Details

sample97.0ms

Algorithm

intervals

Results

36.0ms	29×	body	2560	valid
15.0ms	204×	body	80	valid
11.0ms	31×	body	1280	valid
8.0ms	106×	body	80	nan
3.0ms	9×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify76.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) a)
0.8b	(- (* b b) (* a (* 4.0 c)))
0.8b	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
24.3b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 118

Calls

4 calls:

89.0ms	(/ (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) a)
14.0ms	(- (* b b) (* a (* 4.0 c)))
56.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
18.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) a)
83.0ms	(- (* b b) (* a (* 4.0 c)))
100.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
107.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify2.5s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	2132
1	512
0	199

prune842.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ a (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
0.8b	(- (* b b) (* a (* 4.0 c)))
0.8b	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
24.3b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 117

Calls

4 calls:

68.0ms	(/ a (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
14.0ms	(- (* b b) (* a (* 4.0 c)))
69.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
9.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series616.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(/ a (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
86.0ms	(- (* b b) (* a (* 4.0 c)))
132.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
108.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.7s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	1830
1	470
0	194

prune690.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) (/ 1 a))
0.8b	(- (* b b) (* a (* 4.0 c)))
0.8b	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
24.3b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 119

Calls

4 calls:

149.0ms	(* (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) (/ 1 a))
7.0ms	(- (* b b) (* a (* 4.0 c)))
54.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
19.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) (/ 1 a))
74.0ms	(- (* b b) (* a (* 4.0 c)))
128.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
103.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify2.7s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	3472
1	583
0	219

prune719.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
0.8b	(- (* b b) (* a (* 4.0 c)))
0.8b	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
24.3b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-exp-log` `add-log-exp`
7×	`fma-neg`
6×	`pow1` `associate-/r*` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 121

Calls

4 calls:

45.0ms	(/ 1 (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
7.0ms	(- (* b b) (* a (* 4.0 c)))
67.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
9.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ 1 (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
65.0ms	(- (* b b) (* a (* 4.0 c)))
110.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
109.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify2.6s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	2064
1	482
0	196

prune720.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.7b

regimes532.0ms

Accuracy

83.9% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 34.5b

bsearch174.0ms

Steps

Iters	Range		Point
8	1.5119020269574885e-23	1.8921341643334238e-20	9.136492990928292e-23
6	-1.7989235910837076e+89	-1.4585470499056154e+88	-1.7633154797394035e+89

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	30

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.2s	1057×	body	2560	valid
560.0ms	5865×	body	80	valid
383.0ms	112×	body	160	valid
378.0ms	902×	body	1280	valid
269.0ms	2875×	body	80	nan
171.0ms	434×	body	640	valid
105.0ms	124×	body	5120	valid
50.0ms	224×	body	320	valid