Details

sample74.0ms

Algorithm

intervals

Results

14.0ms	198×	body	80	valid
11.0ms	27×	body	2560	valid
9.0ms	26×	body	1280	valid
7.0ms	101×	body	80	nan
4.0ms	15×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	9×	body	160	valid

simplify133.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	164
6	164
5	160
4	153
3	121
2	64
1	29
0	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite118.0ms

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--` `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 → 157

Calls

4 calls:

65.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms	(- (* b b) (* 4.0 (* a c)))
24.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
70.0ms	(- (* b b) (* 4.0 (* a c)))
109.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
92.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.2s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
2	2467
1	610
0	241

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* a (* c 4.0))))) (* 2.0 a))
0.6b	(- (* b b) (* a (* c 4.0)))
1.9b	(- (- b) (sqrt (- (* b b) (* a (* c 4.0)))))
20.6b	(sqrt (- (* b b) (* a (* c 4.0))))

rewrite182.0ms

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--` `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 → 157

Calls

4 calls:

116.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* c 4.0))))) (* 2.0 a))
7.0ms	(- (* b b) (* a (* c 4.0)))
32.0ms	(- (- b) (sqrt (- (* b b) (* a (* c 4.0)))))
17.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

series440.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* c 4.0))))) (* 2.0 a))
70.0ms	(- (* b b) (* a (* c 4.0)))
118.0ms	(- (- b) (sqrt (- (* b b) (* a (* c 4.0)))))
93.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

simplify2.1s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	2608
1	615
0	243

prune804.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* a (* c 4.0))))) (/ 1 (* 2.0 a)))
0.6b	(- (* b b) (* a (* c 4.0)))
1.9b	(- (- b) (sqrt (- (* b b) (* a (* c 4.0)))))
20.6b	(sqrt (- (* b b) (* a (* c 4.0))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in` `add-exp-log`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sub-neg` `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 → 165

Calls

4 calls:

152.0ms	(* (- (- b) (sqrt (- (* b b) (* a (* c 4.0))))) (/ 1 (* 2.0 a)))
7.0ms	(- (* b b) (* a (* c 4.0)))
29.0ms	(- (- b) (sqrt (- (* b b) (* a (* c 4.0)))))
10.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

series513.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (- (- b) (sqrt (- (* b b) (* a (* c 4.0))))) (/ 1 (* 2.0 a)))
78.0ms	(- (* b b) (* a (* c 4.0)))
149.0ms	(- (- b) (sqrt (- (* b b) (* a (* c 4.0)))))
118.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

simplify2.7s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
2	3151
1	688
0	269

prune802.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* a (* c 4.0))))) (* 2.0 a))
0.6b	(- (* b b) (* a (* c 4.0)))
1.9b	(- (- b) (sqrt (- (* b b) (* a (* c 4.0)))))
20.6b	(sqrt (- (* b b) (* a (* c 4.0))))

rewrite156.0ms

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--` `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 → 157

Calls

4 calls:

72.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* c 4.0))))) (* 2.0 a))
14.0ms	(- (* b b) (* a (* c 4.0)))
46.0ms	(- (- b) (sqrt (- (* b b) (* a (* c 4.0)))))
13.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* c 4.0))))) (* 2.0 a))
74.0ms	(- (* b b) (* a (* c 4.0)))
107.0ms	(- (- b) (sqrt (- (* b b) (* a (* c 4.0)))))
107.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

simplify2.1s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	2608
1	615
0	243

prune818.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

regimes497.0ms

Accuracy

86.6% (3.8b remaining)

Error of 9.3b against oracle of 5.5b and baseline of 33.8b

bsearch295.0ms

Steps

Iters	Range		Point
3	5.437233749566996e+22	6.419404774371196e+22	6.358019085320933e+22
9	-3.164352429737119e-153	-7.716626383315164e-163	-2.5011866771056487e-154
6	-0.042530208599811804	-0.005947574473424517	-0.03099989563658143

simplify17.0ms

Iterations

Iter	Nodes
done	48
2	48
1	47
0	37

end0.0ms

sample3.1s

Algorithm

intervals

Results

666.0ms	5935×	body	80	valid
634.0ms	2964×	body	80	nan
552.0ms	1023×	body	2560	valid
450.0ms	864×	body	1280	valid
175.0ms	492×	body	640	valid
104.0ms	112×	body	5120	valid
96.0ms	237×	body	320	valid
17.0ms	114×	body	160	valid