Details

sample171.0ms

Algorithm

intervals

Results

45.0ms	43×	body	2560	valid
32.0ms	13×	body	640	valid
32.0ms	190×	body	80	valid
20.0ms	25×	body	1280	valid
13.0ms	85×	body	80	nan
5.0ms	11×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	2×	body	160	valid

simplify97.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	95
7	95
6	94
5	92
4	84
3	67
2	43
1	24
0	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a) 2)
0.5b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
1.0b	(- (* b b) (* (* 4 a) c))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-/r*` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 153

Calls

4 calls:

63.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a) 2)
54.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms	(- (* b b) (* (* 4 a) c))
12.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a) 2)
140.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
77.0ms	(- (* b b) (* (* 4 a) c))
103.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify976.0ms

Counts

165 → 165

Iterations

Iter	Nodes
done	2000
2	2000
1	670
0	278

prune889.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* 4 (* a c)))) b) (/ (/ 1 a) 2))
0.5b	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
1.0b	(- (* b b) (* 4 (* a c)))
24.5b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
43×	`associate-r`
41×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`div-exp` `associate-l`
5×	`flip3--` `prod-exp` `sqrt-prod` `flip--`
4×	`insert-posit16` `div-inv` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `cbrt-unprod`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `associate-*l/` `distribute-lft-out--`
1×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 121

Calls

4 calls:

185.0ms	(* (- (sqrt (- (* b b) (* 4 (* a c)))) b) (/ (/ 1 a) 2))
43.0ms	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
8.0ms	(- (* b b) (* 4 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (- (sqrt (- (* b b) (* 4 (* a c)))) b) (/ (/ 1 a) 2))
140.0ms	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
73.0ms	(- (* b b) (* 4 (* a c)))
100.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.3s

Counts

133 → 133

Iterations

Iter	Nodes
done	2000
2	2000
1	724
0	263

prune674.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize38.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4 (* a c)))
1.0b	(- (* b b) (* 4 (* a c)))
24.5b	(sqrt (- (* b b) (* 4 (* a c))))
24.5b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

18.0ms	(- (* b b) (* 4 (* a c)))
8.0ms	(- (* b b) (* 4 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series364.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* b b) (* 4 (* a c)))
69.0ms	(- (* b b) (* 4 (* a c)))
126.0ms	(sqrt (- (* b b) (* 4 (* a c))))
102.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	2005
4	2005
3	1783
2	454
1	156
0	61

prune493.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize49.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4 (* a c)))
24.5b	(sqrt (- (* b b) (* 4 (* a c))))
24.5b	(sqrt (- (* b b) (* 4 (* a c))))
24.5b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 61

Calls

4 calls:

8.0ms	(- (* b b) (* 4 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))
10.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b b) (* 4 (* a c)))
121.0ms	(sqrt (- (* b b) (* 4 (* a c))))
108.0ms	(sqrt (- (* b b) (* 4 (* a c))))
95.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	2005
4	2005
3	1783
2	454
1	156
0	61

prune530.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.5b

regimes381.0ms

Accuracy

82.4% (4.9b remaining)

Error of 10.3b against oracle of 5.4b and baseline of 33.3b

bsearch206.0ms

Steps

Iters	Range		Point
10	1.3859530517218358e-142	9.527435083115218e-125	9.354082991670835e-125
8	-4.336983712965787e+155	-6.488343844980391e+152	-9.088000531423294e+152

simplify9.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.3s	1069×	body	2560	valid
1.0s	5926×	body	80	valid
779.0ms	874×	body	1280	valid
462.0ms	3004×	body	80	nan
271.0ms	467×	body	640	valid
106.0ms	108×	body	5120	valid
87.0ms	218×	body	320	valid
28.0ms	112×	body	160	valid