Details

sample131.0ms

Algorithm

intervals

Results

29.0ms	37×	body	2560	valid
24.0ms	186×	body	80	valid
24.0ms	91×	body	80	nan
19.0ms	28×	body	1280	valid
11.0ms	19×	body	640	valid
5.0ms	11×	body	320	valid
1.0ms	3×	body	160	valid

simplify118.0ms

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* -4 a) c (* b b))
0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
1.1b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
22.9b	(sqrt (fma (* -4 a) c (* b b)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
10×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `diff-log` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `fma-udef` `div-inv`

Counts

4 → 167

Calls

4 calls:

0.0ms	(fma (* -4 a) c (* b b))
25.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
11.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(fma (* -4 a) c (* b b))
132.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
98.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
92.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify2.0s

Counts

179 → 179

Iterations

Iter	Nodes
3	3048
2	1154
1	495
0	222

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (+ (* (* -4 a) c) (* b b)))) a)
0.6b	(+ (* (* -4 a) c) (* b b))
1.1b	(- (- b) (sqrt (+ (* (* -4 a) c) (* b b))))
22.9b	(sqrt (+ (* (* -4 a) c) (* b b)))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
10×	`fma-neg` `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` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3-+` `flip3--` `sqrt-div` `diff-log` `flip-+` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `fma-def` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 173

Calls

4 calls:

143.0ms	(/ (- (- b) (sqrt (+ (* (* -4 a) c) (* b b)))) a)
18.0ms	(+ (* (* -4 a) c) (* b b))
49.0ms	(- (- b) (sqrt (+ (* (* -4 a) c) (* b b))))
45.0ms	(sqrt (+ (* (* -4 a) c) (* b b)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (- (- b) (sqrt (+ (* (* -4 a) c) (* b b)))) a)
89.0ms	(+ (* (* -4 a) c) (* b b))
111.0ms	(- (- b) (sqrt (+ (* (* -4 a) c) (* b b))))
118.0ms	(sqrt (+ (* (* -4 a) c) (* b b)))

simplify3.1s

Counts

185 → 185

Iterations

Iter	Nodes
3	4774
2	1470
1	576
0	239

prune2.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* -4 a) c (* b b))
0.2b	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
1.1b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
22.9b	(sqrt (fma (* -4 a) c (* b b)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
60×	`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`
10×	`fma-neg`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

4 → 165

Calls

4 calls:

0.0ms	(fma (* -4 a) c (* b b))
48.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
21.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(fma (* -4 a) c (* b b))
119.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
133.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
115.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify4.2s

Counts

177 → 177

Iterations

Iter	Nodes
3	3303
2	1355
1	556
0	241

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize90.0ms

Local error

Found 4 expressions with local error:

8.9b	(- (- b) (* (sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b))))) (sqrt (cbrt (fma (* -4 a) c (* b b))))))
23.6b	(cbrt (fma (* -4 a) c (* b b)))
23.6b	(cbrt (fma (* -4 a) c (* b b)))
23.6b	(cbrt (fma (* -4 a) c (* b b)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
9×	`cbrt-prod`
8×	`add-log-exp`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `flip--`

Counts

4 → 79

Calls

4 calls:

18.0ms	(- (- b) (* (sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b))))) (sqrt (cbrt (fma (* -4 a) c (* b b))))))
1.0ms	(cbrt (fma (* -4 a) c (* b b)))
1.0ms	(cbrt (fma (* -4 a) c (* b b)))
1.0ms	(cbrt (fma (* -4 a) c (* b b)))

series874.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (- b) (* (sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b))))) (sqrt (cbrt (fma (* -4 a) c (* b b))))))
252.0ms	(cbrt (fma (* -4 a) c (* b b)))
251.0ms	(cbrt (fma (* -4 a) c (* b b)))
255.0ms	(cbrt (fma (* -4 a) c (* b b)))

simplify1.2s

Counts

91 → 91

Iterations

Iter	Nodes
3	2126
2	735
1	283
0	123

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

regimes361.0ms

Accuracy

79.9% (5.6b remaining)

Error of 11.2b against oracle of 5.6b and baseline of 33.6b

bsearch186.0ms

Steps

Iters	Range		Point
6	1.0281935457265552e+141	5.100996805178893e+141	2.88466596167667e+141
10	-1.305087172727865e-183	-3.833210530916389e-194	-1.2890050783826923e-183

simplify13.0ms

Iterations

Iter	Nodes
2	39
1	39
0	32

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.2s	1101×	body	2560	valid
1.2s	915×	body	1280	valid
923.0ms	5836×	body	80	valid
469.0ms	2978×	body	80	nan
308.0ms	500×	body	640	valid
176.0ms	106×	body	5120	valid
146.0ms	194×	body	320	valid
32.0ms	117×	body	160	valid