Details

sample99.0ms

Algorithm

intervals

Results

21.0ms	193×	body	80	valid
21.0ms	31×	body	2560	valid
10.0ms	97×	body	80	nan
10.0ms	18×	body	1280	valid
8.0ms	18×	body	640	valid
5.0ms	6×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify173.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.4b	(- (* b b) (* 4 (* a c)))
0.6b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
23.1b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite168.0ms

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:

110.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
11.0ms	(- (* b b) (* 4 (* a c)))
28.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
18.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
53.0ms	(- (* b b) (* 4 (* a c)))
110.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
116.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.7s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1254
1	400
0	154

prune961.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
0.4b	(+ (* b b) (* c (* a -4)))
0.6b	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
23.1b	(sqrt (+ (* b b) (* c (* a -4))))

rewrite156.0ms

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:

76.0ms	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
13.0ms	(+ (* b b) (* c (* a -4)))
49.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
16.0ms	(sqrt (+ (* b b) (* c (* a -4))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
61.0ms	(+ (* b b) (* c (* a -4)))
117.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
94.0ms	(sqrt (+ (* b b) (* c (* a -4))))

simplify1.7s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1334
1	412
0	156

prune507.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (+ (* b b) (* c (* a -4)))))))
0.4b	(+ (* b b) (* c (* a -4)))
0.6b	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
23.1b	(sqrt (+ (* b b) (* c (* a -4))))

rewrite180.0ms

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:

95.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (+ (* b b) (* c (* a -4)))))))
20.0ms	(+ (* b b) (* c (* a -4)))
43.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
15.0ms	(sqrt (+ (* b b) (* c (* a -4))))

series477.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (+ (* b b) (* c (* a -4)))))))
77.0ms	(+ (* b b) (* c (* a -4)))
117.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
124.0ms	(sqrt (+ (* b b) (* c (* a -4))))

simplify2.0s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
2	1858
1	585
0	231

prune765.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
23.1b	(sqrt (+ (* b b) (* c (* a -4))))
23.1b	(sqrt (+ (* b b) (* c (* a -4))))
23.1b	(sqrt (+ (* b b) (* c (* a -4))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `flip3--` `neg-log` `flip--`

Counts

4 → 67

Calls

4 calls:

23.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
12.0ms	(sqrt (+ (* b b) (* c (* a -4))))
16.0ms	(sqrt (+ (* b b) (* c (* a -4))))
17.0ms	(sqrt (+ (* b b) (* c (* a -4))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
76.0ms	(sqrt (+ (* b b) (* c (* a -4))))
85.0ms	(sqrt (+ (* b b) (* c (* a -4))))
103.0ms	(sqrt (+ (* b b) (* c (* a -4))))

simplify2.1s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
3	2165
2	644
1	211
0	88

prune607.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.2b

regimes520.0ms

Accuracy

82.8% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 33.1b

bsearch224.0ms

Steps

Iters	Range		Point
8	2.5230591910300896e+45	6.095379443414697e+48	5.6488521390017767e+48
8	-1.0278134165845925e-62	-2.127595877901746e-66	-1.1962309819144974e-65

simplify4.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample3.1s

Algorithm

intervals

Results

894.0ms	903×	body	1280	valid
662.0ms	1066×	body	2560	valid
641.0ms	5849×	body	80	valid
334.0ms	3069×	body	80	nan
142.0ms	464×	body	640	valid
73.0ms	122×	body	5120	valid
56.0ms	218×	body	320	valid
25.0ms	114×	body	160	valid