Details

sample89.0ms

Algorithm

intervals

Results

16.0ms	191×	body	80	valid
13.0ms	28×	body	2560	valid
11.0ms	26×	body	1280	valid
6.0ms	82×	body	80	nan
5.0ms	19×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify549.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	139
7	139
6	137
5	132
4	127
3	106
2	61
1	28
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize139.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 81

Calls

4 calls:

176.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
39.0ms	(- (* b b) (* 4.0 (* a c)))
94.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series502.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
76.0ms	(- (* b b) (* 4.0 (* a c)))
147.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
129.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify7.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5029
3	4634
2	1246
1	406
0	159

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.8b

localize213.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite424.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

309.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
20.0ms	(- (* b b) (* 4.0 (* a c)))
47.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series633.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
105.0ms	(- (* b b) (* 4.0 (* a c)))
149.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
153.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	1653
1	476
0	185

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.8b

localize194.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.0b	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite451.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `times-frac` `associate-/l*`
11×	`add-cube-cbrt`
9×	`add-cbrt-cube` `add-exp-log`
8×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-log-exp`
5×	`pow1` `distribute-lft-out`
4×	`insert-posit16`
3×	`sqrt-prod`
2×	`cbrt-undiv` `neg-mul-1` `flip3-+` `flip3--` `sqrt-div` `div-exp` `flip-+` `flip--` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `distribute-frac-neg` `cbrt-unprod` `div-inv`

Counts

4 → 86

Calls

4 calls:

311.0ms	(/ (- (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
21.0ms	(- (* b b) (* 4.0 (* a c)))
68.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
40.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series584.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (- (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
86.0ms	(- (* b b) (* 4.0 (* a c)))
168.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
149.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1340
1	429
0	171

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.8b

localize160.0ms

Local error

Found 4 expressions with local error:

0.9b	(- b (sqrt (- (* b b) (* 4.0 (* a c)))))
2.8b	(/ (- (/ (+ 0 (* 4.0 (* a c))) (- b (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
10.0b	(/ (+ 0 (* 4.0 (* a c))) (- b (sqrt (- (* b b) (* 4.0 (* a c))))))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite585.0ms

Algorithm

rewrite-expression-head

Rules

142×	`times-frac`
127×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
58×	`add-cube-cbrt`
55×	`associate-/l*`
48×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
34×	`difference-of-squares`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
7×	`associate-/r*` `flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`insert-posit16`
3×	`cbrt-undiv` `div-exp` `associate-/l/`
2×	`clear-num` `neg-mul-1` `frac-2neg` `sqrt-div`
1×	`neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-sub` `prod-exp` `distribute-frac-neg` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

4 → 199

Calls

4 calls:

45.0ms	(- b (sqrt (- (* b b) (* 4.0 (* a c)))))
317.0ms	(/ (- (/ (+ 0 (* 4.0 (* a c))) (- b (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
142.0ms	(/ (+ 0 (* 4.0 (* a c))) (- b (sqrt (- (* b b) (* 4.0 (* a c))))))
44.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series1.1s

Counts

4 → 12

Calls

4 calls:

155.0ms	(- b (sqrt (- (* b b) (* 4.0 (* a c)))))
342.0ms	(/ (- (/ (+ 0 (* 4.0 (* a c))) (- b (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
468.0ms	(/ (+ 0 (* 4.0 (* a c))) (- b (sqrt (- (* b b) (* 4.0 (* a c))))))
176.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify5.6s

Counts

211 → 211

Iterations

Iter	Nodes
done	5002
2	2469
1	823
0	346

prune2.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.7b

regimes905.0ms

Accuracy

88.9% (3.1b remaining)

Error of 8.4b against oracle of 5.4b and baseline of 33.1b

bsearch428.0ms

Steps

Iters	Range	Point
10	1.0955696400612189e+91	1.0202913897586463e+104	2.026128983134594e+103
10	-3.7853197546515783e-110	-6.759455321393433e-120	-6.1927067580012775e-115
9	-2.0190258033009663e+27	-4.429449841721669e+19	-3.234164035284793e+22

Iters

Range

Point

1.0955696400612189e+91

1.0202913897586463e+104

2.026128983134594e+103

-3.7853197546515783e-110

-6.759455321393433e-120

-6.1927067580012775e-115

-2.0190258033009663e+27

-4.429449841721669e+19

-3.234164035284793e+22

simplify90.0ms

Iterations

Iter	Nodes
done	74
3	74
2	61
1	52
0	36

end0.0ms

sample3.8s

Algorithm

intervals

Results

807.0ms	5883×	body	80	valid
779.0ms	2919×	body	80	nan
751.0ms	1082×	body	2560	valid
522.0ms	890×	body	1280	valid
209.0ms	438×	body	640	valid
108.0ms	230×	body	320	valid
84.0ms	112×	body	5120	valid
23.0ms	124×	body	160	valid