Details

Time bar (total: 11.7s)

sample155.0ms

Algorithm
halfpoints
Results

simplify562.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
561.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize137.0ms

Local error

Found 4 expressions with local error:

1.0b
(-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
0.4b
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))
0.3b
(-.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)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
3×p16-flip--
2×sub-neg
1×associate-/l/
Counts
4 → 5
Calls
4 calls:
Slowest
5.0ms
(-.p16 (*.p16 b_2 b_2) (*.p16 a c))
5.0ms
(-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
5.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
0.0ms
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))

series1.0ms

Counts
4 → 4
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))

simplify1.5s

Counts
5 → 9
Calls
5 calls:
Slowest
591.0ms
(-.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)))))
242.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
233.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
205.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
190.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)

prune199.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize331.0ms

Local error

Found 4 expressions with local error:

1.1b
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
0.8b
(/.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))))))
0.4b
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))
0.3b
(-.p16 (*.p16 b_2 b_2) (*.p16 a c))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative associate-/r* sub-neg p16-flip--
Counts
4 → 4
Calls
4 calls:
Slowest
6.0ms
(-.p16 (*.p16 b_2 b_2) (*.p16 a c))
5.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
5.0ms
(/.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)))

series0.0ms

Counts
4 → 4
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 b_2 b_2) (*.p16 a c))))))
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 b_2 b_2) (*.p16 a c))

simplify1.1s

Counts
5 → 8
Calls
5 calls:
Slowest
284.0ms
(/.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))))))
278.0ms
(/.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))))))
251.0ms
(/.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))))))
232.0ms
(/.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))))))
101.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))

prune368.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize301.0ms

Local error

Found 4 expressions with local error:

1.1b
(+.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)
0.4b
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))
0.3b
(/.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)))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative associate-/l/
Counts
4 → 2
Calls
4 calls:
Slowest
19.0ms
(/.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)))))
5.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
3.0ms
(/.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

Counts
4 → 4
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)))

simplify580.0ms

Counts
5 → 6
Calls
5 calls:
Slowest
137.0ms
(+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2))))
124.0ms
(+.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))))
120.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
77.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))

prune126.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.3b

localize211.0ms

Local error

Found 4 expressions with local error:

1.9b
(/.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)))
1.0b
(-.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)))))
0.4b
(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))))
0.3b
(/.p16 (-.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))))) a)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
3×p16-flip--
2×associate-/l/
1×sub-neg associate-/l* difference-of-squares
Counts
4 → 5
Calls
4 calls:
Slowest
11.0ms
(/.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)))
5.0ms
(/.p16 (-.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))))) a)
3.0ms
(-.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))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
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
(/.p16 (-.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))))) a)
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))))

simplify1.6s

Counts
3 → 9
Calls
3 calls:
Slowest
911.0ms
(-.p16 (*.p16 (neg.p16 b_2) (neg.p16 b_2)) (*.p16 (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)))) (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))))))
715.0ms
(-.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))))
7.0ms
(+.p16 (*.p16 b_2 b_2) (*.p16 a c))

prune189.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.3b

regimes630.0ms

Accuracy

-∞% (-63.6b remaining)

Error of 0.4b against oracle of 64.0b and baseline of 64.0b

bsearch10.0ms

end0.0ms

sample3.5s

Algorithm
halfpoints
Results