Details

sample184.0ms

Algorithm

intervals

Results

15.0ms	38×	body	2560	valid
12.0ms	192×	body	80	valid
10.0ms	25×	body	1280	valid
6.0ms	98×	body	80	nan
4.0ms	8×	body	320	valid
4.0ms	15×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify55.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite335.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

233.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
56.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
110.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
66.0ms	(- (* b_2 b_2) (* a c))
138.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts: 92 → 92

prune418.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

100.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
50.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
120.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
54.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts: 174 → 174

prune507.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

152.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
55.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
117.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
56.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify870.0ms

Counts: 96 → 96

prune357.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

localize41.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite53.0ms

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:

9.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* b_2 b_2) (* a c))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts: 69 → 69

prune349.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.6b

regimes445.0ms

Accuracy

83.3% (4.7b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 33.6b

bsearch116.0ms

Steps

Iters	Range		Point
6	3.2999883719107076e-115	1.481810096151352e-114	5.81843322574321e-115
8	-1.3549447721302977e+118	-2.218977696437643e+113	-1.2609617020890706e+118

simplify98.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

596.0ms	461×	body	640	valid
564.0ms	5957×	body	80	valid
526.0ms	1037×	body	2560	valid
384.0ms	857×	body	1280	valid
224.0ms	2888×	body	80	nan
99.0ms	102×	body	5120	valid
46.0ms	246×	body	320	valid
14.0ms	115×	body	160	valid