Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	201×	body	80	valid
6.0ms	35×	body	1280	valid
6.0ms	27×	body	2560	valid
3.0ms	87×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify80.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	63	17
3	114	17
4	130	17
5	136	17
6	139	17
done	139	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
20.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite60.0ms

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:

36.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify494.0ms

Counts

89 → 89

Iterations

Useful iterations: done (491.0ms)

Iter	Nodes	Cost
0	157	1750
1	405	1650
2	1339	1474
done	5000	1465

prune455.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize20.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.7b	(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.3b	(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
20.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite122.0ms

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:

19.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
57.0ms	(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
36.0ms	(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series537.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
170.0ms	(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
209.0ms	(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify800.0ms

Counts

153 → 153

Iterations

Useful iterations: done (794.0ms)

Iter	Nodes	Cost
0	252	5227
1	640	4734
2	2270	4042
done	5001	4040

prune471.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.6b	(/ (* 2.0 a) (/ (- (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
10.3b	(/ (- (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
20.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`*-un-lft-identity`
36×	`add-cube-cbrt`
30×	`associate-/r*`
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×	`flip3--` `flip--` `add-log-exp`
5×	`pow1`
4×	`div-inv` `associate-/l*`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-sub`

Counts

4 → 142

Calls

4 calls:

19.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
39.0ms	(/ (* 2.0 a) (/ (- (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
35.0ms	(/ (- (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
90.0ms	(/ (* 2.0 a) (/ (- (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
207.0ms	(/ (- (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

154 → 154

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	247	4619
1	640	4037
2	3003	3735
done	5000	3734

prune456.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
1.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.1b	(/ (* 2.0 a) (* (* a c) 4.0))
20.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

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:

3.0ms	(- (* b b) (* 4.0 (* a c)))
19.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(/ (* 2.0 a) (* (* a c) 4.0))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b b) (* 4.0 (* a c)))
84.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.0ms	(/ (* 2.0 a) (* (* a c) 4.0))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify675.0ms

Counts

79 → 79

Iterations

Useful iterations: 2 (182.0ms)

Iter	Nodes	Cost
0	150	1250
1	414	1132
2	2163	968
done	5000	968

prune201.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

regimes264.0ms

Accuracy

95.3% (1.1b remaining)

Error of 6.9b against oracle of 5.8b and baseline of 29.1b

bsearch184.0ms

Steps

Iters	Range	Point
8	2.1878188410446244e+107	3.8616146939177386e+111	3.264911199889295e+111
7	9.566243277432845e-222	6.935230677160525e-220	9.700881881466199e-222
10	-1.606057119580561e+132	-2.0971921831952125e+122	-2.775795956144935e+129

Iters

Range

Point

2.1878188410446244e+107

3.8616146939177386e+111

3.264911199889295e+111

9.566243277432845e-222

6.935230677160525e-220

9.700881881466199e-222

-1.606057119580561e+132

-2.0971921831952125e+122

-2.775795956144935e+129

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	59
1	42	59
done	42	59

end0.0ms

sample1.1s

Algorithm

intervals

Results

257.0ms	1110×	body	2560	valid
220.0ms	5789×	body	80	valid
173.0ms	885×	body	1280	valid
113.0ms	2998×	body	80	nan
67.0ms	448×	body	640	valid
31.0ms	101×	body	5120	valid
28.0ms	253×	body	320	valid
9.0ms	126×	body	160	valid