Details

sample166.0ms

Algorithm

intervals

Results

14.0ms	206×	body	80	valid
11.0ms	29×	body	2560	valid
9.0ms	28×	body	1280	valid
6.0ms	96×	body	80	nan
3.0ms	12×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify5.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

117.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
46.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
86.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify96.0ms

Counts: 103 → 103

prune432.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 177

Calls

4 calls:

79.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
34.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
77.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
48.0ms	(- (* b_2 b_2) (* a c))
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify83.0ms

Counts: 189 → 189

prune633.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.6b

localize29.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

14.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify147.0ms

Counts: 69 → 69

prune330.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.6b

localize29.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.0b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.4b	(* (/ 1 a) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.0ms	(* (/ 1 a) (* a c))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b_2 b_2) (* a c))
121.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(* (/ 1 a) (* a c))
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify61.0ms

Counts: 91 → 91

prune361.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.6b

regimes460.0ms

Accuracy

94.2% (1.4b remaining)

Error of 6.9b against oracle of 5.5b and baseline of 29.4b

bsearch289.0ms

Steps

Iters	Range		Point
9	1.2073698495971617e+61	8.75865749938149e+67	1.5309044043864094e+64
10	1.610059141238142e-239	1.618698210595833e-224	1.3940884725297859e-238
9	-1.0235731023437291e+92	-1.1204690717208776e+87	-2.442369070306522e+91

simplify379.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

712.0ms	2844×	body	80	nan
594.0ms	5837×	body	80	valid
514.0ms	1052×	body	2560	valid
425.0ms	898×	body	1280	valid
115.0ms	464×	body	640	valid
64.0ms	112×	body	5120	valid
46.0ms	238×	body	320	valid
14.0ms	108×	body	160	valid