Details

sample94.0ms

Algorithm

intervals

Results

16.0ms	191×	body	80	valid
14.0ms	28×	body	2560	valid
11.0ms	26×	body	1280	valid
6.0ms	19×	body	640	valid
6.0ms	82×	body	80	nan
2.0ms	9×	body	320	valid
2.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify160.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize85.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite467.0ms

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--` `insert-posit16` `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 → 175

Calls

4 calls:

274.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
22.0ms	(- (* b_2 b_2) (* a c))
84.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms	(- (* b_2 b_2) (* a c))
137.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
133.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.2s

Counts

187 → 187

Iterations

Iter	Nodes
done	5001
2	1518
1	578
0	248

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.8b

localize119.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite499.0ms

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` `insert-posit16` `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 → 173

Calls

4 calls:

284.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
42.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
73.0ms	(- (* b_2 b_2) (* a c))
117.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
156.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.9s

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
2	1694
1	640
0	267

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.8b

localize184.0ms

Local error

Found 4 expressions with local error:

2.7b	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0b	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
18.0b	(- (* b_2 b_2) (* b_2 b_2))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
33×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-+l-`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out--` `pow1/2` `+-inverses` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 204

Calls

4 calls:

541.0ms	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
360.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
46.0ms	(- (* b_2 b_2) (* b_2 b_2))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series588.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
292.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
2.0ms	(- (* b_2 b_2) (* b_2 b_2))
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify5.1s

Counts

216 → 216

Iterations

Iter	Nodes
done	5002
2	2144
1	793
0	327

prune2.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

localize263.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0b	(* (/ c (cbrt a)) (/ a (cbrt a)))
4.8b	(* (* (/ c (cbrt a)) (/ a (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

300×	`times-frac`
261×	`add-sqr-sqrt`
192×	`*-un-lft-identity`
170×	`associate-r`
154×	`add-cube-cbrt`
131×	`add-exp-log`
96×	`cbrt-prod`
59×	`add-cbrt-cube`
54×	`div-exp`
49×	`prod-exp`
38×	`difference-of-squares`
34×	`sqrt-prod`
31×	`cbrt-undiv` `cbrt-unprod`
23×	`associate-l`
19×	`distribute-lft-out--`
18×	`prod-diff`
12×	`pow1` `associate-/r/`
9×	`div-inv` `unswap-sqr`
8×	`flip3--` `flip--`
6×	`frac-times` `fma-neg` `associate-*l/` `add-log-exp`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*r/` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-div` `*-commutative`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 345

Calls

4 calls:

225.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
118.0ms	(* (/ c (cbrt a)) (/ a (cbrt a)))
542.0ms	(* (* (/ c (cbrt a)) (/ a (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
53.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series939.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
152.0ms	(* (/ c (cbrt a)) (/ a (cbrt a)))
529.0ms	(* (* (/ c (cbrt a)) (/ a (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
115.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.7s

Counts

357 → 357

Iterations

Iter	Nodes
done	5002
1	1935
0	572

prune4.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.7b

regimes1.0s

Accuracy

89.8% (3.1b remaining)

Error of 8.4b against oracle of 5.4b and baseline of 35.6b

bsearch348.0ms

Steps

Iters	Range	Point
10	1.0955696400612189e+91	1.0202913897586463e+104	1.7205132563858266e+103
9	-1.8840476054243272e-132	-9.612842247692592e-139	-2.4242286502051438e-135
9	-2.0190258033009663e+27	-4.429449841721669e+19	-3.234164035284793e+22

Iters

Range

Point

1.0955696400612189e+91

1.0202913897586463e+104

1.7205132563858266e+103

-1.8840476054243272e-132

-9.612842247692592e-139

-2.4242286502051438e-135

-2.0190258033009663e+27

-4.429449841721669e+19

-3.234164035284793e+22

simplify22.0ms

Iterations

Iter	Nodes
done	41
1	41
0	34

end0.0ms

sample3.3s

Algorithm

intervals

Results

787.0ms	892×	body	1280	valid
650.0ms	1081×	body	2560	valid
633.0ms	5881×	body	80	valid
352.0ms	2917×	body	80	nan
208.0ms	437×	body	640	valid
98.0ms	113×	body	5120	valid
56.0ms	230×	body	320	valid
20.0ms	127×	body	160	valid