Details

sample61.0ms

Algorithm

intervals

Results

18.0ms	193×	body	80	valid
9.0ms	32×	body	2560	valid
6.0ms	28×	body	1280	valid
4.0ms	87×	body	80	nan
3.0ms	20×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	2×	body	160	valid

simplify5.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
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×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
96.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
113.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
48.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify41.0ms

Counts: 82 → 82

prune241.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize23.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.1b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.3b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

25.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
90.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
63.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
157.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
198.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
81.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify106.0ms

Counts: 166 → 166

prune484.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3.0 a) c))
1.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
12.7b	(/ (* 3.0 a) (* 3.0 (* a c)))
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
28.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
10.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 3.0 a) c))
85.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
13.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
81.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify62.0ms

Counts: 82 → 82

prune234.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (/ c 1)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
69×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
44×	`associate-l`
41×	`add-cube-cbrt`
30×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `associate-r` `unswap-sqr`
6×	`1-exp`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `div-inv` `distribute-lft-out--` `difference-of-squares`
3×	`cbrt-undiv` `rec-exp` `diff-log` `cbrt-unprod`
2×	`distribute-rgt-in` `frac-times` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-div` `associate-*r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `associate-/r/` `-commutative`

Counts

4 → 134

Calls

4 calls:

112.0ms	(* (/ 1 (/ c 1)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
14.0ms	(- (* b b) (* (* 3.0 a) c))
23.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (/ 1 (/ c 1)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
54.0ms	(- (* b b) (* (* 3.0 a) c))
92.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
79.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify65.0ms

Counts: 146 → 146

prune418.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.5b

regimes345.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 30.1b

bsearch182.0ms

Steps

Iters	Range	Point
4	9.012561940608131e+125	1.467599966670541e+126	9.171769784769279e+125
9	-1.0819843522862608e-301	-1.218503363246056e-308	-5.975900233814397e-306
10	-2.875458900305947e+147	-4.1230913930237915e+136	-2.3526278988557565e+142

Iters

Range

Point

9.012561940608131e+125

1.467599966670541e+126

9.171769784769279e+125

-1.0819843522862608e-301

-1.218503363246056e-308

-5.975900233814397e-306

-2.875458900305947e+147

-4.1230913930237915e+136

-2.3526278988557565e+142

simplify2.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

700.0ms	5788×	body	80	valid
576.0ms	902×	body	1280	valid
439.0ms	1113×	body	2560	valid
168.0ms	2915×	body	80	nan
151.0ms	461×	body	640	valid
70.0ms	103×	body	5120	valid
32.0ms	233×	body	320	valid
10.0ms	107×	body	160	valid