Details

sample164.0ms

Algorithm

intervals

Results

51.0ms	37×	body	1280	valid
29.0ms	32×	body	2560	valid
28.0ms	184×	body	80	valid
17.0ms	108×	body	80	nan
9.0ms	15×	body	640	valid
5.0ms	4×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify163.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.8b	(- (* b b) (* 4 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
23.2b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 81

Calls

4 calls:

68.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
16.0ms	(- (* b b) (* 4 (* a c)))
23.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series401.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
72.0ms	(- (* b b) (* 4 (* a c)))
123.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
92.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.4s

Counts

93 → 93

Iterations

Iter	Nodes
3	4255
2	1194
1	398
0	154

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 c) a)))) (* 2 a))
0.8b	(+ (* b b) (* (* -4 c) a))
1.1b	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
23.2b	(sqrt (+ (* b b) (* (* -4 c) a)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`insert-posit16`
3×	`distribute-rgt-neg-in`
2×	`cbrt-undiv` `flip3-+` `flip3--` `sqrt-div` `diff-log` `div-exp` `flip-+` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 80

Calls

4 calls:

51.0ms	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 c) a)))) (* 2 a))
9.0ms	(+ (* b b) (* (* -4 c) a))
25.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
10.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (- (- b) (sqrt (+ (* b b) (* (* -4 c) a)))) (* 2 a))
58.0ms	(+ (* b b) (* (* -4 c) a))
119.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
90.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))

simplify3.1s

Counts

92 → 92

Iterations

Iter	Nodes
3	5001
2	1314
1	409
0	156

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))))
0.8b	(+ (* b b) (* (* -4 c) a))
1.1b	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
23.2b	(sqrt (+ (* b b) (* (* -4 c) a)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `flip3--` `div-inv` `flip--`
4×	`insert-posit16`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`flip3-+` `sqrt-div` `diff-log` `flip-+`
1×	`associate--l-` `neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 128

Calls

4 calls:

52.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))))
9.0ms	(+ (* b b) (* (* -4 c) a))
23.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
7.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))))
70.0ms	(+ (* b b) (* (* -4 c) a))
117.0ms	(- (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
106.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))

simplify5.3s

Counts

140 → 140

Iterations

Iter	Nodes
3	6356
2	1792
1	567
0	231

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
0.8b	(+ (* b b) (* (* -4 c) a))
14.7b	(/ (+ (* (* c 4) a) 0) (/ a 1/2))
23.2b	(sqrt (+ (* b b) (* (* -4 c) a)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
51×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
47×	`add-cube-cbrt`
13×	`associate-/r*`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `div-inv`
4×	`flip3-+` `flip-+` `insert-posit16`
3×	`cbrt-undiv` `sum-log` `div-exp` `sqrt-prod` `associate-/l*`
2×	`+-commutative` `sqrt-div` `distribute-lft-out` `associate-/l/`
1×	`neg-sub0` `rem-sqrt-square` `clear-num` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-/r/` `associate-+l-`

Counts

4 → 117

Calls

4 calls:

32.0ms	(+ (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
10.0ms	(+ (* b b) (* (* -4 c) a))
41.0ms	(/ (+ (* (* c 4) a) 0) (/ a 1/2))
7.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(+ (- b) (sqrt (+ (* b b) (* (* -4 c) a))))
62.0ms	(+ (* b b) (* (* -4 c) a))
14.0ms	(/ (+ (* (* c 4) a) 0) (/ a 1/2))
104.0ms	(sqrt (+ (* b b) (* (* -4 c) a)))

simplify837.0ms

Counts

129 → 129

Iterations

Iter	Nodes
2	2363
1	673
0	254

prune2.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

regimes346.0ms

Accuracy

83.5% (4.2b remaining)

Error of 9.9b against oracle of 5.7b and baseline of 31.1b

bsearch265.0ms

Steps

Iters	Range		Point
9	9.393510413029077e+92	8.086830674284809e+100	2.2373425340727037e+98
8	-1.4632440505401307e-54	-4.960915650215066e-57	-1.4266250849096228e-56

simplify5.0ms

Iterations

Iter	Nodes
2	32
1	32
0	26

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.3s	945×	body	1280	valid
1.1s	5917×	body	80	valid
1.0s	987×	body	2560	valid
441.0ms	2881×	body	80	nan
295.0ms	475×	body	640	valid
180.0ms	111×	body	5120	valid
78.0ms	192×	body	320	valid
30.0ms	112×	body	160	valid