Details

sample93.0ms

Algorithm

intervals

Results

22.0ms	31×	body	2560	valid
22.0ms	201×	body	80	valid
14.0ms	26×	body	1280	valid
10.0ms	87×	body	80	nan
5.0ms	11×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify125.0ms

Calls

1 calls:

Slowest

125.0ms

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.5b

localize41.0ms

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)

rewrite21.0ms

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

11.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
7.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -4 a) (* b b)))

series168.0ms

Calls

3 calls:

Slowest

59.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
55.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
53.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify441.0ms

Calls

23 calls:

Slowest

52.0ms	(sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
42.0ms	(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
40.0ms	(sqrt (sqrt (fma c (* -4 a) (* b b))))
39.0ms	(sqrt (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))))
39.0ms	(* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b)))))

prune701.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.4b

localize11.0ms

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))

rewrite19.0ms

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

12.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms	(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
2.0ms	(sqrt (fma c (* -4 a) (* b b)))
1.0ms	(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))

series358.0ms

Calls

4 calls:

Slowest

168.0ms	(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
98.0ms	(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
49.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
42.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify654.0ms

Calls

31 calls:

Slowest

65.0ms	(sqrt (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
64.0ms	(cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
57.0ms	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
47.0ms	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
42.0ms	(sqrt (sqrt (fma c (* -4 a) (* b b))))

prune917.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.3b

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

rewrite12.0ms

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

6.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms	(/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a))
2.0ms	(/ 1 (/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series302.0ms

Calls

4 calls:

Slowest

102.0ms	(/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a))
71.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
68.0ms	(sqrt (fma c (* -4 a) (* b b)))
61.0ms	(/ 1 (/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))

simplify1.3s

Calls

34 calls:

Slowest

175.0ms	(/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a))
149.0ms	(sqrt (/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)))
138.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
128.0ms	(/ 1 (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a))
122.0ms	(cbrt (/ (/ (- (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)

rewrite18.0ms

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

11.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
6.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series187.0ms

Calls

3 calls:

Slowest

72.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
59.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
56.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify426.0ms

Calls

23 calls:

Slowest

51.0ms	(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
43.0ms	(sqrt (sqrt (fma c (* -4 a) (* b b))))
41.0ms	(sqrt (sqrt (fma c (* -4 a) (* b b))))
41.0ms	(sqrt (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))))
41.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)

prune698.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.3b

regimes312.0ms

Accuracy

80.7% (4.0b remaining)

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

bsearch170.0ms

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.3s	5887×	body	80	valid
942.0ms	1021×	body	2560	valid
704.0ms	926×	body	1280	valid
568.0ms	112×	body	5120	valid
380.0ms	3030×	body	80	nan
252.0ms	456×	body	640	valid
83.0ms	220×	body	320	valid
29.0ms	117×	body	160	valid