Details

sample41.0ms

Algorithm

intervals

Results

7.0ms	181×	body	80	valid
6.0ms	27×	body	2560	valid
6.0ms	31×	body	1280	valid
3.0ms	21×	body	640	valid
3.0ms	81×	body	80	nan
2.0ms	8×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify82.0ms

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: 34.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite62.0ms

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:

40.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
50.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify945.0ms

Counts

89 → 89

Iterations

Useful iterations: done (941.0ms)

Iter	Nodes	Cost
0	157	1750
1	405	1650
2	1328	1474
done	5000	1459

prune260.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.2b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite104.0ms

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:

23.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series738.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
175.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
214.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify830.0ms

Counts

153 → 153

Iterations

Useful iterations: done (824.0ms)

Iter	Nodes	Cost
0	250	4579
1	626	4057
2	2390	3753
done	5000	3751

prune438.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (* 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* 2.0 a))
8.2b	(/ (+ 0 (* 4.0 (* a c))) (* 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
30×	`add-cbrt-cube`
18×	`times-frac`
17×	`div-exp`
16×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
12×	`cbrt-undiv` `associate-/l*`
11×	`add-cube-cbrt`
10×	`prod-exp`
6×	`associate-*r/` `associate-/r/` `cbrt-unprod` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`sqrt-prod` `div-inv`
3×	`1-exp` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r*` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+` `distribute-lft-out--`

Counts

4 → 100

Calls

4 calls:

20.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
34.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (* 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* 2.0 a))
21.0ms	(/ (+ 0 (* 4.0 (* a c))) (* 1 (- (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)
171.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (* 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* 2.0 a))
209.0ms	(/ (+ 0 (* 4.0 (* a c))) (* 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify898.0ms

Counts

112 → 112

Iterations

Useful iterations: done (894.0ms)

Iter	Nodes	Cost
0	228	3193
1	620	2606
2	2353	2208
done	5000	2206

prune301.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.8b	(/ (* 2.0 a) (* (* a c) 4.0))
21.1b	(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)
9.0ms	(/ (* 2.0 a) (* (* a c) 4.0))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series215.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* 4.0 (* a c)))
82.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.0ms	(/ (* 2.0 a) (* (* a c) 4.0))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify923.0ms

Counts

79 → 79

Iterations

Useful iterations: 2 (208.0ms)

Iter	Nodes	Cost
0	150	1250
1	414	1132
2	2158	968
done	5000	968

prune198.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

regimes149.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.9b

bsearch190.0ms

Steps

Iters	Range		Point
10	1.1889782913455773e+76	6.845935134449847e+90	6.74838527698993e+90
8	3.0778477937611473e-255	3.0021351299804193e-252	3.119187438943242e-255
9	-3.410794538153641e+109	-1.852183237050365e+100	-1.56882272369853e+105

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	36	61
1	44	59
done	44	59

end0.0ms

sample1.1s

Algorithm

intervals

Results

245.0ms	1059×	body	2560	valid
229.0ms	5841×	body	80	valid
168.0ms	909×	body	1280	valid
105.0ms	2943×	body	80	nan
69.0ms	464×	body	640	valid
28.0ms	102×	body	5120	valid
27.0ms	234×	body	320	valid
10.0ms	111×	body	160	valid