Details

sample221.0ms

Algorithm

intervals

Results

55.0ms	31×	body	2560	valid
22.0ms	35×	body	1280	valid
22.0ms	174×	body	80	valid
14.0ms	20×	body	640	valid
11.0ms	82×	body	80	nan
5.0ms	5×	body	5120	valid
3.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	29
5	29
4	27
3	25
2	22
1	14
0	10

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite294.0ms

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×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

198.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
39.0ms	(- (* b_2 b_2) (* a c))
31.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
39.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify938.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1461
1	387
0	158

prune475.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.4b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

164.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
15.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
65.0ms	(- (* b_2 b_2) (* a c))
128.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.0s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	2850
1	458
0	178

prune433.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b	(sqrt (- (* b_2 b_2) (* a c)))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

44.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
43.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
106.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
114.0ms	(sqrt (- (* b_2 b_2) (* a c)))
109.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
3	3694
2	718
1	193
0	80

prune550.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.9b

localize70.0ms

Local error

Found 4 expressions with local error:

15.8b	(- (* (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt (sqrt (- (* b_2 b_2) (* a c))))) (cbrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
22.0b	(sqrt (- (* b_2 b_2) (* a c)))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite235.0ms

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:

190.0ms	(- (* (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt (sqrt (- (* b_2 b_2) (* a c))))) (cbrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (* (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt (sqrt (- (* b_2 b_2) (* a c))))) (cbrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
3	4179
2	769
1	206
0	80

prune498.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.9b

regimes281.0ms

Accuracy

85.6% (4.1b remaining)

Error of 9.5b against oracle of 5.4b and baseline of 33.9b

bsearch107.0ms

Steps

Iters	Range		Point
6	1.6664801848567985e-94	1.3864776888564433e-93	1.1804820682342164e-93
7	-8.18523145413159e+143	-2.8208844788355687e+142	-3.7064129236785206e+142

simplify5.0ms

Iterations

Iter	Nodes
done	33
1	33
0	26

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.6s	1057×	body	2560	valid
835.0ms	5746×	body	80	valid
738.0ms	976×	body	1280	valid
330.0ms	2911×	body	80	nan
217.0ms	459×	body	640	valid
141.0ms	139×	body	5120	valid
82.0ms	257×	body	320	valid
23.0ms	116×	body	160	valid