Details

sample163.0ms

Algorithm

intervals

Results

58.0ms	38×	body	2560	valid
30.0ms	180×	body	80	valid
18.0ms	23×	body	1280	valid
16.0ms	106×	body	80	nan
12.0ms	19×	body	640	valid
4.0ms	4×	body	5120	valid
2.0ms	5×	body	160	valid
1.0ms	2×	body	320	valid

simplify171.0ms

Calls

1 calls:

Slowest

170.0ms

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.2b

localize33.0ms

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)

rewrite32.0ms

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

15.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
14.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
2.0ms	(sqrt (fma c (* -4 a) (* b b)))
0.0ms	(fma c (* -4 a) (* b b))

series195.0ms

Calls

4 calls:

Slowest

60.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
57.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
44.0ms	(sqrt (fma c (* -4 a) (* b b)))
33.0ms	(fma c (* -4 a) (* b b))

simplify583.0ms

Calls

26 calls:

Slowest

83.0ms	(- (pow b 2) (* 4 (* a c)))
64.0ms	(- (pow b 2) (* 4 (* a c)))
52.0ms	(- (pow b 2) (* 4 (* a c)))
51.0ms	(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
41.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)

prune793.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 29.8b

localize19.0ms

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)

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

23.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
12.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series239.0ms

Calls

4 calls:

Slowest

78.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
65.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
55.0ms	(sqrt (fma (* a c) -4 (* b b)))
42.0ms	(fma (* a c) -4 (* b b))

simplify713.0ms

Calls

26 calls:

Slowest

79.0ms	(- (pow b 2) (* 4 (* a c)))
78.0ms	(- (pow b 2) (* 4 (* a c)))
70.0ms	(- (pow b 2) (* 4 (* a c)))
58.0ms	(* (cbrt (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
51.0ms	(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)

prune874.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 29.8b

localize6.0ms

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

7.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(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))

series237.0ms

Calls

4 calls:

Slowest

96.0ms	(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
57.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
49.0ms	(sqrt (fma (* a c) -4 (* b b)))
35.0ms	(fma (* a c) -4 (* b b))

simplify796.0ms

Calls

27 calls:

Slowest

80.0ms	(/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))
67.0ms	(sqrt (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
66.0ms	(cbrt (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
66.0ms	(- (pow b 2) (* 4 (* a c)))
60.0ms	(/ 1 (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))

prune771.0ms

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)

rewrite16.0ms

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

7.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
6.0ms	(- (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)))

series181.0ms

Calls

4 calls:

Slowest

47.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
47.0ms	(sqrt (fma (* a c) -4 (* b b)))
45.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
42.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify435.0ms

Calls

30 calls:

Slowest

33.0ms	(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))
33.0ms	(* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b)))))
31.0ms	(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))
31.0ms	(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))
31.0ms	(sqrt (sqrt (fma (* a c) -4 (* b b))))

prune922.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 29.8b

regimes246.0ms

Accuracy

82.9% (0.9b remaining)

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

bsearch84.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.1s	5797×	body	80	valid
761.0ms	1032×	body	2560	valid
537.0ms	915×	body	1280	valid
326.0ms	2865×	body	80	nan
204.0ms	488×	body	640	valid
87.0ms	217×	body	320	valid
80.0ms	122×	body	5120	valid
20.0ms	109×	body	160	valid