Details

sample41.0ms

Algorithm

intervals

Results

10.0ms	205×	body	80	valid
5.0ms	26×	body	2560	valid
4.0ms	26×	body	1280	valid
3.0ms	83×	body	80	nan
1.0ms	11×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	9
1	65	9
2	121	9
3	151	9
4	160	9
5	164	9
6	164	9
done	164	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.8b	(- (* b b) (* 4.0 (* a c)))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`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` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

75.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
31.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Counts

169 → 169

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5002	2128
done	5002	2128

prune348.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.1b

localize16.0ms

Local error

Found 4 expressions with local error:

24.4b	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
25.2b	(cbrt (- (* b b) (* 4.0 (* a c))))
25.2b	(cbrt (- (* b b) (* 4.0 (* a c))))
25.2b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 97

Calls

4 calls:

81.0ms	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
6.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
6.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
6.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
102.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
104.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
101.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify201.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	361	1930
1	971	1879
2	4455	1859
3	5001	1859
done	5001	1859

prune357.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.1b

localize19.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* b b) (* 4.0 (* a c)))
12.1b	(- (* (- (* (cbrt b) (cbrt b))) (cbrt b)) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
7×	`prod-diff`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log`

Counts

4 → 71

Calls

4 calls:

13.0ms	(- (* b b) (* 4.0 (* a c)))
40.0ms	(- (* (- (* (cbrt b) (cbrt b))) (cbrt b)) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* 4.0 (* a c)))
105.0ms	(- (* (- (* (cbrt b) (cbrt b))) (cbrt b)) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	313	928
1	1211	719
2	5001	691
done	5001	691

prune328.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 7.1b

localize24.0ms

Local error

Found 4 expressions with local error:

5.6b	(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
18.0b	(- (* (- (* (cbrt b) (cbrt b))) (cbrt b)) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `log-prod` `*-un-lft-identity` `exp-sum` `sqrt-prod`
9×	`prod-diff`
8×	`pow1`
6×	`exp-prod` `sqrt-div` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`sqrt-pow1` `pow1/2` `log-pow`
2×	`rem-sqrt-square` `log-div` `exp-diff`
1×	`sub-neg` `fma-neg` `diff-log` `rem-exp-log`

Counts

4 → 82

Calls

4 calls:

12.0ms	(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
33.0ms	(- (* (- (* (cbrt b) (cbrt b))) (cbrt b)) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
105.0ms	(- (* (- (* (cbrt b) (cbrt b))) (cbrt b)) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify51.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	370	1249
1	1239	885
2	5002	839
done	5002	839

prune354.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 7.1b

regimes400.0ms

Accuracy

88.5% (3.3b remaining)

Error of 8.8b against oracle of 5.6b and baseline of 33.9b

bsearch166.0ms

Steps

Iters	Range		Point
6	9.002760019060421e+93	3.662435776182418e+94	2.3684713380299e+94
11	-1.7080554663773614e-124	-7.974260657123443e-153	-4.593198226330854e-145
6	-1.1479397783227414e+56	-2.609655750368231e+55	-3.8603554551533365e+55

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	39
1	53	39
done	53	39

end0.0ms

sample1.2s

Algorithm

intervals

Results

229.0ms	1084×	body	2560	valid
220.0ms	5914×	body	80	valid
155.0ms	871×	body	1280	valid
98.0ms	2851×	body	80	nan
63.0ms	452×	body	640	valid
29.0ms	112×	body	5120	valid
21.0ms	209×	body	320	valid
7.0ms	103×	body	160	valid