Details

sample107.0ms

Algorithm

intervals

Results

60.0ms	278×	body	80	valid
25.0ms	77×	body	80	nan

simplify124.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	170
7	170
6	168
5	164
4	157
3	132
2	76
1	39
0	20

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize201.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (fma c (* a -4) (* b b))) b)
1.6b	(- (- b) (sqrt (fma c (* a -4) (* b b))))
22.6b	(sqrt (fma c (* a -4) (* b b)))
22.6b	(sqrt (fma c (* a -4) (* b b)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

78×	`prod-diff`
71×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt`
50×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 165

Calls

4 calls:

15.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
23.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
3.0ms	(sqrt (fma c (* a -4) (* b b)))
3.0ms	(sqrt (fma c (* a -4) (* b b)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
108.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
115.0ms	(sqrt (fma c (* a -4) (* b b)))
120.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.3s

Counts

177 → 177

Iterations

Iter	Nodes
3	2234
2	875
1	417
0	194

prune3.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.0b

localize205.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (fma c (* a -4) (* b b))) b)
4.8b	(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
4.9b	(/ a (/ b c))
22.6b	(sqrt (fma c (* a -4) (* b b)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
66×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`add-cube-cbrt`
21×	`add-cbrt-cube` `add-exp-log`
18×	`prod-diff`
16×	`sqrt-prod`
14×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`clear-num` `frac-2neg` `flip3--` `associate-*r/` `flip--` `difference-of-squares` `associate-/l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `distribute-lft-out--`

Counts

4 → 157

Calls

4 calls:

8.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
74.0ms	(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
6.0ms	(/ a (/ b c))
1.0ms	(sqrt (fma c (* a -4) (* b b)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
72.0ms	(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
37.0ms	(/ a (/ b c))
117.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify2.7s

Counts

169 → 169

Iterations

Iter	Nodes
2	2421
1	681
0	285

prune3.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.9b

localize173.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ c b) (/ b a))
0.1b	(/ c (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2))
1.1b	(- (sqrt (fma c (* a -4) (* b b))) b)
22.6b	(sqrt (fma c (* a -4) (* b b)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

387×	`times-frac`
336×	`add-sqr-sqrt`
303×	`*-un-lft-identity`
271×	`add-cube-cbrt`
187×	`prod-diff`
32×	`div-inv`
30×	`difference-of-squares`
28×	`sqrt-prod`
22×	`associate-/r*`
19×	`fma-neg`
15×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/r/` `frac-sub`

Counts

4 → 371

Calls

4 calls:

24.0ms	(- (/ c b) (/ b a))
22.0ms	(/ c (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2))
15.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
2.0ms	(sqrt (fma c (* a -4) (* b b)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ c b) (/ b a))
282.0ms	(/ c (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2))
121.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
98.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.9s

Counts

383 → 383

Iterations

Iter	Nodes
2	3258
1	1309
0	562

prune6.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.9b

localize183.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (fma c (* a -4) (* b b))) b)
4.8b	(/ a (- (/ a (/ b c)) b))
4.9b	(/ a (/ b c))
22.6b	(sqrt (fma c (* a -4) (* b b)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

114×	`add-sqr-sqrt`
108×	`times-frac`
83×	`*-un-lft-identity`
73×	`add-cube-cbrt`
20×	`associate-/r*`
18×	`prod-diff`
16×	`sqrt-prod`
14×	`difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `div-inv` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 179

Calls

4 calls:

16.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
36.0ms	(/ a (- (/ a (/ b c)) b))
12.0ms	(/ a (/ b c))
2.0ms	(sqrt (fma c (* a -4) (* b b)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
203.0ms	(/ a (- (/ a (/ b c)) b))
30.0ms	(/ a (/ b c))
124.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify3.1s

Counts

191 → 191

Iterations

Iter	Nodes
3	4623
2	1722
1	631
0	301

prune3.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.9b

regimes480.0ms

Accuracy

92.5% (0.7b remaining)

Error of 13.2b against oracle of 12.5b and baseline of 21.3b

bsearch352.0ms

Steps

Iters	Range		Point
7	1.602087361235081e+82	9.448026055101687e+83	7.548494687587984e+83
9	3.701747966542155e-305	1.9287453080909552e-299	3.7440019496974325e-305

simplify26.0ms

Iterations

Iter	Nodes
3	55
2	55
1	52
0	44

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.3s	8756×	body	80	valid
533.0ms	2920×	body	80	nan