Details

sample34.0ms

Algorithm

intervals

Results

6.0ms	35×	body	2560	valid
6.0ms	184×	body	80	valid
4.0ms	30×	body	1280	valid
2.0ms	91×	body	80	nan
1.0ms	10×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify7.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite103.0ms

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:

59.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(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	910
2	5001	901
done	5001	901

prune218.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.6b	(- (* b_2 b_2) (* a c))
1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite131.0ms

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:

88.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
10.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
37.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Counts

101 → 101

Iterations

Useful iterations: 2 (39.0ms)

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

prune207.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
0.7b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.5b	(* (/ 1 a) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite66.0ms

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:

8.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0ms	(* (/ 1 a) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(* (/ 1 a) (* a c))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify56.0ms

Counts

91 → 91

Iterations

Useful iterations: 2 (51.0ms)

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

prune211.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (* (/ 1 a) 0) (* (/ 1 1) c)) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.6b	(- (* b_2 b_2) (* a c))
0.7b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite111.0ms

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-/r*`
3×	`flip3-+` `sqrt-prod` `flip-+` `associate-/l/` `associate-/l*`
2×	`flip3--` `sqrt-div` `associate-*l/` `sum-log` `associate-/r/` `flip--`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `neg-log` `frac-add` `clear-num` `div-inv`

Counts

4 → 82

Calls

4 calls:

73.0ms	(/ (+ (* (/ 1 a) 0) (* (/ 1 1) c)) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (+ (* (/ 1 a) 0) (* (/ 1 1) c)) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
34.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify60.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	417	1012
1	1833	872
2	5001	844
done	5001	844

prune232.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.8b

regimes181.0ms

Accuracy

95.5% (1.1b remaining)

Error of 7.1b against oracle of 6.0b and baseline of 29.8b

bsearch163.0ms

Steps

Iters	Range		Point
8	1.2146045965263502e+46	6.67231609761305e+48	6.568668442325333e+48
12	1.813593813062301e-228	6.921499512731232e-188	3.203463322495104e-228
10	-1.2433634659052315e+163	-1.0287718737452788e+153	-9.50165850365896e+153

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	51	26
2	51	26
done	51	26

end0.0ms

sample995.0ms

Algorithm

intervals

Results

188.0ms	1077×	body	2560	valid
182.0ms	5840×	body	80	valid
125.0ms	902×	body	1280	valid
77.0ms	2840×	body	80	nan
45.0ms	420×	body	640	valid
22.0ms	104×	body	5120	valid
20.0ms	246×	body	320	valid
8.0ms	92×	body	160	valid