Details

sample105.0ms

Algorithm

intervals

Results

19.0ms	32×	body	2560	valid
19.0ms	184×	body	80	valid
15.0ms	30×	body	1280	valid
10.0ms	24×	body	640	valid
8.0ms	83×	body	80	nan
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify153.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

112.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
67.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
60.0ms	(- (* b b) (* 4.0 (* a c)))
118.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
94.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify743.0ms

Counts: 89 → 89

prune368.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite260.0ms

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×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

194.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
18.0ms	(- (* b b) (* 4.0 (* a c)))
30.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
63.0ms	(- (* b b) (* 4.0 (* a c)))
112.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
93.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify977.0ms

Counts: 97 → 97

prune343.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
15.4b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
19.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

41.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms	(- (* b b) (* 4.0 (* a c)))
105.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series519.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
52.0ms	(- (* b b) (* 4.0 (* a c)))
227.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
135.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts: 83 → 83

prune428.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

78.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
42.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
52.0ms	(- (* b b) (* 4.0 (* a c)))
109.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
103.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3s

Counts: 137 → 137

prune448.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.4b

regimes387.0ms

Accuracy

88.5% (3.4b remaining)

Error of 8.9b against oracle of 5.5b and baseline of 35.2b

bsearch273.0ms

Steps

Iters	Range	Point
4	9.936283634246925e+77	1.8488019868481542e+78	1.7151811081882383e+78
9	3.6976431258031608e-267	1.8292500652683027e-260	3.7396979939895573e-267
8	-6.990724105819741e+111	-2.6156774686163576e+108	-4.020085128891058e+108

Iters

Range

Point

9.936283634246925e+77

1.8488019868481542e+78

1.7151811081882383e+78

3.6976431258031608e-267

1.8292500652683027e-260

3.7396979939895573e-267

-6.990724105819741e+111

-2.6156774686163576e+108

-4.020085128891058e+108

simplify867.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.2s	891×	body	1280	valid
624.0ms	1081×	body	2560	valid
543.0ms	5913×	body	80	valid
296.0ms	3009×	body	80	nan
204.0ms	468×	body	640	valid
57.0ms	107×	body	5120	valid
45.0ms	216×	body	320	valid
13.0ms	100×	body	160	valid