Details

sample75.0ms

Algorithm

intervals

Results

12.0ms	43×	body	2560	valid
10.0ms	190×	body	80	valid
8.0ms	85×	body	80	nan
6.0ms	24×	body	1280	valid
2.0ms	12×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify530.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	140
7	140
6	138
5	135
4	132
3	113
2	62
1	29
0	14

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize89.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite280.0ms

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-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

168.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms	(- (* b b) (* 4.0 (* a c)))
52.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
36.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series588.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
106.0ms	(- (* b b) (* 4.0 (* a c)))
148.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
162.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.1s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	1801
1	605
0	245

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b) (- (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.8b	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
8×	`distribute-lft-out` `add-log-exp`
6×	`associate-/r*` `fma-def` `add-cbrt-cube` `add-exp-log` `sqrt-prod`
5×	`distribute-lft-neg-in` `pow1` `neg-mul-1` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `div-inv`

Counts

4 → 107

Calls

4 calls:

128.0ms	(/ (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b) (- (* 2.0 a)))
12.0ms	(- (* b b) (* 4.0 (* a c)))
43.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b) (- (* 2.0 a)))
88.0ms	(- (* b b) (* 4.0 (* a c)))
155.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
156.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.2s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	1363
1	434
0	182

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in` `add-exp-log`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sub-neg` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

200.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
24.0ms	(- (* b b) (* 4.0 (* a c)))
82.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series518.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
74.0ms	(- (* b b) (* 4.0 (* a c)))
125.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
134.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.3s

Counts

181 → 181

Iterations

Iter	Nodes
done	5005
2	1976
1	669
0	271

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.8b

localize124.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.8b	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) a)
17.8b	(- (* b b) (* b b))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
10×	`fma-def` `add-log-exp`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r` `sqrt-prod` `associate-/l`
2×	`sum-log` `flip3-+` `flip3--` `sqrt-div` `associate-+l-` `flip-+` `flip--` `distribute-lft-out` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `+-inverses` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 100

Calls

4 calls:

42.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
179.0ms	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) a)
22.0ms	(- (* b b) (* b b))
29.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
34.0ms	(/ (+ (- (* b b) (* b b)) (* 4.0 (* a c))) a)
4.0ms	(- (* b b) (* b b))
153.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify7.3s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	4345
2	1096
1	414
0	171

prune1.4s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.7b

regimes1.3s

Accuracy

92.9% (1.8b remaining)

Error of 7.1b against oracle of 5.3b and baseline of 30.3b

bsearch317.0ms

Steps

Iters	Range		Point
8	4.664337482673326e-05	0.17679972651571432	0.17389787404847717
10	-2.8267030274469295e-306	1.290469777777001e-296	3.411004807395853e-303
8	-1.3198903247987554e+155	-1.1250773400730914e+152	-6.056690026719334e+153

simplify22.0ms

Iterations

Iter	Nodes
done	49
2	49
1	47
0	35

end0.0ms

sample3.0s

Algorithm

intervals

Results

858.0ms	5823×	body	80	valid
552.0ms	1103×	body	2560	valid
375.0ms	877×	body	1280	valid
353.0ms	2975×	body	80	nan
144.0ms	249×	body	320	valid
141.0ms	440×	body	640	valid
65.0ms	125×	body	5120	valid
16.0ms	121×	body	160	valid