Details

Time bar (total: 11.4s)

sample389.0ms

Algorithm
halfpoints
Results

simplify449.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
448.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize175.0ms

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))))
0.3b
(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)
0.3b
(-.p16 (*.p16 b_2 b_2) (*.p16 a c))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
3×p16-flip--
2×sub-neg
1×associate-/l/
Counts
4 → 5
Calls
4 calls:
Slowest
6.0ms
(-.p16 (*.p16 b_2 b_2) (*.p16 a c))
6.0ms
(/.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))))
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))

simplify1.7s

Counts
5 → 9
Calls
5 calls:
Slowest
697.0ms
(-.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)))))
246.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
244.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
244.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)
239.0ms
(/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a)

prune268.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize291.0ms

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))))
0.7b
(/.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))))))
0.3b
(sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))
0.3b
(-.p16 (*.p16 b_2 b_2) (*.p16 a c))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative associate-/r* sub-neg p16-flip--
Counts
4 → 4
Calls
4 calls:
Slowest
3.0ms
(/.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))))))
3.0ms
(-.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))))
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))

simplify1.0s

Counts
5 → 8
Calls
5 calls:
Slowest
255.0ms
(/.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))))))
247.0ms
(/.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))))))
235.0ms
(/.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))))))
170.0ms
(/.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))))))
93.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))

prune292.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize345.0ms

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))))
0.4b
(/.p16 (+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2)))) a)
0.3b
(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)))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative associate-/l/
Counts
4 → 2
Calls
4 calls:
Slowest
18.0ms
(/.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))))
2.0ms
(/.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)))

simplify490.0ms

Counts
5 → 6
Calls
5 calls:
Slowest
124.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
120.0ms
(+.p16 (*.p16 a c) (*.p16 (+.p16 (neg.p16 b_2) b_2) (+.p16 (neg.p16 b_2) (neg.p16 b_2))))
83.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
81.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))
81.0ms
(+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c))))

prune155.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.3b

localize267.0ms

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)))
1.1b
(-.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)))))
0.3b
(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)

rewrite13.0ms

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
8.0ms
(/.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)))
3.0ms
(/.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)
2.0ms
(-.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 (-.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
(-.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))))

simplify1.4s

Counts
3 → 9
Calls
3 calls:
Slowest
927.0ms
(-.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))))))
515.0ms
(-.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))))
4.0ms
(+.p16 (*.p16 b_2 b_2) (*.p16 a c))

prune236.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.3b

regimes588.0ms

Accuracy

-∞% (-63.5b remaining)

Error of 0.5b against oracle of 64.0b and baseline of 64.0b

bsearch12.0ms

end0.0ms

sample3.2s

Algorithm
halfpoints
Results