Details

sample81.0ms

Algorithm

intervals

Results

15.0ms	43×	body	2560	valid
11.0ms	189×	body	80	valid
7.0ms	24×	body	1280	valid
5.0ms	85×	body	80	nan
3.0ms	12×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	4×	body	160	valid

simplify102.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite289.0ms

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:

136.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
21.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
62.0ms	(- (* b_2 b_2) (* a c))
120.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.5s

Counts

187 → 187

Iterations

Iter	Nodes
done	5001
2	1518
1	578
0	248

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
0.8b	(- (* b_2 b_2) (* a c))
0.8b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite339.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
36×	`times-frac`
33×	`add-sqr-sqrt`
32×	`add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/l*`
9×	`distribute-lft-out`
8×	`add-log-exp`
6×	`fma-def` `add-cbrt-cube` `add-exp-log` `sqrt-prod`
5×	`pow1`
4×	`expm1-log1p-u` `neg-mul-1` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
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 → 126

Calls

4 calls:

222.0ms	(/ (- (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
23.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (- (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
62.0ms	(- (* b_2 b_2) (* a c))
146.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
125.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify7.1s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
3	4974
2	1298
1	470
0	203

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite238.0ms

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:

146.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
11.0ms	(- (* b_2 b_2) (* a c))
51.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
61.0ms	(- (* b_2 b_2) (* a c))
149.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.7s

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
2	1694
1	640
0	267

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize73.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b	(sqrt (- (* b_2 b_2) (* a c)))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `fma-def` `sqrt-prod`
10×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `flip-+` `flip--` `distribute-lft-out`

Counts

4 → 78

Calls

4 calls:

56.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
34.0ms	(sqrt (- (* b_2 b_2) (* a c)))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series590.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
173.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
119.0ms	(sqrt (- (* b_2 b_2) (* a c)))
124.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.3s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
3	1966
2	610
1	198
0	76

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

regimes1.3s

Accuracy

82.7% (5.0b remaining)

Error of 10.4b against oracle of 5.4b and baseline of 34.3b

bsearch165.0ms

Steps

Iters	Range		Point
8	4.664337482673326e-05	0.17679972651571432	0.17389787404847717
7	-2.1239343788780832e-66	-2.400891841159577e-68	-1.264659490877098e-67

simplify28.0ms

Iterations

Iter	Nodes
done	35
2	35
1	34
0	25

end0.0ms

sample2.9s

Algorithm

intervals

Results

939.0ms	5819×	body	80	valid
581.0ms	1105×	body	2560	valid
282.0ms	877×	body	1280	valid
273.0ms	2973×	body	80	nan
101.0ms	439×	body	640	valid
95.0ms	125×	body	5120	valid
56.0ms	122×	body	160	valid
45.0ms	252×	body	320	valid