Details

sample127.0ms

Algorithm

intervals

Results

32.0ms	29×	body	2560	valid
29.0ms	196×	body	80	valid
18.0ms	27×	body	1280	valid
13.0ms	99×	body	80	nan
9.0ms	14×	body	640	valid
2.0ms	6×	body	320	valid
2.0ms	2×	body	5120	valid
1.0ms	2×	body	160	valid

simplify280.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize25.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (fma (* a c) -4 (* b b)))
0.9b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.6b	(fma (* a c) -4 (* b b))
0.1b	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-sqr-sqrt`
168×	`*-un-lft-identity`
159×	`times-frac`
116×	`add-cube-cbrt`
60×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/l*`
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` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`diff-log` `div-sub`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `neg-log` `fma-udef` `flip--` `associate-/l/`

Counts

4 → 240

Calls

4 calls:

Slowest

26.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
18.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series416.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

134.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
110.0ms	(sqrt (fma (* a c) -4 (* b b)))
99.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
74.0ms	(fma (* a c) -4 (* b b))

simplify441.0ms

Counts: 394 → 252

prune3.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.7b

localize53.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (fma (* a c) -4 (* b b)))
0.9b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.6b	(fma (* a c) -4 (* b b))
0.2b	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

792×	`times-frac`
512×	`add-sqr-sqrt`
511×	`*-un-lft-identity`
363×	`add-cube-cbrt`
80×	`associate-/r*`
74×	`distribute-lft-out--` `difference-of-squares`
70×	`sqrt-prod`
60×	`prod-diff`
58×	`distribute-rgt-neg-in`
25×	`add-exp-log`
21×	`distribute-lft-neg-in`
17×	`div-inv`
15×	`div-exp`
13×	`add-cbrt-cube`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1` `cbrt-undiv`
5×	`associate-/r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `associate-/l*`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `neg-log` `fma-udef` `pow-flip` `flip--` `inv-pow`

Counts

4 → 469

Calls

4 calls:

Slowest

34.0ms	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
29.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
3.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series453.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

139.0ms	(sqrt (fma (* a c) -4 (* b b)))
132.0ms	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
111.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
71.0ms	(fma (* a c) -4 (* b b))

simplify1.4s

Counts: 786 → 481

prune6.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.7b

localize51.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (fma (* a c) -4 (* b b)))
0.9b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.6b	(fma (* a c) -4 (* b b))
0.1b	(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (/ a (/ 1 2)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

836×	`times-frac`
556×	`add-sqr-sqrt`
555×	`*-un-lft-identity`
371×	`add-cube-cbrt`
92×	`distribute-lft-out--` `difference-of-squares`
79×	`sqrt-prod`
67×	`distribute-rgt-neg-in`
60×	`prod-diff`
44×	`associate-/r*`
33×	`div-inv`
21×	`distribute-lft-neg-in`
19×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`div-exp`
10×	`fma-neg`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
6×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`flip3--` `diff-log` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-sub` `neg-log` `fma-udef`

Counts

4 → 502

Calls

4 calls:

Slowest

46.0ms	(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (/ a (/ 1 2)))
20.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series398.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

121.0ms	(sqrt (fma (* a c) -4 (* b b)))
115.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
102.0ms	(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (/ a (/ 1 2)))
59.0ms	(fma (* a c) -4 (* b b))

simplify1.1s

Counts: 889 → 514

prune7.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.7b

localize41.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (fma (* a c) -4 (* b b)))
0.9b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.6b	(fma (* a c) -4 (* b b))
0.4b	(/ a (sqrt 1/2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 160

Calls

4 calls:

Slowest

11.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
9.0ms	(/ a (sqrt 1/2))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series409.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

120.0ms	(sqrt (fma (* a c) -4 (* b b)))
112.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
96.0ms	(/ a (sqrt 1/2))
81.0ms	(fma (* a c) -4 (* b b))

simplify505.0ms

Counts: 256 → 172

prune2.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.7b

regimes312.0ms

Accuracy

82.9% (4.7b remaining)

Error of 10.2b against oracle of 5.6b and baseline of 32.8b

bsearch260.0ms

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.5s	1054×	body	2560	valid
967.0ms	5901×	body	80	valid
717.0ms	884×	body	1280	valid
527.0ms	2927×	body	80	nan
325.0ms	421×	body	640	valid
126.0ms	229×	body	320	valid
120.0ms	116×	body	5120	valid
35.0ms	118×	body	160	valid