Details

sample42.0ms

Algorithm

intervals

Results

7.0ms	42×	body	1280	valid
6.0ms	176×	body	80	valid
6.0ms	29×	body	2560	valid
3.0ms	91×	body	80	nan
2.0ms	18×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9
done	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize11.0ms

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)))
0.7b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite105.0ms

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:

63.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
23.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify41.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674
done	5002	674

prune202.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
8.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite175.0ms

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:

21.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
83.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
53.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series502.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
158.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
189.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify98.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	640	2692
1	2944	2439
2	5001	2426
done	5001	2426

prune399.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.8b

localize18.0ms

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)))
0.7b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite136.0ms

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:

97.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
8.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
50.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	479	920
1	2139	790
2	5002	777
done	5002	777

prune221.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.7b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

47.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
23.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series357.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
52.0ms	(- (* b b) (* 4.0 (* a c)))
86.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify66.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	521	1588
1	2522	1375
2	5002	1308
done	5002	1308

prune240.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.8b

regimes167.0ms

Accuracy

82.1% (4.7b remaining)

Error of 10.8b against oracle of 6.0b and baseline of 32.5b

bsearch121.0ms

Steps

Iters	Range		Point
9	5.8001850246574435e-136	2.3374458796783105e-129	2.3065444773801163e-129
10	-1.2433634659052315e+163	-5.7824766130184975e+150	-6.371698442415157e+150

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	38	16
done	38	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

224.0ms	5892×	body	80	valid
212.0ms	974×	body	2560	valid
167.0ms	930×	body	1280	valid
98.0ms	2863×	body	80	nan
66.0ms	483×	body	640	valid
25.0ms	97×	body	5120	valid
23.0ms	229×	body	320	valid
8.0ms	112×	body	160	valid