Details

sample131.0ms

Algorithm

intervals

Results

28.0ms	30×	body	2560	valid
26.0ms	193×	body	80	valid
23.0ms	31×	body	1280	valid
13.0ms	91×	body	80	nan
9.0ms	14×	body	640	valid
5.0ms	10×	body	320	valid
4.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify174.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.3b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.4b	(- (* b b) (* 4 (* a c)))
22.7b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite127.0ms

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:

68.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
34.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
13.0ms	(- (* b b) (* 4 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
101.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
75.0ms	(- (* b b) (* 4 (* a c)))
109.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify4.8s

Counts

173 → 173

Iterations

Iter	Nodes
3	6465
2	1699
1	595
0	239

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
0.3b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.4b	(- (* b b) (* 4 (* a c)))
22.7b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite152.0ms

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:

80.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
38.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
15.0ms	(- (* b b) (* 4 (* a c)))
15.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
118.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
59.0ms	(- (* b b) (* 4 (* a c)))
98.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify3.0s

Counts

181 → 181

Iterations

Iter	Nodes
3	6100
2	1805
1	643
0	262

prune2.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 1/2) a)
0.3b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.4b	(fma (* a c) -4 (* b b))
22.7b	(sqrt (fma (* a c) -4 (* b b)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 144

Calls

4 calls:

28.0ms	(/ (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 1/2) a)
10.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.0ms	(fma (* a c) -4 (* b b))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 1/2) a)
146.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
94.0ms	(fma (* a c) -4 (* b b))
133.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.1s

Counts

156 → 156

Iterations

Iter	Nodes
3	4148
2	1281
1	504
0	213

prune2.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 1/2)))
0.3b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.4b	(fma (* a c) -4 (* b b))
22.7b	(sqrt (fma (* a c) -4 (* b b)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
64×	`add-cube-cbrt`
60×	`prod-diff`
39×	`times-frac`
34×	`sqrt-prod`
25×	`add-exp-log`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
12×	`div-exp`
10×	`fma-neg`
9×	`associate-/r*` `associate-/r/`
8×	`associate-*l/` `add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
5×	`cbrt-undiv` `flip3--` `div-inv` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 185

Calls

4 calls:

41.0ms	(/ 1 (/ a (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 1/2)))
12.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.0ms	(fma (* a c) -4 (* b b))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ 1 (/ a (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 1/2)))
103.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
95.0ms	(fma (* a c) -4 (* b b))
128.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify5.4s

Counts

197 → 197

Iterations

Iter	Nodes
3	5405
2	1760
1	646
0	285

prune3.0s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.1b

regimes458.0ms

Accuracy

82.4% (4.9b remaining)

Error of 10.4b against oracle of 5.5b and baseline of 33.3b

bsearch206.0ms

Steps

Iters	Range		Point
7	1.3534154308951418e+51	2.3844270322569095e+52	2.3648644896474148e+52
9	-5.573104320306828e-19	-3.9027827987942555e-24	-4.179137486378021e-24

simplify6.0ms

Iterations

Iter	Nodes
2	27
1	27
0	23

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.6s	1013×	body	2560	valid
995.0ms	5885×	body	80	valid
742.0ms	909×	body	1280	valid
369.0ms	2878×	body	80	nan
309.0ms	440×	body	640	valid
245.0ms	122×	body	5120	valid
100.0ms	242×	body	320	valid
30.0ms	112×	body	160	valid