Details

sample329.0ms

Algorithm

intervals

Results

7.0ms	205×	body	80	valid
5.0ms	26×	body	2560	valid
4.0ms	26×	body	1280	valid
4.0ms	83×	body	80	nan
1.0ms	11×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7
done	44	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite122.0ms

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:

72.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
76.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901
done	5001	901

prune262.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

101.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
75.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Counts

101 → 101

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	428	881
1	1823	791
2	5003	771
done	5003	771

prune240.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite116.0ms

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:

69.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
75.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	911
2	5002	902
done	5002	902

prune267.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* b_2 b_2) (* a c))
2.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.6b	(* (/ 1 a) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite75.0ms

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))))
28.0ms	(* (/ 1 a) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(* (/ 1 a) (* a c))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify61.0ms

Counts

91 → 91

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	416	490
1	1971	383
2	5002	371
done	5002	371

prune221.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.0b

regimes294.0ms

Accuracy

96% (1.0b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.8b

bsearch136.0ms

Steps

Iters	Range	Point
6	9.002760019060421e+93	3.662435776182418e+94	3.0526259186982142e+94
9	-6.337876436014474e-306	3.2635001309178313e-304	4.963004351321349e-308
8	-3.942677352963429e+147	-2.908826449852181e+144	-1.590533515710924e+145

Iters

Range

Point

9.002760019060421e+93

3.662435776182418e+94

3.0526259186982142e+94

-6.337876436014474e-306

3.2635001309178313e-304

4.963004351321349e-308

-3.942677352963429e+147

-2.908826449852181e+144

-1.590533515710924e+145

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	31
1	50	31
done	50	31

end0.0ms

sample1.1s

Algorithm

intervals

Results

195.0ms	1087×	body	2560	valid
195.0ms	5912×	body	80	valid
130.0ms	871×	body	1280	valid
86.0ms	2847×	body	80	nan
53.0ms	448×	body	640	valid
25.0ms	112×	body	5120	valid
18.0ms	213×	body	320	valid
6.0ms	102×	body	160	valid