Details

sample92.0ms

Algorithm

intervals

Results

19.0ms	35×	body	2560	valid
17.0ms	185×	body	80	valid
11.0ms	23×	body	1280	valid
9.0ms	103×	body	80	nan
7.0ms	19×	body	640	valid
1.0ms	7×	body	160	valid
1.0ms	4×	body	320	valid

simplify154.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
0.6b	(- (* b b) (* a (* 4.0 c)))
2.0b	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
22.7b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite127.0ms

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:

65.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
7.0ms	(- (* b b) (* a (* 4.0 c)))
39.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
15.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series430.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
59.0ms	(- (* b b) (* a (* 4.0 c)))
114.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
105.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify892.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1700
1	416
0	157

prune538.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
0.6b	(- (* b b) (* a (* 4.0 c)))
2.0b	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
22.7b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite143.0ms

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:

87.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
14.0ms	(- (* b b) (* a (* 4.0 c)))
27.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
7.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
61.0ms	(- (* b b) (* a (* 4.0 c)))
115.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
108.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.0s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	2588
1	595
0	228

prune503.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (/ 1 (* 2.0 a)))
0.6b	(- (* b b) (* a (* 4.0 c)))
2.0b	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
22.7b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite181.0ms

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:

129.0ms	(* (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (/ 1 (* 2.0 a)))
7.0ms	(- (* b b) (* a (* 4.0 c)))
27.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
14.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (/ 1 (* 2.0 a)))
72.0ms	(- (* b b) (* a (* 4.0 c)))
134.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
96.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	2395
1	491
0	183

prune536.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 2.0 (- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))) a)
0.6b	(- (* b b) (* 4.0 (* c a)))
2.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))
22.7b	(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
27×	`associate-l`
22×	`times-frac`
17×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1` `sqrt-prod`
4×	`distribute-rgt-neg-in` `flip3--` `flip--`
3×	`diff-log` `associate-r`
2×	`sub-neg` `sqrt-div` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 91

Calls

4 calls:

87.0ms	(* (/ 2.0 (- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))) a)
7.0ms	(- (* b b) (* 4.0 (* c a)))
24.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (/ 2.0 (- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))) a)
67.0ms	(- (* b b) (* 4.0 (* c a)))
117.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))
107.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))

simplify1.2s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	2132
1	450
0	180

prune648.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

regimes498.0ms

Accuracy

87.6% (3.6b remaining)

Error of 9.0b against oracle of 5.4b and baseline of 34.5b

bsearch261.0ms

Steps

Iters	Range	Point
9	6.258218916731328e+93	1.8883840965187804e+99	3.424685282990076e+98
7	-1.9525004674970017e-146	-8.640740768077714e-148	-8.752414306529149e-148
6	-1.745417689399421e+60	-1.2092396089946692e+59	-7.890025456402397e+59

Iters

Range

Point

6.258218916731328e+93

1.8883840965187804e+99

3.424685282990076e+98

-1.9525004674970017e-146

-8.640740768077714e-148

-8.752414306529149e-148

-1.745417689399421e+60

-1.2092396089946692e+59

-7.890025456402397e+59

simplify6.0ms

Iterations

Iter	Nodes
done	51
1	51
0	39

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	5781×	body	80	valid
531.0ms	1114×	body	2560	valid
454.0ms	884×	body	1280	valid
394.0ms	2931×	body	80	nan
191.0ms	464×	body	640	valid
98.0ms	250×	body	320	valid
67.0ms	110×	body	5120	valid
22.0ms	127×	body	160	valid