Details

sample191.0ms

Algorithm

intervals

Results

15.0ms	189×	body	80	valid
14.0ms	36×	body	2560	valid
8.0ms	25×	body	1280	valid
7.0ms	104×	body	80	nan
4.0ms	16×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify71.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	49
4	49
3	46
2	33
1	19
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 171

Calls

4 calls:

64.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
42.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series626.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
126.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
112.0ms	(- (* b_2 b_2) (* a c))
175.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	1505
1	573
0	244

prune869.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 169

Calls

4 calls:

107.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
48.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
115.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(- (* b_2 b_2) (* a c))
121.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	1786
1	639
0	263

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* c a))))) a)
0.7b	(+ b_2 (sqrt (- (* b_2 b_2) (* c a))))
0.8b	(- (* b_2 b_2) (* c a))
26.2b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
36×	`times-frac`
32×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/l*`
9×	`distribute-lft-out`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `neg-mul-1` `log1p-expm1-u`
3×	`associate-/r*` `fma-def` `sqrt-prod`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `distribute-frac-neg` `div-inv`

Counts

4 → 119

Calls

4 calls:

68.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* c a))))) a)
14.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* c a))))
6.0ms	(- (* b_2 b_2) (* c a))
9.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* c a))))) a)
76.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* c a))))
36.0ms	(- (* b_2 b_2) (* c a))
76.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify3.0s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
3	4857
2	1278
1	464
0	198

prune798.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

localize57.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
16.0b	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* c a)) a)
20.3b	(- (* b_2 b_2) (* b_2 b_2))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `sqrt-prod` `flip--` `associate-/l`
2×	`sub-neg` `fma-neg` `sqrt-div` `diff-log` `prod-diff` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out--` `pow1/2` `+-inverses` `div-sub` `div-exp` `associate-+l-` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

6.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* c a)) a)
12.0ms	(- (* b_2 b_2) (* b_2 b_2))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* c a)) a)
1.0ms	(- (* b_2 b_2) (* b_2 b_2))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	5036
3	2534
2	774
1	346
0	149

prune594.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

regimes398.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.6b

bsearch217.0ms

Steps

Iters	Range	Point
6	5.84949006905106e+100	6.027833473435204e+101	3.355858625783055e+101
9	-1.4598085821258646e-291	-1.0697531889019586e-297	-1.0850002786366243e-297
6	-1.7989235910837076e+89	-1.4585470499056154e+88	-1.7633154797394035e+89

Iters

Range

Point

5.84949006905106e+100

6.027833473435204e+101

3.355858625783055e+101

-1.4598085821258646e-291

-1.0697531889019586e-297

-1.0850002786366243e-297

-1.7989235910837076e+89

-1.4585470499056154e+88

-1.7633154797394035e+89

simplify13.0ms

Iterations

Iter	Nodes
done	42
2	42
1	41
0	33

end0.0ms

sample3.5s

Algorithm

intervals

Results

702.0ms	2885×	body	80	nan
475.0ms	1063×	body	2560	valid
429.0ms	5821×	body	80	valid
413.0ms	950×	body	1280	valid
245.0ms	475×	body	640	valid
152.0ms	239×	body	320	valid
60.0ms	116×	body	5120	valid
12.0ms	105×	body	160	valid