Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	197×	body	80	valid
6.0ms	28×	body	2560	valid
5.0ms	31×	body	1280	valid
3.0ms	77×	body	80	nan
1.0ms	11×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9
done	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

65.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
22.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series527.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	854
1	1658	750
2	5001	735
done	5001	735

prune297.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
3.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.7b	(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×	`expm1-log1p-u` `log1p-expm1-u` `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` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

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))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* 4.0 (* a c)))
149.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
177.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify115.0ms

Counts

170 → 170

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	665	2663
1	3259	2412
2	5001	2405
done	5001	2405

prune428.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.7b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
3.8b	(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))) (* 2.0 a))
11.7b	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

609×	`times-frac`
256×	`add-sqr-sqrt`
255×	`*-un-lft-identity`
159×	`add-cube-cbrt`
154×	`add-exp-log`
117×	`associate-/l*`
94×	`div-exp`
72×	`add-cbrt-cube`
48×	`distribute-lft-out--` `difference-of-squares`
40×	`cbrt-undiv`
30×	`prod-exp`
27×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
18×	`div-inv`
12×	`cbrt-unprod`
10×	`rec-exp` `1-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `frac-2neg` `sqrt-div` `div-sub` `clear-num` `associate-/r*` `associate-/r/` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 348

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
99.0ms	(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))) (* 2.0 a))
69.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* 4.0 (* a c)))
123.0ms	(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))) (* 2.0 a))
108.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify80.0ms

Counts

360 → 360

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1757	6116
1	5002	5494
done	5002	5494

prune772.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
14.5b	(/ (* a c) a)
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `times-frac` `diff-log` `associate-/r*` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 146

Calls

4 calls:

31.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(/ (* a c) a)
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(/ (* a c) a)
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify68.0ms

Counts

158 → 158

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	500	2930
1	1976	1883
2	5001	1788
done	5001	1788

prune299.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.7b

regimes229.0ms

Accuracy

87.9% (3.2b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 32.1b

bsearch176.0ms

Steps

Iters	Range		Point
8	5.30600492772346e+88	1.193256888551369e+92	4.74850993349346e+91
10	8.134666143579123e-130	4.886277919964174e-120	7.666823646884852e-125
8	-5.7211821970331905e+156	-1.4082798590396656e+153	-8.889080831912834e+153

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	28
1	45	28
done	45	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

229.0ms	1069×	body	2560	valid
222.0ms	5791×	body	80	valid
166.0ms	933×	body	1280	valid
113.0ms	2974×	body	80	nan
70.0ms	442×	body	640	valid
36.0ms	122×	body	5120	valid
25.0ms	244×	body	320	valid
10.0ms	126×	body	160	valid