Details

sample41.0ms

Algorithm

intervals

Results

6.0ms	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

simplify11.0ms

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

localize15.0ms

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)))

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:

68.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* 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)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
46.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674
done	5001	674

prune216.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.1b

localize16.0ms

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)))

rewrite167.0ms

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:

8.0ms	(- (* b b) (* (* 4.0 a) c))
85.0ms	(/ (/ (+ 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)))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
151.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
186.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Counts

160 → 160

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	640	2579
1	3155	2333
2	5001	2320
done	5001	2320

prune402.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.9b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
24×	`sqrt-pow1` `sqrt-div`
22×	`pow1`
21×	`times-frac`
18×	`add-cube-cbrt`
11×	`pow1/2` `sqrt-prod`
9×	`flip3--` `flip--`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `distribute-rgt-neg-in` `add-log-exp`
3×	`rem-sqrt-square` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`associate-r/` `associate-l/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 109

Calls

4 calls:

37.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(sqrt (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify82.0ms

Counts

121 → 121

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	435	1781
1	1972	1578
2	5002	1556
done	5002	1556

prune363.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.9b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
21×	`times-frac`
19×	`add-cube-cbrt`
13×	`sqrt-prod`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1` `associate-/r*`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
4×	`flip3--` `distribute-rgt-neg-in` `flip--` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 92

Calls

4 calls:

57.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify72.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	346	1251
1	1713	1177
2	5001	1165
done	5001	1165

prune394.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.9b

regimes327.0ms

Accuracy

88.1% (3.2b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 32.4b

bsearch156.0ms

Steps

Iters	Range	Point
4	9.113314976006761e+77	1.3987841324983815e+78	9.191824015256067e+77
10	1.0608417311709853e-197	3.7252229925148765e-182	2.8749878520377998e-182
8	-3.942677352963429e+147	-2.908826449852181e+144	-1.3882094406717058e+145

Iters

Range

Point

9.113314976006761e+77

1.3987841324983815e+78

9.191824015256067e+77

1.0608417311709853e-197

3.7252229925148765e-182

2.8749878520377998e-182

-3.942677352963429e+147

-2.908826449852181e+144

-1.3882094406717058e+145

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	35
1	50	35
2	50	35
done	50	35

end0.0ms

sample1.2s

Algorithm

intervals

Results

246.0ms	1149×	body	2560	valid
224.0ms	5800×	body	80	valid
159.0ms	887×	body	1280	valid
112.0ms	2854×	body	80	nan
65.0ms	474×	body	640	valid
26.0ms	254×	body	320	valid
24.0ms	92×	body	5120	valid
8.0ms	108×	body	160	valid