Details

sample109.0ms

Algorithm

intervals

Results

19.0ms	39×	body	1280	valid
18.0ms	32×	body	2560	valid
18.0ms	183×	body	80	valid
9.0ms	98×	body	80	nan
6.0ms	14×	body	640	valid
3.0ms	4×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	3×	body	160	valid

simplify8.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* a c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.1b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

17.0ms	(* 4.0 (* a c))
90.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
58.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* 4.0 (* a c))
143.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
124.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
118.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Counts: 88 → 88

prune340.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
7.2b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite276.0ms

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:

50.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
123.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
83.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series768.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
221.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
284.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
117.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify90.0ms

Counts: 166 → 166

prune670.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.1b	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

116.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
28.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
82.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series656.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
115.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
268.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
90.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify98.0ms

Counts: 100 → 100

prune386.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.3b	(/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
1.1b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

58×	`times-frac`
55×	`*-un-lft-identity`
30×	`add-exp-log`
28×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
18×	`add-cbrt-cube`
16×	`associate-/r*`
14×	`div-exp` `distribute-lft-out`
11×	`associate-/r/`
8×	`add-log-exp`
7×	`cbrt-undiv` `distribute-rgt-neg-in`
6×	`pow1` `flip3-+` `flip-+` `div-inv`
4×	`prod-exp` `associate-/l*`
3×	`rec-exp` `1-exp` `sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num` `sum-log` `cbrt-unprod`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `pow-flip` `sqrt-pow1` `pow1/2` `neg-log` `flip--` `inv-pow`

Counts

4 → 129

Calls

4 calls:

91.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
92.0ms	(/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
53.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series811.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
342.0ms	(/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
117.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
110.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Counts: 141 → 141

prune504.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 4.8b

regimes457.0ms

Accuracy

84.6% (4.2b remaining)

Error of 9.9b against oracle of 5.7b and baseline of 32.7b

bsearch247.0ms

Steps

Iters	Range		Point
7	32504.544960343763	1949745.7636754776	813278.224583504
4	1.6161117664628025e-216	2.7690258942452712e-216	1.7241974659424088e-216
8	-0.19973978490672425	-0.00024022063624403673	-0.1973887031618164

simplify121.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	5889×	body	80	valid
573.0ms	1082×	body	2560	valid
380.0ms	2886×	body	80	nan
327.0ms	897×	body	1280	valid
247.0ms	430×	body	640	valid
151.0ms	225×	body	320	valid
56.0ms	102×	body	5120	valid
19.0ms	103×	body	160	valid