Details

sample82.0ms

Algorithm

intervals

Results

16.0ms	198×	body	80	valid
14.0ms	34×	body	1280	valid
14.0ms	29×	body	2560	valid
7.0ms	94×	body	80	nan
4.0ms	12×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	4×	body	160	valid

simplify173.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	139
7	139
6	137
5	132
4	127
3	106
2	61
1	28
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.0b	(- (* b b) (* 4.0 (* a c)))
22.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

63.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
34.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series496.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
135.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(- (* b b) (* 4.0 (* a c)))
132.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
3	4961
2	1246
1	402
0	155

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.0b	(- (* b b) (* 4.0 (* a c)))
22.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

168.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
38.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
107.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
56.0ms	(- (* b b) (* 4.0 (* a c)))
107.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	1644
1	467
0	181

prune670.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize47.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (* b b) (* 4.0 (* a c)))
14.8b	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (* a 2.0))
18.8b	(- (* b b) (* b b))
22.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

14.0ms	(- (* b b) (* 4.0 (* a c)))
104.0ms	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (* a 2.0))
9.0ms	(- (* b b) (* b b))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series198.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) (* a 2.0))
1.0ms	(- (* b b) (* b b))
121.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

79 → 79

Iterations

Iter	Nodes
done	5006
2	939
1	342
0	131

prune539.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
1.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.0b	(- (* b b) (* 4.0 (* a c)))
22.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

36.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
33.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
113.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms	(- (* b b) (* 4.0 (* a c)))
84.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1289
1	381
0	142

prune482.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.2b

regimes395.0ms

Accuracy

95.6% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 30.2b

bsearch304.0ms

Steps

Iters	Range	Point
5	6.972240796235003e+85	2.4695855038465726e+86	2.3609083740516956e+86
8	1.228229358642072e-304	2.9835778558822928e-300	2.8665574893004447e-301
9	-6.117539429929052e+154	-3.6285784997486435e+148	-3.3364449588859886e+152

Iters

Range

Point

6.972240796235003e+85

2.4695855038465726e+86

2.3609083740516956e+86

1.228229358642072e-304

2.9835778558822928e-300

2.8665574893004447e-301

-6.117539429929052e+154

-3.6285784997486435e+148

-3.3364449588859886e+152

simplify22.0ms

Iterations

Iter	Nodes
done	45
1	45
0	35

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	5858×	body	80	valid
770.0ms	1086×	body	2560	valid
517.0ms	901×	body	1280	valid
277.0ms	2954×	body	80	nan
159.0ms	481×	body	640	valid
60.0ms	97×	body	5120	valid
48.0ms	191×	body	320	valid
21.0ms	111×	body	160	valid