Details

sample71.0ms

Algorithm

intervals

Results

14.0ms	35×	body	2560	valid
12.0ms	196×	body	80	valid
8.0ms	31×	body	1280	valid
5.0ms	89×	body	80	nan
3.0ms	11×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	3×	body	160	valid
0.0ms	2×	body	320	valid

simplify187.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	156
6	156
5	152
4	142
3	115
2	64
1	28
0	14

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
0.2b	(- (* b b) (* a (* 4.0 c)))
0.8b	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
23.0b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `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 → 77

Calls

4 calls:

74.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
14.0ms	(- (* b b) (* a (* 4.0 c)))
37.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
13.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
81.0ms	(- (* b b) (* a (* 4.0 c)))
140.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
105.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify823.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1700
1	416
0	157

prune563.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
0.2b	(- (* b b) (* a (* 4.0 c)))
0.8b	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
23.0b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 125

Calls

4 calls:

66.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
7.0ms	(- (* b b) (* a (* 4.0 c)))
20.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
8.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
64.0ms	(- (* b b) (* a (* 4.0 c)))
131.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
109.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.0s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	2588
1	595
0	228

prune575.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* a (* 4.0 c)))
0.2b	(* (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (/ 1 (* 2.0 a)))
0.8b	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
23.0b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sub-neg` `distribute-rgt-neg-in` `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 → 85

Calls

4 calls:

12.0ms	(- (* b b) (* a (* 4.0 c)))
96.0ms	(* (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (/ 1 (* 2.0 a)))
20.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
11.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* b b) (* a (* 4.0 c)))
128.0ms	(* (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (/ 1 (* 2.0 a)))
131.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
85.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	2439
1	491
0	183

prune484.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
3.8b	(/ (/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b)) (* 2.0 a))
10.6b	(/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
23.0b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
22×	`difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
14×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 141

Calls

4 calls:

46.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
130.0ms	(/ (/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b)) (* 2.0 a))
66.0ms	(/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
7.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series788.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
263.0ms	(/ (/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b)) (* 2.0 a))
300.0ms	(/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
130.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.7s

Counts

153 → 153

Iterations

Iter	Nodes
done	5001
2	3716
1	649
0	251

prune784.0ms

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 5.4b

regimes509.0ms

Accuracy

88.9% (3.2b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 33.9b

bsearch298.0ms

Steps

Iters	Range	Point
10	4.0721326822252617e+40	3.6590220876252264e+50	3.628799960716312e+50
9	-1.2594150945566125e-253	-8.579100536702327e-262	-1.0187986635785929e-256
6	-1.278587798556269e+59	-1.7736353873113924e+58	-1.9700105655521088e+58

Iters

Range

Point

4.0721326822252617e+40

3.6590220876252264e+50

3.628799960716312e+50

-1.2594150945566125e-253

-8.579100536702327e-262

-1.0187986635785929e-256

-1.278587798556269e+59

-1.7736353873113924e+58

-1.9700105655521088e+58

simplify7.0ms

Iterations

Iter	Nodes
done	41
1	41
0	35

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	1136×	body	2560	valid
902.0ms	5797×	body	80	valid
469.0ms	867×	body	1280	valid
271.0ms	2819×	body	80	nan
170.0ms	448×	body	640	valid
95.0ms	238×	body	320	valid
57.0ms	109×	body	5120	valid
15.0ms	103×	body	160	valid