Details

sample47.0ms

Algorithm

intervals

Results

8.0ms	206×	body	80	valid
7.0ms	107×	body	80	nan
6.0ms	28×	body	2560	valid
5.0ms	28×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	6×	body	160	valid
0.0ms	4×	body	320	valid

simplify67.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	91	16
5	99	16
done	99	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite108.0ms

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:

66.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
10.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
51.0ms	(- (* b b) (* (* 4.0 a) c))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts

82 → 82

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	154	1565
1	401	1461
2	1353	1245
done	5001	1233

prune216.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite107.0ms

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:

66.0ms	(/ (+ (- 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)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
46.0ms	(- (* b b) (* (* 4.0 a) c))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify826.0ms

Counts

82 → 82

Iterations

Useful iterations: done (823.0ms)

Iter	Nodes	Cost
0	154	1565
1	401	1461
2	1353	1245
done	5001	1233

prune225.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

57.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
41.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
47.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify854.0ms

Counts

130 → 130

Iterations

Useful iterations: done (849.0ms)

Iter	Nodes	Cost
0	220	3137
1	497	2801
2	1461	2561
done	5000	2481

prune258.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)))
1.0b	(- (pow b 2) (* 4.0 (* a c)))
1.2b	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
21.3b	(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

75.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)))
14.0ms	(- (pow b 2) (* 4.0 (* a c)))
66.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
16.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

series348.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)))
46.0ms	(- (pow b 2) (* 4.0 (* a c)))
82.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
74.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify833.0ms

Counts

130 → 130

Iterations

Useful iterations: done (829.0ms)

Iter	Nodes	Cost
0	217	3137
1	490	2793
2	1402	2565
done	5001	2485

prune248.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.4b

regimes297.0ms

Accuracy

83.5% (4.6b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 33.5b

bsearch215.0ms

Steps

Iters	Range		Point
6	2.0335150395734557e+19	1.0746392320557105e+20	2.9494967590524297e+19
6	3.6410892437809104e-110	3.0960233903298005e-109	3.7052502960789305e-110
8	1.0691773024250323e-170	5.5548132533506025e-168	2.175674080408203e-169
9	-1.4924982923623064e+60	-5.817343306680769e+54	-1.4784065354805617e+60

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	44	85
1	60	71
done	60	71

end0.0ms

sample1.3s

Algorithm

intervals

Results

252.0ms	1042×	body	2560	valid
242.0ms	5926×	body	80	valid
176.0ms	905×	body	1280	valid
107.0ms	2856×	body	80	nan
73.0ms	463×	body	640	valid
32.0ms	102×	body	5120	valid
28.0ms	225×	body	320	valid
7.0ms	95×	body	160	valid