Details

sample124.0ms

Algorithm

intervals

Results

37.0ms	180×	body	80	valid
29.0ms	38×	body	2560	valid
15.0ms	23×	body	1280	valid
12.0ms	106×	body	80	nan
9.0ms	19×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	5×	body	160	valid
1.0ms	2×	body	320	valid

simplify127.0ms

Calls

1 calls:

Slowest

127.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize41.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (fma b b (* (* a c) -4)))
1.1b	(- (sqrt (fma b b (* (* a c) -4))) b)
0.8b	(fma b b (* (* a c) -4))
0.1b	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite41.0ms

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

19.0ms	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
13.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
8.0ms	(sqrt (fma b b (* (* a c) -4)))
0.0ms	(fma b b (* (* a c) -4))

series219.0ms

Calls

4 calls:

Slowest

82.0ms	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
53.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
44.0ms	(fma b b (* (* a c) -4))
40.0ms	(sqrt (fma b b (* (* a c) -4)))

simplify1.3s

Calls

26 calls:

Slowest

245.0ms	(- b (* 2 (/ (* a c) b)))
139.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
76.0ms	(- (* 2 (/ (* a c) b)) b)
70.0ms	(- (pow b 2) (* 4 (* a c)))
63.0ms	(* -2 (/ (* a c) b))

prune908.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.8b

localize12.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (fma b b (* (* a c) -4)))
1.1b	(- (sqrt (fma b b (* (* a c) -4))) b)
0.8b	(fma b b (* (* a c) -4))
0.2b	(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

22.0ms	(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))
13.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms	(sqrt (fma b b (* (* a c) -4)))
0.0ms	(fma b b (* (* a c) -4))

series271.0ms

Calls

4 calls:

Slowest

86.0ms	(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))
74.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
72.0ms	(sqrt (fma b b (* (* a c) -4)))
39.0ms	(fma b b (* (* a c) -4))

simplify2.2s

Calls

34 calls:

Slowest

292.0ms	(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))
223.0ms	(+ (log (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (log (/ 1 a)))
202.0ms	(- b (* 2 (/ (* a c) b)))
194.0ms	(* (* (* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
140.0ms	(* (- (sqrt (fma b b (* (* a c) -4))) b) (/ 1 a))

prune959.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.8b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

3 calls:

Slowest

13.0ms	(/ (- (sqrt (fma a (* -4 c) (* b b))) b) a)
10.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
2.0ms	(sqrt (fma a (* -4 c) (* b b)))

series193.0ms

Calls

3 calls:

Slowest

88.0ms	(/ (- (sqrt (fma a (* -4 c) (* b b))) b) a)
53.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
52.0ms	(sqrt (fma a (* -4 c) (* b b)))

simplify1.0s

Calls

23 calls:

Slowest

490.0ms	(- (* (sqrt (fma a (* -4 c) (* b b))) (sqrt (fma a (* -4 c) (* b b)))) (* b b))
206.0ms	(- (pow (sqrt (fma a (* -4 c) (* b b))) 3) (pow b 3))
53.0ms	(* (cbrt (- (sqrt (fma a (* -4 c) (* b b))) b)) (cbrt (- (sqrt (fma a (* -4 c) (* b b))) b)))
39.0ms	(sqrt (- (sqrt (fma a (* -4 c) (* b b))) b))
33.0ms	(/ (sqrt (fma a (* -4 c) (* b b))) a)

prune596.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

localize15.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (fma a (* -4 c) (* b b)))
1.1b	(- (sqrt (fma a (* -4 c) (* b b))) b)
0.2b	(/ 1 (/ a (- (sqrt (fma a (* -4 c) (* b b))) b)))
0.1b	(/ a (- (sqrt (fma a (* -4 c) (* b b))) b))

rewrite21.0ms

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` `associate-/r/`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `div-inv` `flip--`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `rec-exp` `sub-neg` `pow1/2` `pow-flip` `inv-pow`

Calls

4 calls:

Slowest

13.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
3.0ms	(/ a (- (sqrt (fma a (* -4 c) (* b b))) b))
2.0ms	(/ 1 (/ a (- (sqrt (fma a (* -4 c) (* b b))) b)))
2.0ms	(sqrt (fma a (* -4 c) (* b b)))

series344.0ms

Calls

4 calls:

Slowest

157.0ms	(/ a (- (sqrt (fma a (* -4 c) (* b b))) b))
86.0ms	(/ 1 (/ a (- (sqrt (fma a (* -4 c) (* b b))) b)))
54.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
47.0ms	(sqrt (fma a (* -4 c) (* b b)))

simplify931.0ms

Calls

34 calls:

Slowest

153.0ms	(+ (* (sqrt (fma a (* -4 c) (* b b))) (sqrt (fma a (* -4 c) (* b b)))) (+ (* b b) (* (sqrt (fma a (* -4 c) (* b b))) b)))
130.0ms	(+ (* (sqrt (fma a (* -4 c) (* b b))) (sqrt (fma a (* -4 c) (* b b)))) (+ (* b b) (* (sqrt (fma a (* -4 c) (* b b))) b)))
50.0ms	(/ 1 (- (sqrt (fma a (* -4 c) (* b b))) b))
44.0ms	(* (cbrt (sqrt (fma a (* -4 c) (* b b)))) (cbrt (sqrt (fma a (* -4 c) (* b b)))))
44.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)

prune874.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.8b

regimes313.0ms

Accuracy

85.3% (4.1b remaining)

Error of 9.5b against oracle of 5.4b and baseline of 33.6b

bsearch136.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.3s	1032×	body	2560	valid
947.0ms	5797×	body	80	valid
689.0ms	915×	body	1280	valid
441.0ms	2865×	body	80	nan
336.0ms	488×	body	640	valid
155.0ms	122×	body	5120	valid
112.0ms	217×	body	320	valid
29.0ms	109×	body	160	valid