Details

sample56.0ms

Algorithm

intervals

Results

10.0ms	184×	body	80	valid
9.0ms	32×	body	2560	valid
7.0ms	30×	body	1280	valid
5.0ms	24×	body	640	valid
4.0ms	83×	body	80	nan
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify126.0ms

Counts: 1 → 1

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize17.0ms

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))))

rewrite188.0ms

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:

116.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
19.0ms	(- (* b b) (* 4.0 (* a c)))
33.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series425.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
61.0ms	(- (* b b) (* 4.0 (* a c)))
106.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
107.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify763.0ms

Counts: 89 → 89

prune407.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize20.0ms

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))))

rewrite182.0ms

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:

124.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
10.0ms	(- (* b b) (* 4.0 (* a c)))
26.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
84.0ms	(- (* b b) (* 4.0 (* a c)))
115.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
110.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify944.0ms

Counts: 97 → 97

prune359.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize41.0ms

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))))

rewrite150.0ms

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:

31.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(- (* b b) (* 4.0 (* a c)))
93.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series554.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(- (* b b) (* 4.0 (* a c)))
236.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
94.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts: 83 → 83

prune415.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize45.0ms

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))))

rewrite162.0ms

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:

75.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
15.0ms	(- (* b b) (* 4.0 (* a c)))
48.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series520.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
72.0ms	(- (* b b) (* 4.0 (* a c)))
134.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
130.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify971.0ms

Counts: 137 → 137

prune502.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.4b

regimes395.0ms

Accuracy

88.5% (3.4b remaining)

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

bsearch276.0ms

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

simplify1.0s

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.1s	5913×	body	80	valid
969.0ms	3009×	body	80	nan
605.0ms	1081×	body	2560	valid
391.0ms	891×	body	1280	valid
188.0ms	468×	body	640	valid
65.0ms	107×	body	5120	valid
48.0ms	216×	body	320	valid
15.0ms	100×	body	160	valid