Details

sample81.0ms

Algorithm

intervals

Results

20.0ms	189×	body	80	valid
14.0ms	36×	body	2560	valid
8.0ms	25×	body	1280	valid
7.0ms	104×	body	80	nan
4.0ms	16×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify156.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
26.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite143.0ms

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--` `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 → 77

Calls

4 calls:

80.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
23.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
118.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
84.0ms	(- (* b b) (* 4.0 (* a c)))
113.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.8s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
3	4961
2	1246
1	402
0	155

prune662.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite175.0ms

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--` `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 → 77

Calls

4 calls:

108.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
118.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms	(- (* b b) (* (* 4.0 a) c))
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1288
1	407
0	157

prune508.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite179.0ms

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` `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 → 85

Calls

4 calls:

132.0ms	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
20.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
125.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
61.0ms	(- (* b b) (* (* 4.0 a) c))
92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	1689
1	472
0	183

prune590.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
15.9b	(/ (+ (- (* b b) (* b b)) (* a (* 4.0 c))) (* a 2.0))
20.3b	(- (* b b) (* b b))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite468.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`times-frac` `flip3--` `sqrt-prod` `flip--` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out--` `pow1/2` `+-inverses` `div-sub` `prod-exp` `associate-+l-` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

12.0ms	(- (* b b) (* (* 4.0 a) c))
438.0ms	(/ (+ (- (* b b) (* b b)) (* a (* 4.0 c))) (* a 2.0))
6.0ms	(- (* b b) (* b b))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* b b) (* (* 4.0 a) c))
20.0ms	(/ (+ (- (* b b) (* b b)) (* a (* 4.0 c))) (* a 2.0))
1.0ms	(- (* b b) (* b b))
117.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1099
1	364
0	137

prune524.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.5b

regimes489.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.6b

bsearch241.0ms

Steps

Iters	Range	Point
6	5.84949006905106e+100	6.027833473435204e+101	3.355858625783055e+101
9	-1.4598085821258646e-291	-1.0697531889019586e-297	-1.0850002786366243e-297
6	-1.7989235910837076e+89	-1.4585470499056154e+88	-1.7633154797394035e+89

Iters

Range

Point

5.84949006905106e+100

6.027833473435204e+101

3.355858625783055e+101

-1.4598085821258646e-291

-1.0697531889019586e-297

-1.0850002786366243e-297

-1.7989235910837076e+89

-1.4585470499056154e+88

-1.7633154797394035e+89

simplify7.0ms

Iterations

Iter	Nodes
done	40
1	40
0	33

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	5822×	body	80	valid
642.0ms	1065×	body	2560	valid
420.0ms	948×	body	1280	valid
193.0ms	2889×	body	80	nan
130.0ms	471×	body	640	valid
68.0ms	115×	body	5120	valid
47.0ms	241×	body	320	valid
17.0ms	107×	body	160	valid