Details

sample167.0ms

Algorithm

intervals

Results

36.0ms	198×	body	80	valid
33.0ms	31×	body	2560	valid
27.0ms	87×	body	80	nan
25.0ms	28×	body	1280	valid
12.0ms	17×	body	640	valid
5.0ms	4×	body	5120	valid
4.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify131.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	142
7	142
6	140
5	135
4	130
3	110
2	63
1	29
0	14

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.4b	(- (* b b) (* 4 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
24.3b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`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 → 161

Calls

4 calls:

46.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
22.0ms	(- (* b b) (* 4 (* a c)))
37.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
12.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series426.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
73.0ms	(- (* b b) (* 4 (* a c)))
97.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
112.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.0s

Counts

173 → 173

Iterations

Iter	Nodes
done	5001
2	1867
1	599
0	239

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a))
0.4b	(- (* b b) (* 4 (* a c)))
7.5b	(- (/ (- b) (* 2 a)) (/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a)))
24.3b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
141×	`prod-diff`
101×	`*-un-lft-identity`
98×	`add-sqr-sqrt`
95×	`add-cube-cbrt`
51×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
33×	`distribute-lft-neg-in`
28×	`div-inv`
15×	`fma-neg`
11×	`neg-mul-1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-sub` `prod-exp` `frac-sub` `cbrt-unprod` `sub-div` `difference-of-squares`

Counts

4 → 244

Calls

4 calls:

22.0ms	(/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a))
10.0ms	(- (* b b) (* 4 (* a c)))
51.0ms	(- (/ (- b) (* 2 a)) (/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a)))
9.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a))
63.0ms	(- (* b b) (* 4 (* a c)))
131.0ms	(- (/ (- b) (* 2 a)) (/ (sqrt (- (* b b) (* 4 (* a c)))) (* 2 a)))
118.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.9s

Counts

256 → 256

Iterations

Iter	Nodes
done	5009
2	2364
1	844
0	351

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (- (* b b) (* 4 (* a c)))) (/ 1 (* 2 a)))
0.4b	(- (* b b) (* 4 (* a c)))
12.6b	(- (/ (- b) (* 2 a)) (* (sqrt (- (* b b) (* 4 (* a c)))) (/ 1 (* 2 a))))
24.3b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

23×	`times-frac` `add-exp-log`
22×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
15×	`fma-neg` `prod-diff`
13×	`add-cbrt-cube`
10×	`sqrt-div` `prod-exp`
8×	`add-log-exp`
7×	`pow1` `flip3--` `associate-r` `sqrt-prod` `flip--`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-l` `frac-sub`
4×	`expm1-log1p-u` `frac-times` `div-exp` `associate-*l/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`associate-*r/` `un-div-inv`
2×	`cbrt-undiv` `rec-exp` `neg-mul-1` `sub-neg` `diff-log` `1-exp` `sub-div` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 131

Calls

4 calls:

59.0ms	(* (sqrt (- (* b b) (* 4 (* a c)))) (/ 1 (* 2 a)))
8.0ms	(- (* b b) (* 4 (* a c)))
72.0ms	(- (/ (- b) (* 2 a)) (* (sqrt (- (* b b) (* 4 (* a c)))) (/ 1 (* 2 a))))
18.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (sqrt (- (* b b) (* 4 (* a c)))) (/ 1 (* 2 a)))
49.0ms	(- (* b b) (* 4 (* a c)))
162.0ms	(- (/ (- b) (* 2 a)) (* (sqrt (- (* b b) (* 4 (* a c)))) (/ 1 (* 2 a))))
85.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.0s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	2600
1	704
0	260

prune723.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2 a) (sqrt (- (* b b) (* 4 (* a c))))))
0.4b	(- (* b b) (* 4 (* a c)))
11.5b	(- (/ (- b) (* 2 a)) (/ 1 (/ (* 2 a) (sqrt (- (* b b) (* 4 (* a c)))))))
24.3b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

1238×	`times-frac`
575×	`prod-diff`
514×	`add-sqr-sqrt`
510×	`*-un-lft-identity`
506×	`add-cube-cbrt`
141×	`sqrt-prod`
126×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
107×	`associate-/r/`
104×	`div-inv`
94×	`sqrt-div`
49×	`flip3--` `flip--`
42×	`neg-mul-1`
25×	`add-exp-log`
15×	`fma-neg`
13×	`add-cbrt-cube`
12×	`associate-/r*` `div-exp`
8×	`add-log-exp`
6×	`pow1`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*` `difference-of-squares`
2×	`sub-neg` `diff-log` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `frac-sub` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 724

Calls

4 calls:

24.0ms	(/ 1 (/ (* 2 a) (sqrt (- (* b b) (* 4 (* a c))))))
17.0ms	(- (* b b) (* 4 (* a c)))
75.0ms	(- (/ (- b) (* 2 a)) (/ 1 (/ (* 2 a) (sqrt (- (* b b) (* 4 (* a c)))))))
12.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ 1 (/ (* 2 a) (sqrt (- (* b b) (* 4 (* a c))))))
50.0ms	(- (* b b) (* 4 (* a c)))
127.0ms	(- (/ (- b) (* 2 a)) (/ 1 (/ (* 2 a) (sqrt (- (* b b) (* 4 (* a c)))))))
108.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.5s

Counts

736 → 736

Iterations

Iter	Nodes
done	5000
2	4560
1	2184
0	902

prune4.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.6b

regimes686.0ms

Accuracy

83% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 34.2b

bsearch370.0ms

Steps

Iters	Range		Point
9	6.2301214455520334e+75	1.9082112581546424e+85	1.6691257204922504e+85
4	-2.3602019652593256e-123	-1.5355849018748885e-123	-2.3344326820285623e-123
9	-2.9300981025422624e-27	-1.2024011261401705e-33	-6.936587154412951e-28
8	-1.0943378505721803e-12	-1.4409381956716427e-15	-7.363255598823911e-15

simplify8.0ms

Iterations

Iter	Nodes
done	46
1	46
0	37

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.5s	1057×	body	2560	valid
886.0ms	5842×	body	80	valid
665.0ms	891×	body	1280	valid
528.0ms	2845×	body	80	nan
315.0ms	456×	body	640	valid
165.0ms	114×	body	5120	valid
87.0ms	228×	body	320	valid
30.0ms	117×	body	160	valid