Details

sample93.0ms

Algorithm

intervals

Results

16.0ms	9×	body	320	valid
16.0ms	36×	body	2560	valid
12.0ms	176×	body	80	valid
11.0ms	33×	body	1280	valid
5.0ms	20×	body	640	valid
5.0ms	79×	body	80	nan
3.0ms	6×	body	5120	valid
0.0ms	3×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
4	44
3	41
2	32
1	18
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.6b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
36×	`times-frac`
31×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/l*`
9×	`distribute-lft-out`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`neg-mul-1`
3×	`associate-/r*` `sqrt-prod`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `distribute-frac-neg` `div-inv`

Counts

4 → 106

Calls

4 calls:

85.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
6.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
63.0ms	(- (* b_2 b_2) (* a c))
86.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify907.0ms

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	1823
1	448
0	186

prune643.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.7b

localize20.0ms

Local error

Found 4 expressions with local error:

1.1b	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
5.2b	(/ (- (/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
6.9b	(/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

318×	`times-frac`
270×	`add-sqr-sqrt`
211×	`*-un-lft-identity`
153×	`add-cube-cbrt`
96×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
58×	`difference-of-squares`
55×	`associate-/l*`
32×	`sqrt-prod`
29×	`distribute-lft-out--`
18×	`associate-/r/`
11×	`flip3--` `flip--`
10×	`div-inv`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`pow1`
4×	`neg-mul-1`
3×	`associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-div` `div-exp`
1×	`neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-sub` `distribute-frac-neg` `flip-+` `distribute-neg-frac`

Counts

4 → 299

Calls

4 calls:

15.0ms	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
105.0ms	(/ (- (/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
74.0ms	(/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series718.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
237.0ms	(/ (- (/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
305.0ms	(/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify639.0ms

Counts

311 → 311

Iterations

Iter	Nodes
done	5000
1	1185
0	473

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.6b

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
5.3b	(* (- (/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))) (/ 1 a))
6.9b	(/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
65×	`times-frac`
52×	`associate-l`
44×	`add-cube-cbrt`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
22×	`difference-of-squares`
15×	`add-exp-log`
14×	`sqrt-prod`
13×	`associate-r`
11×	`add-cbrt-cube` `distribute-lft-out--`
7×	`pow1`
6×	`associate-/r*` `associate-/r/` `add-log-exp`
5×	`flip3--` `flip--`
4×	`prod-exp` `div-inv`
3×	`div-exp` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `sqrt-div` `cbrt-unprod` `distribute-neg-frac` `associate-/l/`
1×	`distribute-lft-neg-out` `frac-times` `rem-sqrt-square` `rec-exp` `clear-num` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 161

Calls

4 calls:

13.0ms	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
228.0ms	(* (- (/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))) (/ 1 a))
76.0ms	(/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series662.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- b_2 (sqrt (- (* b_2 b_2) (* a c))))
231.0ms	(* (- (/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))) (/ 1 a))
267.0ms	(/ (+ 0 (* a c)) (- b_2 (sqrt (- (* b_2 b_2) (* a c)))))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	4568
1	822
0	277

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ -1 (* a (- b_2 (sqrt (- (pow b_2 2) (* c a))))))
1.1b	(- b_2 (sqrt (- (pow b_2 2) (* c a))))
14.2b	(* (* c a) (/ -1 (* a (- b_2 (sqrt (- (pow b_2 2) (* c a)))))))
24.4b	(sqrt (- (pow b_2 2) (* c a)))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
12×	`prod-exp` `cbrt-unprod`
11×	`*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `add-cube-cbrt`
6×	`cbrt-undiv` `times-frac` `div-exp` `add-log-exp`
5×	`associate-*r/`
4×	`flip3--` `associate-/r/` `sqrt-prod` `flip--`
3×	`pow-prod-down` `associate-/l*`
2×	`sqrt-div` `div-inv` `difference-of-squares`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `-commutative` `distribute-lft-out--`

Counts

4 → 86

Calls

4 calls:

29.0ms	(/ -1 (* a (- b_2 (sqrt (- (pow b_2 2) (* c a))))))
40.0ms	(- b_2 (sqrt (- (pow b_2 2) (* c a))))
144.0ms	(* (* c a) (/ -1 (* a (- b_2 (sqrt (- (pow b_2 2) (* c a)))))))
11.0ms	(sqrt (- (pow b_2 2) (* c a)))

series705.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(/ -1 (* a (- b_2 (sqrt (- (pow b_2 2) (* c a))))))
108.0ms	(- b_2 (sqrt (- (pow b_2 2) (* c a))))
260.0ms	(* (* c a) (/ -1 (* a (- b_2 (sqrt (- (pow b_2 2) (* c a)))))))
94.0ms	(sqrt (- (pow b_2 2) (* c a)))

simplify2.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	3032
1	514
0	189

prune573.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.6b

regimes462.0ms

Accuracy

88.2% (3.3b remaining)

Error of 8.6b against oracle of 5.3b and baseline of 33.1b

bsearch255.0ms

Steps

Iters	Range		Point
9	2.1340360609407003e+79	6.102484722804822e+84	1.7649737847920912e+83
7	-2.648738865760589e-143	-3.958861499835511e-145	-4.7924462561183435e-145
9	-31812840434242.992	-117892343.0362464	-9661478263987.111

simplify21.0ms

Iterations

Iter	Nodes
done	77
3	77
2	71
1	54
0	37

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	5798×	body	80	valid
448.0ms	1066×	body	2560	valid
387.0ms	921×	body	1280	valid
279.0ms	2878×	body	80	nan
121.0ms	458×	body	640	valid
48.0ms	238×	body	320	valid
45.0ms	85×	body	5120	valid
17.0ms	110×	body	160	valid