Details

sample105.0ms

Algorithm

intervals

Results

39.0ms	36×	body	2560	valid
14.0ms	188×	body	80	valid
8.0ms	24×	body	1280	valid
8.0ms	108×	body	80	nan
5.0ms	17×	body	640	valid
3.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify106.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite177.0ms

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:

102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
16.0ms	(- (* b b) (* (* 4.0 a) c))
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series504.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
64.0ms	(- (* b b) (* (* 4.0 a) c))
116.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
117.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

102 → 102

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	167	1697
1	451	1588
2	2113	1361
done	5000	1352

prune606.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize39.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.0b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

50.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
162.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
111.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
27.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series749.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
241.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
281.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
115.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts

244 → 244

Iterations

Useful iterations: 2 (888.0ms)

Iter	Nodes	Cost
0	335	10067
1	848	7629
2	4744	6524
done	5000	6524

prune687.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

localize27.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b	(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
8.0b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
71×	`add-cube-cbrt`
60×	`prod-diff`
51×	`add-exp-log`
46×	`times-frac`
41×	`sqrt-prod`
29×	`distribute-rgt-neg-in`
27×	`associate-l` `add-cbrt-cube`
21×	`distribute-lft-neg-in`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
10×	`fma-neg`
8×	`cbrt-undiv` `cbrt-unprod` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-/r*`
4×	`expm1-log1p-u` `rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `diff-log` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 227

Calls

4 calls:

37.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
148.0ms	(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
99.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
177.0ms	(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
229.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
99.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify434.0ms

Counts

239 → 239

Iterations

Useful iterations: done (425.0ms)

Iter	Nodes	Cost
0	340	9661
1	950	7185
done	5000	6071

prune603.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.4b	(/ (* (* 4.0 a) c) (* 2.0 a))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
32.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
30.0ms	(/ (* (* 4.0 a) c) (* 2.0 a))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b b) (* (* 4.0 a) c))
90.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(/ (* (* 4.0 a) c) (* 2.0 a))
86.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

162 → 162

Iterations

Useful iterations: 2 (714.0ms)

Iter	Nodes	Cost
0	240	6252
1	628	4277
2	3819	3321
done	5000	3321

prune393.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.0b

regimes119.0ms

Accuracy

94.5% (1.3b remaining)

Error of 6.6b against oracle of 5.3b and baseline of 29.5b

bsearch192.0ms

Steps

Iters	Range	Point
6	1.9101351599902807e+102	2.525038855038462e+103	1.4066822953018111e+103
5	-1.7140185252229956e-250	-6.426569281983545e-251	-8.441935351115962e-251
10	-2.8734245235493903e+48	-2.602501271628617e+37	-2.8472042802820317e+48

Iters

Range

Point

1.9101351599902807e+102

2.525038855038462e+103

1.4066822953018111e+103

-1.7140185252229956e-250

-6.426569281983545e-251

-8.441935351115962e-251

-2.8734245235493903e+48

-2.602501271628617e+37

-2.8472042802820317e+48

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	36	63
1	44	61
done	44	61

end0.0ms

sample2.5s

Algorithm

intervals

Results

562.0ms	2902×	body	80	nan
442.0ms	1074×	body	2560	valid
423.0ms	5856×	body	80	valid
375.0ms	903×	body	1280	valid
132.0ms	451×	body	640	valid
93.0ms	223×	body	320	valid
47.0ms	112×	body	5120	valid
11.0ms	111×	body	160	valid