Details

Time bar (total: 19.7s)

sample652.0ms

Algorithm
halfpoints
Results

simplify724.0ms

Calls
1 calls:
Slowest
723.0ms
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))

prune103.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.5b

localize543.0ms

Local error

Found 4 expressions with local error:

1.6b
(-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
0.5b
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))
0.4b
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))
0.3b
(*.p16 (real->posit16 4) (*.p16 a c))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip--
1×associate-/r* sub-neg associate-*r* *-commutative associate-/l/
Calls
4 calls:
Slowest
23.0ms
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))
6.0ms
(-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
3.0ms
(*.p16 (real->posit16 4) (*.p16 a c))
0.0ms
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))

series1.0ms

Calls
4 calls:
Slowest
0.0ms
(-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
0.0ms
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))
0.0ms
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))
0.0ms
(*.p16 (real->posit16 4) (*.p16 a c))

simplify2.2s

Calls
5 calls:
Slowest
668.0ms
(-.p16 (*.p16 (neg.p16 b) (neg.p16 b)) (*.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))))
404.0ms
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))
401.0ms
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))
383.0ms
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))
317.0ms
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))

prune969.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize369.0ms

Local error

Found 4 expressions with local error:

1.2b
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
1.0b
(/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (*.p16 (real->posit16 2) a) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))))
0.5b
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))
0.3b
(*.p16 (real->posit16 4) (*.p16 a c))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative associate-/r* associate-*r* *-commutative
Calls
4 calls:
Slowest
6.0ms
(/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (*.p16 (real->posit16 2) a) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))))
5.0ms
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
3.0ms
(*.p16 (real->posit16 4) (*.p16 a c))
0.0ms
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))

series0.0ms

Calls
4 calls:
Slowest
0.0ms
(/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (*.p16 (real->posit16 2) a) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))))
0.0ms
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
0.0ms
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))
0.0ms
(*.p16 (real->posit16 4) (*.p16 a c))

simplify1.6s

Calls
5 calls:
Slowest
425.0ms
(/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (*.p16 (real->posit16 2) a) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))))
410.0ms
(/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (*.p16 (real->posit16 2) a) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))))
338.0ms
(/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (*.p16 (real->posit16 2) a) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))))
269.0ms
(/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (*.p16 (real->posit16 2) a) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))))
179.0ms
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))

prune801.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize65.0ms

Local error

Found 4 expressions with local error:

1.2b
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
0.7b
(/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (real->posit16 2) a))
0.5b
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))
0.5b
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (real->posit16 2) a)) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative associate-/r* associate-/l/
Calls
4 calls:
Slowest
3.0ms
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (real->posit16 2) a)) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))))
3.0ms
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
2.0ms
(/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (real->posit16 2) a))
0.0ms
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))

series0.0ms

Calls
4 calls:
Slowest
0.0ms
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
0.0ms
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (real->posit16 2) a)) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))))
0.0ms
(/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (*.p16 (real->posit16 2) a))
0.0ms
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))

simplify709.0ms

Calls
5 calls:
Slowest
187.0ms
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
159.0ms
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
136.0ms
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
126.0ms
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
100.0ms
(+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c)))

prune648.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

localize96.0ms

Local error

Found 4 expressions with local error:

1.2b
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
0.6b
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (real->posit16 2)) a)
0.5b
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))
0.5b
(/.p16 (/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (real->posit16 2)) a) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
2×associate-/l/
1×+-commutative
Calls
4 calls:
Slowest
4.0ms
(/.p16 (/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (real->posit16 2)) a) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))))
3.0ms
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
2.0ms
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (real->posit16 2)) a)
0.0ms
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))

series0.0ms

Calls
4 calls:
Slowest
0.0ms
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
0.0ms
(/.p16 (/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (real->posit16 2)) a) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))))
0.0ms
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (real->posit16 2)) a)
0.0ms
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))

simplify1.2s

Calls
2 calls:
Slowest
1.1s
(/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (real->posit16 2))
105.0ms
(+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c)))

prune528.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.5b

regimes2.0s

Accuracy

-∞% (-63.2b remaining)

Error of 0.8b against oracle of 64.0b and baseline of 64.0b

bsearch8.0ms

end0.0ms

sample6.4s

Algorithm
halfpoints
Results