Details

Time bar (total: 15.3s)

sample218.0ms

Algorithm
halfpoints
Results

simplify488.0ms

Calls
1 calls:
Slowest
488.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)

prune70.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.5b

localize344.0ms

Local error

Found 4 expressions with local error:

1.8b
(-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
0.5b
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))
0.3b
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
0.2b
(-.p16 (*.p16 b_2 b_2) (*.p16 a c))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
3×p16-flip--
2×sub-neg
1×associate-/l/
Calls
4 calls:
Slowest
8.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
6.0ms
(-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
2.0ms
(-.p16 (*.p16 b_2 b_2) (*.p16 a c))
0.0ms
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))

series1.0ms

Calls
4 calls:
Slowest
0.0ms
(-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
0.0ms
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))
0.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
0.0ms
(-.p16 (*.p16 b_2 b_2) (*.p16 a c))

simplify1.7s

Calls
5 calls:
Slowest
719.0ms
(-.p16 (*.p16 (neg.p16 b_2) (neg.p16 b_2)) (*.p16 (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))))
270.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
268.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
259.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
226.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)

prune413.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize312.0ms

Local error

Found 4 expressions with local error:

1.4b
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
0.7b
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) (*.p16 a (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))))
0.5b
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))
0.2b
(-.p16 (*.p16 b_2 b_2) (*.p16 a c))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative associate-/r* sub-neg p16-flip--
Calls
4 calls:
Slowest
3.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
2.0ms
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) (*.p16 a (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))))
2.0ms
(-.p16 (*.p16 b_2 b_2) (*.p16 a c))
0.0ms
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))

series0.0ms

Calls
4 calls:
Slowest
0.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
0.0ms
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) (*.p16 a (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))))
0.0ms
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))
0.0ms
(-.p16 (*.p16 b_2 b_2) (*.p16 a c))

simplify1.3s

Calls
5 calls:
Slowest
319.0ms
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) (*.p16 a (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))))
314.0ms
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) (*.p16 a (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))))
296.0ms
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) (*.p16 a (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))))
267.0ms
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) (*.p16 a (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))))
78.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))

prune455.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize75.0ms

Local error

Found 4 expressions with local error:

1.4b
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
0.5b
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) a)
0.5b
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))
0.4b
(/.p16 (/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) a) (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative associate-/l/
Calls
4 calls:
Slowest
3.0ms
(/.p16 (/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) a) (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))))
3.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
1.0ms
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) a)
0.0ms
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))

series0.0ms

Calls
4 calls:
Slowest
0.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
0.0ms
(/.p16 (/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) a) (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))))
0.0ms
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) a)
0.0ms
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))

simplify576.0ms

Calls
5 calls:
Slowest
127.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
125.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
121.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
118.0ms
(+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2))))
84.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))

prune401.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.3b

localize380.0ms

Local error

Found 4 expressions with local error:

1.7b
(/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c)))
1.4b
(+.p16 (neg.p16 b_2) (sqrt.p16 (/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c)))))
0.7b
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) (*.p16 a (+.p16 (neg.p16 b_2) (sqrt.p16 (/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c)))))))
0.5b
(sqrt.p16 (/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative associate-/r* p16-flip-- associate-/l* difference-of-squares associate-/l/
Calls
4 calls:
Slowest
7.0ms
(/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c)))
6.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c)))))
4.0ms
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) (*.p16 a (+.p16 (neg.p16 b_2) (sqrt.p16 (/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c)))))))
0.0ms
(sqrt.p16 (/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c))))

series0.0ms

Calls
4 calls:
Slowest
0.0ms
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) (*.p16 a (+.p16 (neg.p16 b_2) (sqrt.p16 (/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c)))))))
0.0ms
(/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c)))
0.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c)))))
0.0ms
(sqrt.p16 (/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c))))

simplify1.1s

Calls
3 calls:
Slowest
682.0ms
(-.p16 (*.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2))) (*.p16 (*.p16 (*.p16 a c) (*.p16 a c)) (*.p16 (*.p16 a c) (*.p16 a c))))
449.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (/.p16 (-.p16 (*.p16 (*.p16 b_2 b_2) (*.p16 b_2 b_2)) (*.p16 (*.p16 a c) (*.p16 a c))) (+.p16 (*.p16 b_2 b_2) (*.p16 a c)))))
7.0ms
(+.p16 (*.p16 b_2 b_2) (*.p16 a c))

prune479.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.3b

regimes1.4s

Accuracy

-∞% (-63.4b remaining)

Error of 0.6b against oracle of 64.0b and baseline of 64.0b

bsearch8.0ms

end0.0ms

sample5.4s

Algorithm
halfpoints
Results