Details

sample141.0ms

Algorithm

intervals

Results

43.0ms	189×	body	80	valid
34.0ms	38×	body	2560	valid
23.0ms	30×	body	1280	valid
12.0ms	87×	body	80	nan
8.0ms	15×	body	640	valid
2.0ms	6×	body	320	valid
2.0ms	2×	body	5120	valid

simplify112.0ms

Counts: 1 → 1

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize39.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (fma (* a c) -4 (* b b)))
0.3b	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.2b	(fma (* a c) -4 (* b b))
0.1b	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
18×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`div-sub`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `fma-udef` `flip--` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

Slowest

35.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
24.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
3.0ms	(sqrt (fma (* a c) -4 (* b b)))
1.0ms	(fma (* a c) -4 (* b b))

series502.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

175.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
122.0ms	(sqrt (fma (* a c) -4 (* b b)))
119.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
86.0ms	(fma (* a c) -4 (* b b))

simplify908.0ms

Counts: 191 → 191

prune2.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 27.6b

localize42.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (fma (* a c) -4 (* b b)))
5.2b	(- (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a) (/ (/ b 2) a))
0.2b	(fma (* a c) -4 (* b b))
0.1b	(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

10113×	`times-frac`
5326×	`add-sqr-sqrt`
5300×	`*-un-lft-identity`
5274×	`add-cube-cbrt`
3010×	`prod-diff`
1230×	`sqrt-prod`
469×	`div-inv`
70×	`fma-neg`
22×	`associate-/l*`
13×	`distribute-lft-out--`
12×	`difference-of-squares`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-out--` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `fma-udef` `flip--` `sub-div` `associate-/l/`

Counts

4 → 3262

Calls

4 calls:

Slowest

47.0ms	(- (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a) (/ (/ b 2) a))
8.0ms	(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series454.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

147.0ms	(- (/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a) (/ (/ b 2) a))
110.0ms	(sqrt (fma (* a c) -4 (* b b)))
109.0ms	(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)
89.0ms	(fma (* a c) -4 (* b b))

simplify6.7s

Counts: 3274 → 3274

prune1.1m

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 27.6b

localize31.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (fma (* a c) -4 (* b b)))
0.3b	(- (/ (sqrt (fma (* a c) -4 (* b b))) 2) (/ b 2))
0.2b	(fma (* a c) -4 (* b b))
0.1b	(/ (- (/ (sqrt (fma (* a c) -4 (* b b))) 2) (/ b 2)) a)

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

557×	`times-frac`
466×	`add-sqr-sqrt`
410×	`*-un-lft-identity`
370×	`add-cube-cbrt`
286×	`prod-diff`
139×	`sqrt-prod`
47×	`div-inv`
30×	`difference-of-squares`
22×	`fma-neg`
20×	`distribute-lft-out--`
14×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow1` `distribute-rgt-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`associate-/r*`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef`

Counts

4 → 442

Calls

4 calls:

Slowest

61.0ms	(/ (- (/ (sqrt (fma (* a c) -4 (* b b))) 2) (/ b 2)) a)
27.0ms	(- (/ (sqrt (fma (* a c) -4 (* b b))) 2) (/ b 2))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series544.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

207.0ms	(/ (- (/ (sqrt (fma (* a c) -4 (* b b))) 2) (/ b 2)) a)
145.0ms	(- (/ (sqrt (fma (* a c) -4 (* b b))) 2) (/ b 2))
115.0ms	(sqrt (fma (* a c) -4 (* b b)))
77.0ms	(fma (* a c) -4 (* b b))

simplify713.0ms

Counts: 454 → 454

prune7.2s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 27.6b

localize37.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (fma (* a c) -4 (* b b)))
0.3b	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.2b	(fma (* a c) -4 (* b b))
0.2b	(/ (/ 1 2) (/ a (- (sqrt (fma (* a c) -4 (* b b))) b)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
507×	`add-sqr-sqrt`
420×	`*-un-lft-identity`
334×	`add-cube-cbrt`
86×	`difference-of-squares`
58×	`sqrt-prod`
43×	`distribute-lft-out--`
40×	`div-inv`
29×	`associate-/r/`
26×	`add-exp-log`
24×	`associate-/r*`
18×	`prod-diff`
16×	`add-cbrt-cube` `div-exp`
15×	`flip3--` `flip--`
13×	`associate-/l*`
8×	`cbrt-undiv`
6×	`fma-neg` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `1-exp`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `fma-udef` `associate-/l/`

Counts

4 → 445

Calls

4 calls:

Slowest

16.0ms	(/ (/ 1 2) (/ a (- (sqrt (fma (* a c) -4 (* b b))) b)))
7.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series455.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

192.0ms	(/ (/ 1 2) (/ a (- (sqrt (fma (* a c) -4 (* b b))) b)))
103.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
100.0ms	(sqrt (fma (* a c) -4 (* b b)))
60.0ms	(fma (* a c) -4 (* b b))

simplify848.0ms

Counts: 457 → 457

prune5.6s

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 27.6b

regimes641.0ms

Accuracy

91.2% (0.4b remaining)

Error of 28.6b against oracle of 28.2b and baseline of 32.9b

bsearch159.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	1070×	body	2560	valid
699.0ms	5902×	body	80	valid
521.0ms	864×	body	1280	valid
267.0ms	2867×	body	80	nan
204.0ms	458×	body	640	valid
82.0ms	207×	body	320	valid
67.0ms	102×	body	5120	valid
20.0ms	112×	body	160	valid