Details

sample44.0ms

Algorithm

intervals

Results

7.0ms	173×	body	80	valid
6.0ms	29×	body	2560	valid
5.0ms	27×	body	1280	valid
3.0ms	83×	body	80	nan
3.0ms	21×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	12×	body	320	valid
1.0ms	11×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9
done	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.8b	(- (* b b) (* 4.0 (* a c)))
2.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite109.0ms

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:

65.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
24.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms	(- (* b b) (* 4.0 (* a c)))
86.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674
done	5002	674

prune230.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* b b) (* 4.0 (* a c)))
3.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
84.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
58.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* 4.0 (* a c)))
164.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
195.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify94.0ms

Counts

160 → 160

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	628	2579
1	2954	2333
2	5001	2320
done	5001	2320

prune409.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* b b) (* 4.0 (* a c)))
3.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* 4.0 (* a c))) 1)))) (* 2.0 a))
13.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* 4.0 (* a c))) 1))))
24.6b	(sqrt (pow (- (* b b) (* 4.0 (* a c))) 1))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
114×	`times-frac`
86×	`*-un-lft-identity`
46×	`add-cube-cbrt`
40×	`difference-of-squares`
37×	`sqrt-prod`
36×	`associate-/l*`
20×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube`
14×	`unpow-prod-down`
12×	`sqr-pow`
10×	`distribute-rgt-neg-in` `associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `flip3--` `flip--` `div-inv`
3×	`rem-sqrt-square` `associate-/l/`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 172

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
123.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* 4.0 (* a c))) 1)))) (* 2.0 a))
86.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* 4.0 (* a c))) 1))))
16.0ms	(sqrt (pow (- (* b b) (* 4.0 (* a c))) 1))

series495.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* 4.0 (* a c)))
168.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* 4.0 (* a c))) 1)))) (* 2.0 a))
200.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* 4.0 (* a c))) 1))))
79.0ms	(sqrt (pow (- (* b b) (* 4.0 (* a c))) 1))

simplify113.0ms

Counts

184 → 184

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	726	3201
1	3320	2887
2	5002	2857
done	5002	2857

prune508.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ b (pow (- (* b b) (* 4.0 (* a c))) 1/2))
1.8b	(- (* b b) (* 4.0 (* a c)))
16.5b	(/ (* 4.0 (* a c)) a)
24.6b	(pow (- (* b b) (* 4.0 (* a c))) 1/2)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
5×	`pow1`
3×	`cbrt-undiv` `unpow-prod-down` `pow-unpow` `times-frac` `div-exp` `prod-exp` `associate-/r*` `cbrt-unprod`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `pow-exp` `clear-num` `sum-log` `flip--` `flip-+` `div-inv` `distribute-lft-out` `associate-/l*` `unpow1/2` `sqr-pow`

Counts

4 → 65

Calls

4 calls:

26.0ms	(+ b (pow (- (* b b) (* 4.0 (* a c))) 1/2))
9.0ms	(- (* b b) (* 4.0 (* a c)))
23.0ms	(/ (* 4.0 (* a c)) a)
11.0ms	(pow (- (* b b) (* 4.0 (* a c))) 1/2)

series206.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ b (pow (- (* b b) (* 4.0 (* a c))) 1/2))
49.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(/ (* 4.0 (* a c)) a)
74.0ms	(pow (- (* b b) (* 4.0 (* a c))) 1/2)

simplify48.0ms

Counts

77 → 77

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	364	484
1	1720	425
2	5002	411
done	5002	411

prune208.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.0b

regimes467.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.4b

bsearch171.0ms

Steps

Iters	Range		Point
6	9.002760019060421e+93	3.662435776182418e+94	1.6239010391513743e+94
10	1.893883468504485e-228	8.282891733345819e-215	1.923093372319421e-228
8	-3.942677352963429e+147	-2.908826449852181e+144	-1.3882094406717058e+145

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	26
1	53	26
2	53	26
done	53	26

end0.0ms

sample1.3s

Algorithm

intervals

Results

261.0ms	1149×	body	2560	valid
243.0ms	5800×	body	80	valid
161.0ms	887×	body	1280	valid
107.0ms	2854×	body	80	nan
70.0ms	474×	body	640	valid
30.0ms	254×	body	320	valid
28.0ms	92×	body	5120	valid
8.0ms	108×	body	160	valid