Details

sample108.0ms

Algorithm

intervals

Results

26.0ms	44×	body	2560	valid
17.0ms	167×	body	80	valid
15.0ms	32×	body	1280	valid
9.0ms	100×	body	80	nan
5.0ms	14×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify135.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	119	16
5	128	16
done	128	16

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
25.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

118.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
41.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series490.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
134.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
68.0ms	(- (* b b) (* 4.0 (* a c)))
115.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

102 → 102

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	165	1697
1	452	1588
2	1989	1361
done	5000	1352

prune526.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
3.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `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` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

19.0ms	(- (* b b) (* 4.0 (* a c)))
144.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
69.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series646.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (* b b) (* 4.0 (* a c)))
201.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
264.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
112.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.9s

Counts

170 → 170

Iterations

Useful iterations: 2 (897.0ms)

Iter	Nodes	Cost
0	260	5076
1	689	4517
2	4393	4197
done	5000	4197

prune637.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
3.3b	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
11.3b	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
25.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
37×	`add-sqr-sqrt`
30×	`*-un-lft-identity` `add-cbrt-cube`
27×	`associate-r`
24×	`times-frac`
17×	`add-cube-cbrt` `prod-exp`
16×	`div-exp`
9×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1`
6×	`sqrt-prod` `associate-/l/` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `associate-*l/` `flip-+` `log1p-expm1-u`
3×	`rec-exp` `flip3--` `distribute-rgt-neg-in` `1-exp` `associate-l` `flip--` `unswap-sqr`
2×	`sqrt-div` `associate-*r/` `associate-/r/` `un-div-inv` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 126

Calls

4 calls:

13.0ms	(- (* b b) (* 4.0 (* a c)))
43.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
124.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series722.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (* b b) (* 4.0 (* a c)))
255.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
268.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
107.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify558.0ms

Counts

138 → 138

Iterations

Useful iterations: done (551.0ms)

Iter	Nodes	Cost
0	248	3579
1	755	2953
done	5001	2519

prune572.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
3.3b	(/ (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.3b	(/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
34×	`times-frac`
28×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt`
8×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
7×	`sqrt-prod`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u` `div-inv`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 124

Calls

4 calls:

16.0ms	(- (* b b) (* 4.0 (* a c)))
102.0ms	(/ (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
63.0ms	(/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series611.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b b) (* 4.0 (* a c)))
219.0ms	(/ (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
218.0ms	(/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
109.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.4s

Counts

136 → 136

Iterations

Useful iterations: 2 (741.0ms)

Iter	Nodes	Cost
0	242	3535
1	704	3345
2	4633	2792
done	5000	2792

prune485.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.6b

regimes256.0ms

Accuracy

90.4% (2.5b remaining)

Error of 8.2b against oracle of 5.6b and baseline of 32.1b

bsearch288.0ms

Steps

Iters	Range		Point
7	517946.10598021303	17102963.46615162	1813249.6292001975
10	-2.4810350231976038e-293	2.102313690554005e-306	-1.4219793874705905e-304
8	-1.471055469501053e+100	-2.16094220789435e+96	-1.8069356592732734e+98

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	67
1	46	67
done	46	67

end0.0ms

sample3.9s

Algorithm

intervals

Results

862.0ms	936×	body	1280	valid
832.0ms	2905×	body	80	nan
757.0ms	1127×	body	2560	valid
529.0ms	5717×	body	80	valid
138.0ms	448×	body	640	valid
97.0ms	111×	body	5120	valid
49.0ms	223×	body	320	valid
16.0ms	112×	body	160	valid