Details

Time bar (total: 21.0s)

sample323.0ms

Algorithm
halfpoints
Results

simplify579.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
578.0ms
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize215.0ms

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)))))
0.4b
(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))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip--
1×associate-/r* sub-neg associate-*r* *-commutative associate-/l/
Counts
4 → 6
Calls
4 calls:
Slowest
4.0ms
(*.p16 (real->posit16 4) (*.p16 a c))
3.0ms
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))
3.0ms
(-.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))))

series0.0ms

Counts
4 → 4
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))

simplify3.8s

Counts
10 → 10
Calls
10 calls:
Slowest
834.0ms
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (real->posit16 2))
791.0ms
(-.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))))))
433.0ms
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))
415.0ms
(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))
333.0ms
(*.p16 (*.p16 (real->posit16 2) a) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))))

prune463.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize443.0ms

Local error

Found 4 expressions with local error:

0.9b
(+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))
0.5b
(/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))))
0.4b
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))
0.4b
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))) (*.p16 (real->posit16 2) a))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
1×+-commutative associate-/r* associate-/l/
Counts
4 → 3
Calls
4 calls:
Slowest
6.0ms
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))) (*.p16 (real->posit16 2) a))
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 (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)))))
0.0ms
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))

series0.0ms

Counts
4 → 4
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 (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 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))) (*.p16 (real->posit16 2) a))
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))))

simplify2.1s

Counts
6 → 7
Calls
6 calls:
Slowest
413.0ms
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))) (*.p16 (real->posit16 2) a))
410.0ms
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))) (*.p16 (real->posit16 2) a))
367.0ms
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))) (*.p16 (real->posit16 2) a))
348.0ms
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))) (real->posit16 2))
335.0ms
(/.p16 (/.p16 (+.p16 (*.p16 (+.p16 (neg.p16 b) b) (+.p16 (neg.p16 b) (neg.p16 b))) (*.p16 (real->posit16 4) (*.p16 a c))) (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c)))))) (*.p16 (real->posit16 2) a))

prune433.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize234.0ms

Local error

Found 4 expressions with local error:

0.9b
(-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 c a)))) b)
0.6b
(/.p16 (+.p16 (real->posit16 0.0) (*.p16 (real->posit16 4) (*.p16 c a))) (*.p16 (real->posit16 2) (-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 c a)))) b)))
0.4b
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 c a))))
0.3b
(*.p16 (real->posit16 4) (*.p16 c a))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip--
1×associate-/r* sub-neg associate-*r* associate-*r/ associate-/r/ *-commutative
Counts
4 → 6
Calls
4 calls:
Slowest
5.0ms
(/.p16 (+.p16 (real->posit16 0.0) (*.p16 (real->posit16 4) (*.p16 c a))) (*.p16 (real->posit16 2) (-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 c a)))) b)))
4.0ms
(*.p16 (real->posit16 4) (*.p16 c a))
2.0ms
(-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 c a)))) b)
0.0ms
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 c a))))

series0.0ms

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

simplify2.1s

Counts
10 → 10
Calls
10 calls:
Slowest
659.0ms
(-.p16 (*.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 c a)))) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 c a))))) (*.p16 b b))
261.0ms
(/.p16 (/.p16 (+.p16 (real->posit16 0.0) (*.p16 (real->posit16 4) (*.p16 c a))) (*.p16 (real->posit16 2) (-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 c a)))) b))) a)
247.0ms
(/.p16 (/.p16 (+.p16 (real->posit16 0.0) (*.p16 (real->posit16 4) (*.p16 c a))) (*.p16 (real->posit16 2) (-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 c a)))) b))) a)
243.0ms
(/.p16 (/.p16 (+.p16 (real->posit16 0.0) (*.p16 (real->posit16 4) (*.p16 c a))) (*.p16 (real->posit16 2) (-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 c a)))) b))) a)
238.0ms
(/.p16 (/.p16 (+.p16 (real->posit16 0.0) (*.p16 (real->posit16 4) (*.p16 c a))) (*.p16 (real->posit16 2) (-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 c a)))) b))) a)

prune592.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.4b

localize305.0ms

Local error

Found 4 expressions with local error:

0.9b
(-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4))))) b)
0.8b
(/.p16 (*.p16 c (*.p16 a (real->posit16 4))) (*.p16 (*.p16 (real->posit16 2) a) (-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4))))) b)))
0.4b
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4)))))
0.2b
(-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
3×p16-flip--
2×sub-neg
1×associate-/r* p16-times-frac associate-*r/ associate-/r/ associate-/l*
Counts
4 → 8
Calls
4 calls:
Slowest
11.0ms
(/.p16 (*.p16 c (*.p16 a (real->posit16 4))) (*.p16 (*.p16 (real->posit16 2) a) (-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4))))) b)))
8.0ms
(-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4))))
4.0ms
(-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4))))) b)
0.0ms
(sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4)))))

series0.0ms

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

simplify4.3s

Counts
15 → 12
Calls
15 calls:
Slowest
855.0ms
(-.p16 (*.p16 (*.p16 b b) (*.p16 b b)) (*.p16 (*.p16 c (*.p16 a (real->posit16 4))) (*.p16 c (*.p16 a (real->posit16 4)))))
832.0ms
(-.p16 (*.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4))))) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4)))))) (*.p16 b b))
472.0ms
(/.p16 (*.p16 a (real->posit16 4)) (-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4))))) b))
367.0ms
(/.p16 (*.p16 c (*.p16 a (real->posit16 4))) (*.p16 (*.p16 (real->posit16 2) a) (-.p16 (*.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4))))) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4)))))) (*.p16 b b))))
298.0ms
(/.p16 (*.p16 c (*.p16 a (real->posit16 4))) (*.p16 (*.p16 (real->posit16 2) a) (-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4))))) b)))

prune611.0ms

Pruning

13 alts after pruning (9 fresh and 4 done)

Merged error: 0.3b

regimes986.0ms

Accuracy

-∞% (-63.5b remaining)

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

bsearch10.0ms

end0.0ms

sample3.4s

Algorithm
halfpoints
Results