Details

sample143.0ms

Algorithm

intervals

Results

16.0ms	206×	body	80	valid
13.0ms	29×	body	2560	valid
10.0ms	28×	body	1280	valid
6.0ms	96×	body	80	nan
4.0ms	12×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify110.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	46	13
4	49	13
done	49	13

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize26.0ms

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))))
1.2b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite235.0ms

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-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

112.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(- (* b_2 b_2) (* a c))
26.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
125.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(- (* b_2 b_2) (* a c))
119.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

183 → 183

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	242	5993
1	546	4313
2	1414	3549
done	5001	3001

prune513.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 257

Calls

4 calls:

62.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
34.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
110.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
53.0ms	(- (* b_2 b_2) (* a c))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

269 → 269

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	351	8660
1	754	6525
2	1728	5553
done	5000	4912

prune571.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.6b

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.0b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.3b	(/ (+ 0 (* a c)) a)
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite87.0ms

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-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
27.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms	(/ (+ 0 (* a c)) a)
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(/ (+ 0 (* a c)) a)
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.6s

Counts

103 → 103

Iterations

Useful iterations: 3 (3.0s)

Iter	Nodes	Cost
0	157	1176
1	358	993
2	1188	902
3	4318	852
done	5000	852

prune422.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.2b	(- (* b_2 b_2) (* a c))
2.0b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

80.0ms	(/ c (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
17.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(/ c (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
48.0ms	(- (* b_2 b_2) (* a c))
130.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

111 → 111

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	154	1589
1	351	1476
2	961	1301
3	2615	1284
done	5000	1275

prune369.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 7.6b

regimes351.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.3b

bsearch261.0ms

Steps

Iters	Range		Point
9	1.2073698495971617e+61	8.75865749938149e+67	5.099089738165329e+67
10	1.610059141238142e-239	1.618698210595833e-224	2.094358742794728e-239
10	-3.742210988141449e+103	-1.0235731023437291e+92	-3.359953003549157e+103

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	53
1	33	53
done	33	53

end0.0ms

sample3.4s

Algorithm

intervals

Results

993.0ms	5837×	body	80	valid
927.0ms	1052×	body	2560	valid
425.0ms	898×	body	1280	valid
223.0ms	2844×	body	80	nan
110.0ms	464×	body	640	valid
96.0ms	112×	body	5120	valid
43.0ms	238×	body	320	valid
15.0ms	108×	body	160	valid