Details

sample163.0ms

Algorithm

intervals

Results

42.0ms	180×	body	80	valid
41.0ms	38×	body	2560	valid
20.0ms	23×	body	1280	valid
17.0ms	106×	body	80	nan
13.0ms	19×	body	640	valid
5.0ms	4×	body	5120	valid
2.0ms	5×	body	160	valid
1.0ms	2×	body	320	valid

simplify201.0ms

Calls

1 calls:

Slowest

201.0ms

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

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.2b

localize41.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (fma c (* -4 a) (* b b)))
1.1b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.5b	(fma c (* -4 a) (* b b))
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

22.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
13.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -4 a) (* b b)))
0.0ms	(fma c (* -4 a) (* b b))

series220.0ms

Calls

4 calls:

Slowest

61.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
55.0ms	(sqrt (fma c (* -4 a) (* b b)))
55.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
50.0ms	(fma c (* -4 a) (* b b))

simplify721.0ms

Calls

26 calls:

Slowest

92.0ms	(- (pow b 2) (* 4 (* a c)))
70.0ms	(- (pow b 2) (* 4 (* a c)))
59.0ms	(- (pow b 2) (* 4 (* a c)))
56.0ms	(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
52.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)

prune967.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 29.8b

localize22.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (fma (* a c) -4 (* b b)))
1.1b	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.6b	(fma (* a c) -4 (* b b))
0.1b	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

12.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
9.0ms	(- (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))

series216.0ms

Calls

4 calls:

Slowest

91.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
45.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
43.0ms	(sqrt (fma (* a c) -4 (* b b)))
37.0ms	(fma (* a c) -4 (* b b))

simplify772.0ms

Calls

26 calls:

Slowest

93.0ms	(- (pow b 2) (* 4 (* a c)))
77.0ms	(- (pow b 2) (* 4 (* a c)))
75.0ms	(* (cbrt (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
61.0ms	(sqrt (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))
58.0ms	(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))

prune936.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 29.8b

localize12.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (fma (* a c) -4 (* b b)))
1.1b	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.6b	(fma (* a c) -4 (* b b))
0.2b	(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

6.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))
1.0ms	(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
0.0ms	(fma (* a c) -4 (* b b))

series225.0ms

Calls

4 calls:

Slowest

97.0ms	(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
50.0ms	(sqrt (fma (* a c) -4 (* b b)))
47.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
30.0ms	(fma (* a c) -4 (* b b))

simplify771.0ms

Calls

27 calls:

Slowest

81.0ms	(/ 1 (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))
79.0ms	(- (pow b 2) (* 4 (* a c)))
71.0ms	(sqrt (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
69.0ms	(- (pow b 2) (* 4 (* a c)))
58.0ms	(- (pow b 2) (* 4 (* a c)))

prune814.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 29.8b

localize9.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (fma (* a c) -4 (* b b)))
26.1b	(sqrt (fma (* a c) -4 (* b b)))
1.1b	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.1b	(- (sqrt (fma (* a c) -4 (* b b))) b)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `fma-neg` `sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sub-neg` `flip3--` `pow1/2` `flip--`

Calls

4 calls:

Slowest

9.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
8.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series236.0ms

Calls

4 calls:

Slowest

65.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
59.0ms	(sqrt (fma (* a c) -4 (* b b)))
57.0ms	(sqrt (fma (* a c) -4 (* b b)))
55.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)

simplify499.0ms

Calls

30 calls:

Slowest

47.0ms	(* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b)))))
46.0ms	(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))
42.0ms	(sqrt (sqrt (fma (* a c) -4 (* b b))))
41.0ms	(sqrt (sqrt (fma (* a c) -4 (* b b))))
36.0ms	(* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b)))))

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 29.8b

regimes281.0ms

Accuracy

82.9% (0.9b remaining)

Error of 29.7b against oracle of 28.8b and baseline of 34.3b

bsearch449.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

988.0ms	915×	body	1280	valid
985.0ms	1032×	body	2560	valid
808.0ms	5797×	body	80	valid
378.0ms	2865×	body	80	nan
282.0ms	488×	body	640	valid
156.0ms	122×	body	5120	valid
98.0ms	217×	body	320	valid
26.0ms	109×	body	160	valid