Details

sample158.0ms

Algorithm

intervals

Results

52.0ms	185×	body	80	valid
30.0ms	33×	body	2560	valid
23.0ms	32×	body	1280	valid
14.0ms	97×	body	80	nan
8.0ms	12×	body	640	valid
6.0ms	5×	body	5120	valid
4.0ms	8×	body	320	valid
1.0ms	3×	body	160	valid

simplify86.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4 a) c)
0.6b	(- (* b b) (* (* 4 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
22.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

13.0ms	(* (* 4 a) c)
9.0ms	(- (* b b) (* (* 4 a) c))
44.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* 4 a) c)
47.0ms	(- (* b b) (* (* 4 a) c))
97.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
117.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify876.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2004
3	2004
2	927
1	300
0	123

prune361.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (+ (* b b) (* -4 (* a c)))) b) a)
0.6b	(+ (* b b) (* -4 (* a c)))
1.1b	(- (sqrt (+ (* b b) (* -4 (* a c)))) b)
22.2b	(sqrt (+ (* b b) (* -4 (* a c))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`insert-posit16`
3×	`associate-/r*`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

107.0ms	(/ (- (sqrt (+ (* b b) (* -4 (* a c)))) b) a)
8.0ms	(+ (* b b) (* -4 (* a c)))
47.0ms	(- (sqrt (+ (* b b) (* -4 (* a c)))) b)
12.0ms	(sqrt (+ (* b b) (* -4 (* a c))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (- (sqrt (+ (* b b) (* -4 (* a c)))) b) a)
54.0ms	(+ (* b b) (* -4 (* a c)))
125.0ms	(- (sqrt (+ (* b b) (* -4 (* a c)))) b)
105.0ms	(sqrt (+ (* b b) (* -4 (* a c))))

simplify1.0s

Counts

99 → 99

Iterations

Iter	Nodes
done	2003
3	2003
2	1163
1	410
0	160

prune513.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (+ (* b b) (* (* a c) -4))) b) a)
0.6b	(+ (* b b) (* (* a c) -4))
1.1b	(- (sqrt (+ (* b b) (* (* a c) -4))) b)
22.2b	(sqrt (+ (* b b) (* (* a c) -4)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`insert-posit16`
3×	`associate-/r*`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

80.0ms	(/ (- (sqrt (+ (* b b) (* (* a c) -4))) b) a)
7.0ms	(+ (* b b) (* (* a c) -4))
49.0ms	(- (sqrt (+ (* b b) (* (* a c) -4))) b)
10.0ms	(sqrt (+ (* b b) (* (* a c) -4)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (- (sqrt (+ (* b b) (* (* a c) -4))) b) a)
50.0ms	(+ (* b b) (* (* a c) -4))
96.0ms	(- (sqrt (+ (* b b) (* (* a c) -4))) b)
106.0ms	(sqrt (+ (* b b) (* (* a c) -4)))

simplify1.2s

Counts

99 → 99

Iterations

Iter	Nodes
done	2000
3	2000
2	1157
1	410
0	160

prune482.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (+ (* b b) (* (* a c) -4))) b)))
0.6b	(+ (* b b) (* (* a c) -4))
1.1b	(- (sqrt (+ (* b b) (* (* a c) -4))) b)
22.2b	(sqrt (+ (* b b) (* (* a c) -4)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`flip3--` `div-inv` `flip--`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `flip3-+` `sqrt-div` `1-exp` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 165

Calls

4 calls:

71.0ms	(/ 1 (/ a (- (sqrt (+ (* b b) (* (* a c) -4))) b)))
14.0ms	(+ (* b b) (* (* a c) -4))
58.0ms	(- (sqrt (+ (* b b) (* (* a c) -4))) b)
13.0ms	(sqrt (+ (* b b) (* (* a c) -4)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ 1 (/ a (- (sqrt (+ (* b b) (* (* a c) -4))) b)))
75.0ms	(+ (* b b) (* (* a c) -4))
113.0ms	(- (sqrt (+ (* b b) (* (* a c) -4))) b)
116.0ms	(sqrt (+ (* b b) (* (* a c) -4)))

simplify1.4s

Counts

177 → 177

Iterations

Iter	Nodes
done	2010
3	2010
2	1775
1	659
0	264

prune710.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.9b

regimes457.0ms

Accuracy

83.9% (4.4b remaining)

Error of 10.1b against oracle of 5.8b and baseline of 32.9b

bsearch205.0ms

Steps

Iters	Range		Point
9	2.0671083276743448e-101	1.4914771383599542e-96	1.489031291672483e-98
5	-3.3440263710910746e+131	-9.921521910190385e+130	-1.7512236628315378e+131

simplify11.0ms

Iterations

Iter	Nodes
done	35
1	35
0	29

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.4s	842×	body	1280	valid
1.1s	1106×	body	2560	valid
983.0ms	5933×	body	80	valid
346.0ms	2940×	body	80	nan
316.0ms	437×	body	640	valid
139.0ms	120×	body	5120	valid
109.0ms	210×	body	320	valid
27.0ms	113×	body	160	valid