Details

sample77.0ms

Algorithm

intervals

Results

24.0ms	38×	body	2560	valid
12.0ms	178×	body	80	valid
8.0ms	24×	body	1280	valid
6.0ms	104×	body	80	nan
4.0ms	16×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify108.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	98
7	98
6	97
5	95
4	87
3	72
2	42
1	24
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize29.0ms

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))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

87.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
14.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
68.0ms	(- (* b b) (* (* 4.0 a) c))
132.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

82 → 82

Iterations

Iter	Nodes
done	5002
2	1368
1	412
0	154

prune539.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize35.0ms

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))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

130.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
13.0ms	(- (* b b) (* (* 4.0 a) c))
34.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
91.0ms	(- (* b b) (* (* 4.0 a) c))
134.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5002
2	1832
1	484
0	181

prune620.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) (* 2.0 a))
0.4b	(- (* b b) (* a (* c 4.0)))
1.4b	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
21.3b	(sqrt (- (* b b) (* a (* c 4.0))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-lft-out--`
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` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 72

Calls

4 calls:

97.0ms	(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) (* 2.0 a))
8.0ms	(- (* b b) (* a (* c 4.0)))
47.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
14.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) (* 2.0 a))
73.0ms	(- (* b b) (* a (* c 4.0)))
91.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
92.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

simplify1.5s

Counts

84 → 84

Iterations

Iter	Nodes
done	5002
2	1283
1	399
0	154

prune568.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
47×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`associate-/r*` `div-exp`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod` `add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 118

Calls

4 calls:

80.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
11.0ms	(- (* b b) (* (* 4.0 a) c))
64.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
74.0ms	(- (* b b) (* (* 4.0 a) c))
99.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

130 → 130

Iterations

Iter	Nodes
done	5002
2	1855
1	555
0	220

prune721.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 5.9b

regimes727.0ms

Accuracy

87.7% (3.5b remaining)

Error of 9.0b against oracle of 5.5b and baseline of 34.0b

bsearch380.0ms

Steps

Iters	Range	Point
8	4.2042874054093966e-16	2.4761653582430886e-13	1.0923148588849599e-13
7	1.7480849449175914e-168	2.914975044111078e-166	3.2439279647460865e-167
10	-8.897020078895062e+156	-1.101416214509623e+146	-8.035809894237901e+152

Iters

Range

Point

4.2042874054093966e-16

2.4761653582430886e-13

1.0923148588849599e-13

1.7480849449175914e-168

2.914975044111078e-166

3.2439279647460865e-167

-8.897020078895062e+156

-1.101416214509623e+146

-8.035809894237901e+152

simplify41.0ms

Iterations

Iter	Nodes
done	47
1	47
0	39

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.0s	5812×	body	80	valid
780.0ms	2885×	body	80	nan
575.0ms	1027×	body	2560	valid
377.0ms	885×	body	1280	valid
212.0ms	505×	body	640	valid
74.0ms	118×	body	5120	valid
49.0ms	217×	body	320	valid
18.0ms	120×	body	160	valid