prod
1254×distribute-lft-out
724×associate-/l*
149×div-inv
34×add-exp-log add-cbrt-cube
20×cbrt-undiv div-exp
19×associate-/r*
5×associate-/l/
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×flip3-+ associate-/r/ flip-+
Counts
4 → 3606
Calls
4 calls:
78.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
205.0ms
(/ (/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
34.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
20.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))

series524.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
172.0ms
(/ (/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))
88.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
106.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))

simplify1.5s

Counts
3618 → 3618
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02558255791
done5000240757

prune7.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (/ 1 (sqrt 1)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
0.6b
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
1.8b
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
2.1b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))

rewrite404.0ms

Algorithm
rewrite-expression-head
Rules
4940×times-frac
2940×*-un-lft-identity
2215×sqrt-prod
2138×add-sqr-sqrt add-cube-cbrt
401×distribute-lft-out
256×associate-/l*
96×div-inv
35×add-exp-log
29×add-cbrt-cube
23×associate-/r*
21×div-exp
16×cbrt-undiv
5×associate-/l/
4×pow1 expm1-log1p-u frac-2neg sqrt-div clear-num associate-/r/ log1p-expm1-u add-log-exp
3×flip3-+ flip-+
1×rec-exp 1-exp
Counts
4 → 2032
Calls
4 calls:
72.0ms
(/ (/ (/ 1 (sqrt 1)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
66.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
28.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
24.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))

series747.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(/ (/ (/ 1 (sqrt 1)) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
309.0ms
(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
211.0ms
(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
106.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))

simplify2.1s

Counts
2044 → 2044
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01807107617
1392988691
done500087036

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.6b

localize27.0ms

Local error

Found 4 expressions with local error:

2.1b
(/ (* (cbrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))) (* (cbrt (sqrt (fma 1.0 2.0 (+ alpha beta)))) (cbrt (sqrt (fma 1.0 2.0 (+ alpha beta))))))
3.4b
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
3.4b
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
3.4b
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
16×add-exp-log
13×*-un-lft-identity
12×cbrt-prod
9×flip3-+ flip-+
8×add-cbrt-cube associate-/l/
7×add-sqr-sqrt add-cube-cbrt
4×pow1 cbrt-undiv expm1-log1p-u frac-times div-exp prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow1/3 distribute-lft-out
2×associate-*r/ associate-*l/
1×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 79
Calls
4 calls:
29.0ms
(/ (* (cbrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))) (* (cbrt (sqrt (fma 1.0 2.0 (+ alpha beta)))) (cbrt (sqrt (fma 1.0 2.0 (+ alpha beta))))))
4.0ms
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
4.0ms
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
4.0ms
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series366.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(/ (* (cbrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))) (* (cbrt (sqrt (fma 1.0 2.0 (+ alpha beta)))) (cbrt (sqrt (fma 1.0 2.0 (+ alpha beta))))))
70.0ms
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
63.0ms
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))
70.0ms
(cbrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify1.8s

Counts
91 → 91
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01572699
14232464
211802126
338332003
done50001945

prune447.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

regimes82.0ms

Accuracy

49.7% (1.3b remaining)

Error of 2.5b against oracle of 1.2b and baseline of 3.8b

bsearch72.0ms

Steps
ItersRangePoint
9
3.1387747080438726e+212
4.106804305971336e+220
1.8384367044071604e+213

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
037105
146105
done46105

end0.0ms

sample573.0ms

Algorithm
intervals
Results
281.0ms8000×body80valid
91.0ms8000×pre80true