Details

sample93.0ms

Algorithm

intervals

Results

22.0ms	28×	body	1280	valid
17.0ms	41×	body	2560	valid
13.0ms	186×	body	80	valid
7.0ms	108×	body	80	nan
5.0ms	17×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify172.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	64	17
3	114	17
4	130	17
5	137	17
6	141	17
done	141	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

113.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
28.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
72.0ms	(- (* b b) (* 4.0 (* a c)))
117.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
90.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.2s

Counts

89 → 89

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	157	1750
1	402	1650
2	1317	1474
3	4966	1459
done	5000	1459

prune353.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize35.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.1b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.3b	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
22×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 141

Calls

4 calls:

77.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
183.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
98.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series813.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
269.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
308.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
113.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

153 → 153

Iterations

Useful iterations: 2 (576.0ms)

Iter	Nodes	Cost
0	253	4579
1	619	4057
2	2460	3753
done	5000	3753

prune630.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize18.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.2b	(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
10.3b	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite380.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
51×	`add-exp-log`
44×	`*-un-lft-identity`
40×	`times-frac`
28×	`add-cube-cbrt`
27×	`add-cbrt-cube`
24×	`associate-l`
20×	`prod-exp`
16×	`div-exp` `difference-of-squares`
11×	`sqrt-prod`
8×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
7×	`pow1` `associate-r`
6×	`associate-/r*` `add-log-exp`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 139

Calls

4 calls:

57.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
186.0ms	(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
113.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series743.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
239.0ms	(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
267.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
111.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

151 → 151

Iterations

Useful iterations: 2 (519.0ms)

Iter	Nodes	Cost
0	258	4293
1	678	3713
2	2668	3279
done	5000	3279

prune625.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.5b	(/ (* (* 4.0 a) c) (* 2.0 a))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

21.0ms	(- (* b b) (* 4.0 (* a c)))
57.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
57.0ms	(/ (* (* 4.0 a) c) (* 2.0 a))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b b) (* 4.0 (* a c)))
115.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
20.0ms	(/ (* (* 4.0 a) c) (* 2.0 a))
90.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

79 → 79

Iterations

Useful iterations: 2 (333.0ms)

Iter	Nodes	Cost
0	150	1246
1	393	1128
2	1989	964
done	5000	964

prune271.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

regimes226.0ms

Accuracy

77.2% (5.5b remaining)

Error of 11.3b against oracle of 5.9b and baseline of 30.0b

bsearch119.0ms

Steps

Iters	Range		Point
6	1.6855676195581707e-170	7.565529323099765e-170	7.455592343308264e-170
5	-2.3823986784004295e+101	-6.644598008915225e+100	-1.8696623466311214e+101

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	38
1	31	38
done	31	38

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	5893×	body	80	valid
629.0ms	1050×	body	2560	valid
454.0ms	831×	body	1280	valid
232.0ms	2996×	body	80	nan
219.0ms	449×	body	640	valid
79.0ms	135×	body	5120	valid
53.0ms	225×	body	320	valid
19.0ms	123×	body	160	valid