Details

sample136.0ms

Algorithm

intervals

Results

31.0ms	36×	body	2560	valid
27.0ms	177×	body	80	valid
20.0ms	81×	body	80	nan
19.0ms	25×	body	1280	valid
11.0ms	19×	body	640	valid
4.0ms	9×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify187.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	142
7	142
6	140
5	135
4	130
3	110
2	63
1	29
0	14

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.2b	(- (* b b) (* 4 (* a c)))
23.5b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite136.0ms

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:

84.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
30.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
9.0ms	(- (* b b) (* 4 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
82.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
57.0ms	(- (* b b) (* 4 (* a c)))
101.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify5.3s

Counts

173 → 173

Iterations

Iter	Nodes
3	6465
2	1699
1	595
0	239

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (/ a 1/2) (- (+ (sqrt (fma -4 (* a c) (* b b))) b))))
1.1b	(+ (sqrt (fma -4 (* a c) (* b b))) b)
1.2b	(fma -4 (* a c) (* b b))
23.5b	(sqrt (fma -4 (* a c) (* b b)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

1542×	`times-frac`
876×	`*-un-lft-identity`
667×	`add-sqr-sqrt`
666×	`add-cube-cbrt`
208×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
162×	`associate-/r*`
105×	`distribute-lft-out`
53×	`div-inv`
52×	`neg-mul-1`
25×	`add-exp-log`
15×	`div-exp`
13×	`add-cbrt-cube`
9×	`associate-/r/`
8×	`distribute-neg-frac`
6×	`pow1` `cbrt-undiv` `fma-def` `sqrt-prod` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `associate-/l*`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 727

Calls

4 calls:

27.0ms	(/ 1 (/ (/ a 1/2) (- (+ (sqrt (fma -4 (* a c) (* b b))) b))))
6.0ms	(+ (sqrt (fma -4 (* a c) (* b b))) b)
0.0ms	(fma -4 (* a c) (* b b))
1.0ms	(sqrt (fma -4 (* a c) (* b b)))

series559.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ 1 (/ (/ a 1/2) (- (+ (sqrt (fma -4 (* a c) (* b b))) b))))
146.0ms	(+ (sqrt (fma -4 (* a c) (* b b))) b)
95.0ms	(fma -4 (* a c) (* b b))
131.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify2.9s

Counts

739 → 739

Iterations

Iter	Nodes
1	2796
0	1032

prune10.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.2b	(- (* b b) (* 4 (* a c)))
23.5b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`*-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`
11×	`fma-neg`
10×	`times-frac` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

63.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
23.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
9.0ms	(- (* b b) (* 4 (* a c)))
10.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
144.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
74.0ms	(- (* b b) (* 4 (* a c)))
108.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify3.2s

Counts

181 → 181

Iterations

Iter	Nodes
3	6100
2	1805
1	643
0	262

prune2.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.2b

localize75.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (/ 1 (sqrt 1/2)))
1.1b	(+ (sqrt (fma -4 (* c a) (* b b))) b)
1.2b	(fma -4 (* c a) (* b b))
23.5b	(sqrt (fma -4 (* c a) (* b b)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
84×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
82×	`add-cube-cbrt`
42×	`sqrt-prod`
23×	`add-exp-log`
22×	`associate-/r*`
14×	`div-exp`
9×	`add-cbrt-cube`
8×	`pow1` `pow-flip`
7×	`rec-exp` `1-exp`
6×	`fma-def` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `inv-pow`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `flip3-+` `associate-/r/` `flip-+` `fma-udef` `distribute-lft-out` `remove-double-div`

Counts

4 → 174

Calls

4 calls:

16.0ms	(/ 1 (/ 1 (sqrt 1/2)))
12.0ms	(+ (sqrt (fma -4 (* c a) (* b b))) b)
0.0ms	(fma -4 (* c a) (* b b))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))

series316.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(/ 1 (/ 1 (sqrt 1/2)))
118.0ms	(+ (sqrt (fma -4 (* c a) (* b b))) b)
60.0ms	(fma -4 (* c a) (* b b))
138.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify857.0ms

Counts

184 → 184

Iterations

Iter	Nodes
3	2026
2	907
1	548
0	246

prune2.6s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.2b

regimes520.0ms

Accuracy

84.9% (4.3b remaining)

Error of 10.1b against oracle of 5.8b and baseline of 34.1b

bsearch316.0ms

Steps

Iters	Range		Point
6	8.723340275486535e+149	1.060972495465945e+151	1.4404833532724588e+150
11	-5.190492772730695e-87	-3.518766096303871e-111	-4.32337788234514e-89

simplify8.0ms

Iterations

Iter	Nodes
3	42
2	42
1	41
0	30

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.7s	1119×	body	2560	valid
1000.0ms	5783×	body	80	valid
744.0ms	901×	body	1280	valid
512.0ms	128×	body	5120	valid
495.0ms	2863×	body	80	nan
302.0ms	471×	body	640	valid
100.0ms	230×	body	320	valid
30.0ms	108×	body	160	valid