Details

sample86.0ms

Algorithm

intervals

Results

16.0ms	36×	body	2560	valid
14.0ms	188×	body	80	valid
9.0ms	24×	body	1280	valid
8.0ms	108×	body	80	nan
4.0ms	17×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify134.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	79	16
4	99	16
5	107	16
done	107	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize374.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

93.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
32.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
51.0ms	(- (* b b) (* (* 4.0 a) c))
132.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts

82 → 82

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	154	1565
1	421	1461
2	1932	1245
done	5000	1239

prune298.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.1b

localize23.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.0b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

32.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
108.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
89.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series587.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
181.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
238.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

166 → 166

Iterations

Useful iterations: 2 (634.0ms)

Iter	Nodes	Cost
0	254	5113
1	660	4543
2	3720	4219
done	5001	4219

prune475.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

localize23.0ms

Local error

Found 4 expressions with local error:

12.0b	(cbrt (* c (* 4.0 a)))
12.0b	(cbrt (* c (* 4.0 a)))
12.0b	(cbrt (* c (* 4.0 a)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 42

Calls

4 calls:

12.0ms	(cbrt (* c (* 4.0 a)))
18.0ms	(cbrt (* c (* 4.0 a)))
11.0ms	(cbrt (* c (* 4.0 a)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (* c (* 4.0 a)))
100.0ms	(cbrt (* c (* 4.0 a)))
102.0ms	(cbrt (* c (* 4.0 a)))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

54 → 54

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	89	636
1	217	597
2	763	538
3	4019	517
done	5000	493

prune243.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

111.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
9.0ms	(- (* b b) (* (* 4.0 a) c))
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
55.0ms	(- (* b b) (* (* 4.0 a) c))
90.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

92 → 92

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	181	1881
1	502	1715
2	2748	1410
done	5000	1406

prune260.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.0b

regimes203.0ms

Accuracy

87.6% (3.5b remaining)

Error of 8.8b against oracle of 5.3b and baseline of 33.3b

bsearch229.0ms

Steps

Iters	Range	Point
6	1.9101351599902807e+102	2.525038855038462e+103	1.9425375319337521e+102
9	5.099515951519033e-140	4.3257429736328996e-131	1.0349406332011121e-134
9	-9.502057580036763e+144	-6.537164733756459e+138	-4.7395197774900957e+139

Iters

Range

Point

1.9101351599902807e+102

2.525038855038462e+103

1.9425375319337521e+102

5.099515951519033e-140

4.3257429736328996e-131

1.0349406332011121e-134

-9.502057580036763e+144

-6.537164733756459e+138

-4.7395197774900957e+139

simplify7.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	40	82
1	47	80
done	47	80

end0.0ms

sample2.5s

Algorithm

intervals

Results

831.0ms	5856×	body	80	valid
445.0ms	1074×	body	2560	valid
291.0ms	903×	body	1280	valid
249.0ms	2902×	body	80	nan
90.0ms	451×	body	640	valid
44.0ms	111×	body	160	valid
42.0ms	112×	body	5120	valid
34.0ms	223×	body	320	valid