Details

sample102.0ms

Algorithm

intervals

Results

22.0ms	37×	body	2560	valid
19.0ms	191×	body	80	valid
11.0ms	23×	body	1280	valid
8.0ms	90×	body	80	nan
6.0ms	15×	body	640	valid
1.0ms	5×	body	160	valid
1.0ms	3×	body	320	valid
1.0ms	1×	body	5120	valid

simplify257.0ms

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	141	17
5	151	17
6	155	17
done	155	17

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize37.0ms

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)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite217.0ms

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:

128.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms	(- (* b b) (* 4.0 (* a c)))
42.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
74.0ms	(- (* b b) (* 4.0 (* a c)))
135.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
132.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

89 → 89

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	157	1750
1	418	1650
2	1644	1474
done	5000	1466

prune700.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

191.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
24.0ms	(- (* b b) (* 4.0 (* a c)))
40.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
94.0ms	(- (* b b) (* 4.0 (* a c)))
131.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
119.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts

97 → 97

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	183	2003
1	492	1837
2	2398	1573
done	5000	1569

prune662.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

97.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
17.0ms	(- (* b b) (* 4.0 (* a c)))
55.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
88.0ms	(- (* b b) (* 4.0 (* a c)))
142.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
128.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

137 → 137

Iterations

Useful iterations: 2 (573.0ms)

Iter	Nodes	Cost
0	226	3421
1	588	3066
2	2593	2852
done	5001	2852

prune771.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.6b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
12.5b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite473.0ms

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:

87.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
211.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
139.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series1.1s

Counts

4 → 12

Calls

4 calls:

160.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
350.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
412.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
145.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.4s

Counts

153 → 153

Iterations

Useful iterations: 2 (1.0s)

Iter	Nodes	Cost
0	250	4579
1	649	4063
2	3620	3761
done	5001	3761

prune1.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.6b

regimes508.0ms

Accuracy

84.2% (4.5b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 33.9b

bsearch225.0ms

Steps

Iters	Range		Point
10	9.08791783933159e+82	5.750161104817302e+93	9.623020473898683e+86
5	-1.2210963557284012e-33	-3.582918381276583e-34	-3.8424248185280593e-34

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	39
1	36	39
done	36	39

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.4s	5910×	body	80	valid
849.0ms	1110×	body	2560	valid
617.0ms	901×	body	1280	valid
384.0ms	3015×	body	80	nan
166.0ms	436×	body	640	valid
75.0ms	104×	body	5120	valid
61.0ms	217×	body	320	valid
25.0ms	111×	body	160	valid