Details

sample84.0ms

Algorithm

intervals

Results

20.0ms	32×	body	2560	valid
13.0ms	183×	body	80	valid
12.0ms	39×	body	1280	valid
6.0ms	98×	body	80	nan
4.0ms	14×	body	640	valid
2.0ms	4×	body	5120	valid
2.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify6.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b b) (* (* 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)))

rewrite167.0ms

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:

9.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
59.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 4.0 a) c))
162.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
117.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Counts: 82 → 82

prune271.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize23.0ms

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)))

rewrite275.0ms

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:

42.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
127.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
85.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series703.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
205.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
282.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
98.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Counts: 166 → 166

prune670.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

84.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series536.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
103.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
190.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Counts: 100 → 100

prune417.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c)
0.4b	(/ 4.0 (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
0.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

36.0ms	(/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c)
35.0ms	(/ 4.0 (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
30.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c)
143.0ms	(/ 4.0 (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
90.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Counts: 118 → 118

prune435.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.8b

regimes271.0ms

Accuracy

90.9% (2.2b remaining)

Error of 7.9b against oracle of 5.7b and baseline of 30.1b

bsearch269.0ms

Steps

Iters	Range		Point
8	6.830756908302209e+71	2.772849885831336e+75	2.730494439370032e+75
9	-9.135136184186538e-305	3.248654678508165e-307	-7.171823963984e-310
8	-0.19973978490672425	-0.00024022063624403673	-0.1973887031618164

simplify45.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

580.0ms	1082×	body	2560	valid
535.0ms	2886×	body	80	nan
400.0ms	5889×	body	80	valid
314.0ms	897×	body	1280	valid
153.0ms	430×	body	640	valid
67.0ms	225×	body	320	valid
44.0ms	102×	body	5120	valid
11.0ms	103×	body	160	valid