Details

sample149.0ms

Algorithm

intervals

Results

43.0ms	31×	body	2560	valid
35.0ms	201×	body	80	valid
23.0ms	26×	body	1280	valid
15.0ms	87×	body	80	nan
7.0ms	11×	body	640	valid
3.0ms	3×	body	5120	valid
2.0ms	3×	body	320	valid
1.0ms	2×	body	160	valid

simplify175.0ms

Calls

1 calls:

Slowest

175.0ms

(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.5b

localize40.0ms

Local error

Found 3 expressions with local error:

19.5b	(sqrt (fma c (* -4 a) (* b b)))
0.5b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`fma-neg` `sqrt-prod`
4×	`associate-/l*`
3×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`div-sub` `div-inv`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `flip3--` `pow1/2` `flip--` `associate-/l/`

Calls

3 calls:

Slowest

24.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
12.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -4 a) (* b b)))

series184.0ms

Calls

3 calls:

Slowest

77.0ms	(sqrt (fma c (* -4 a) (* b b)))
56.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
52.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify408.0ms

Calls

23 calls:

Slowest

46.0ms	(sqrt (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))))
43.0ms	(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
41.0ms	(sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
38.0ms	(* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b)))))
37.0ms	(sqrt (sqrt (fma c (* -4 a) (* b b))))

prune782.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.4b

localize6.0ms

Local error

Found 4 expressions with local error:

19.5b	(sqrt (fma c (* -4 a) (* b b)))
0.5b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b	(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
0.1b	(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`associate-/r` `-un-lft-identity` `add-cube-cbrt`
6×	`fma-neg` `sqrt-prod`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-/r/`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `rec-exp` `sub-neg` `flip3--` `pow1/2` `pow-flip` `flip--` `inv-pow`

Calls

4 calls:

Slowest

7.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms	(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))
1.0ms	(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))

series747.0ms

Calls

4 calls:

Slowest

463.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
140.0ms	(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
94.0ms	(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
50.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify600.0ms

Calls

31 calls:

Slowest

64.0ms	(/ 1 (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
58.0ms	(cbrt (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
57.0ms	(sqrt (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
52.0ms	(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
44.0ms	(sqrt (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.3b

localize12.0ms

Local error

Found 4 expressions with local error:

19.5b	(sqrt (fma c (* -4 a) (* b b)))
0.5b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b	(/ 1 (/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))
0.2b	(/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`associate-/r` `-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`fma-neg` `sqrt-prod`
5×	`pow-flip`
4×	`expm1-log1p-u` `rec-exp` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-/r/` `inv-pow`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `pow1/2` `flip--` `remove-double-div`

Calls

4 calls:

Slowest

12.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
8.0ms	(/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a))
3.0ms	(/ 1 (/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))
2.0ms	(sqrt (fma c (* -4 a) (* b b)))

series310.0ms

Calls

4 calls:

Slowest

129.0ms	(/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a))
70.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
67.0ms	(/ 1 (/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))
44.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify1.3s

Calls

34 calls:

Slowest

191.0ms	(cbrt (/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))
185.0ms	(/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a))
158.0ms	(sqrt (/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))
155.0ms	(/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a))
98.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.3b

localize1.0ms

Local error

Found 3 expressions with local error:

19.5b	(sqrt (fma c (* -4 a) (* b b)))
0.5b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`fma-neg` `sqrt-prod`
4×	`associate-/l*`
3×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`div-sub` `div-inv`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `flip3--` `pow1/2` `flip--` `associate-/l/`

Calls

3 calls:

Slowest

23.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
12.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -4 a) (* b b)))

series148.0ms

Calls

3 calls:

Slowest

54.0ms	(sqrt (fma c (* -4 a) (* b b)))
49.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
44.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify465.0ms

Calls

23 calls:

Slowest

48.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
44.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
43.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
42.0ms	(sqrt (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))))
40.0ms	(sqrt (sqrt (fma c (* -4 a) (* b b))))

prune808.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.3b

regimes328.0ms

Accuracy

80.7% (4.0b remaining)

Error of 16.7b against oracle of 12.7b and baseline of 33.5b

bsearch127.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	1021×	body	2560	valid
928.0ms	5887×	body	80	valid
590.0ms	926×	body	1280	valid
379.0ms	3030×	body	80	nan
351.0ms	456×	body	640	valid
129.0ms	112×	body	5120	valid
82.0ms	220×	body	320	valid
31.0ms	117×	body	160	valid