Details

sample138.0ms

Algorithm

intervals

Results

50.0ms	41×	body	2560	valid
18.0ms	186×	body	80	valid
15.0ms	28×	body	1280	valid
10.0ms	108×	body	80	nan
6.0ms	17×	body	640	valid
4.0ms	5×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify155.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	29	17
2	64	17
3	120	17
4	145	17
5	152	17
6	156	17
done	156	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize14.0ms

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))))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`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 → 157

Calls

4 calls:

143.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms	(- (* b b) (* 4.0 (* a c)))
33.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series450.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
75.0ms	(- (* b b) (* 4.0 (* a c)))
123.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
101.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

169 → 169

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	243	6690
1	587	4705
2	1753	3760
done	5000	3113

prune555.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
78×	`times-frac`
72×	`*-un-lft-identity`
50×	`add-cube-cbrt`
27×	`associate-/l*`
26×	`sqrt-prod`
22×	`difference-of-squares`
18×	`add-exp-log` `prod-diff` `add-cbrt-cube`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`fma-neg` `associate-/r/` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 171

Calls

4 calls:

21.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
76.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
84.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
3.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series797.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
257.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
271.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
124.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.4s

Counts

183 → 183

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	275	5401
1	655	4711
2	2291	4237
done	5001	4169

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
51×	`add-exp-log`
42×	`add-cube-cbrt`
40×	`times-frac`
27×	`add-cbrt-cube`
24×	`associate-l`
23×	`sqrt-prod`
20×	`prod-exp`
18×	`prod-diff`
16×	`div-exp` `difference-of-squares`
8×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
7×	`pow1` `associate-r`
6×	`fma-neg` `associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `flip--` `div-inv` `associate-/l*`
2×	`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 → 169

Calls

4 calls:

27.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
127.0ms	(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
55.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
2.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series824.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
265.0ms	(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
309.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
103.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.7s

Counts

181 → 181

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	280	5119
1	714	4377
2	2502	3764
done	5000	3696

prune688.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma b b (- (* 4.0 (* a c))))
1.4b	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
14.5b	(/ (* (* a c) 4.0) (* 2.0 a))
24.0b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
9×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `fma-neg` `div-exp` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `diff-log` `clear-num` `associate-/r` `flip--` `fma-udef` `div-inv` `associate-/l` `distribute-lft-out--`

Counts

4 → 93

Calls

4 calls:

1.0ms	(fma b b (- (* 4.0 (* a c))))
23.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
51.0ms	(/ (* (* a c) 4.0) (* 2.0 a))
2.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(fma b b (- (* 4.0 (* a c))))
116.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
14.0ms	(/ (* (* a c) 4.0) (* 2.0 a))
132.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.0s

Counts

105 → 105

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	168	1926
1	413	1650
2	1805	1333
done	5000	1266

prune356.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

regimes224.0ms

Accuracy

77.2% (5.5b remaining)

Error of 11.3b against oracle of 5.8b and baseline of 30.0b

bsearch110.0ms

Steps

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

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	38
1	35	38
2	43	38
done	43	38

end0.0ms

sample3.3s

Algorithm

intervals

Results

990.0ms	1050×	body	2560	valid
708.0ms	5893×	body	80	valid
459.0ms	831×	body	1280	valid
278.0ms	2996×	body	80	nan
179.0ms	449×	body	640	valid
74.0ms	135×	body	5120	valid
53.0ms	225×	body	320	valid
17.0ms	123×	body	160	valid