Details

sample122.0ms

Algorithm

intervals

Results

32.0ms	28×	body	1280	valid
26.0ms	38×	body	2560	valid
21.0ms	178×	body	80	valid
11.0ms	97×	body	80	nan
9.0ms	20×	body	640	valid
3.0ms	5×	body	320	valid
2.0ms	2×	body	5120	valid
2.0ms	6×	body	160	valid

simplify160.0ms

Calls

1 calls:

Slowest

159.0ms

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize38.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (fma c (* -4 a) (* b b)))
1.5b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
156×	`times-frac`
127×	`*-un-lft-identity`
93×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
28×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Calls

4 calls:

Slowest

28.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
18.0ms	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
11.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms	(sqrt (fma c (* -4 a) (* b b)))

series571.0ms

Calls

4 calls:

Slowest

148.0ms	(sqrt (fma c (* -4 a) (* b b)))
144.0ms	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
141.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
136.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

simplify14.9s

Calls

272 calls:

Slowest

409.0ms	(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
334.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
253.0ms	(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
208.0ms	(/ (* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b)) (* (* 2 2) 2))
202.0ms	(/ (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (* (* a a) a))

prune2.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 33.2b

localize23.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (fma c (* -4 a) (* b b)))
1.5b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
0.2b	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
52×	`times-frac`
47×	`add-cube-cbrt`
28×	`add-exp-log`
23×	`sqrt-prod`
22×	`associate-l`
18×	`add-cbrt-cube` `prod-diff`
16×	`difference-of-squares`
13×	`associate-r`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--`
7×	`pow1`
6×	`fma-neg` `associate-/l*` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative`

Calls

4 calls:

Slowest

30.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
16.0ms	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
7.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series360.0ms

Calls

4 calls:

Slowest

97.0ms	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
88.0ms	(sqrt (fma c (* -4 a) (* b b)))
87.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
87.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))

simplify7.8s

Calls

173 calls:

Slowest

382.0ms	(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
364.0ms	(/ (- (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (sqrt 2))
242.0ms	(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
225.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
187.0ms	(* (/ (* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b)) (* (* 2 2) 2)) (/ (* (* 1 1) 1) (* (* a a) a)))

prune1.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 33.2b

localize26.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (fma c (* -4 a) (* b b)))
25.3b	(sqrt (fma c (* -4 a) (* b b)))
12.7b	(- (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) b)
0.5b	(* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
52×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`prod-diff`
2×	`rem-sqrt-square`
1×	`pow2` `sub-neg` `rem-square-sqrt` `pow-plus` `flip3--` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `difference-of-squares`

Calls

4 calls:

Slowest

18.0ms	(- (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) b)
12.0ms	(* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))))
2.0ms	(sqrt (fma c (* -4 a) (* b b)))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series339.0ms

Calls

4 calls:

Slowest

89.0ms	(sqrt (fma c (* -4 a) (* b b)))
87.0ms	(- (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) b)
84.0ms	(sqrt (fma c (* -4 a) (* b b)))
78.0ms	(* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))))

simplify3.4s

Calls

138 calls:

Slowest

255.0ms	(* (* (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) (* (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) (sqrt (sqrt (fma c (* -4 a) (* b b))))))
204.0ms	(* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b)))
199.0ms	(* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b)))
159.0ms	(/ (exp (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))))) (exp b))
96.0ms	(* (* (cbrt (sqrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (sqrt (fma c (* -4 a) (* b b)))))) (* (cbrt (sqrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (sqrt (fma c (* -4 a) (* b b)))))))

prune1.4s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 33.2b

localize20.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (fma c (* -4 a) (* b b)))
1.5b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
156×	`times-frac`
127×	`*-un-lft-identity`
93×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
28×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Calls

4 calls:

Slowest

22.0ms	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
16.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
8.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -4 a) (* b b)))

series361.0ms

Calls

4 calls:

Slowest

96.0ms	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
90.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
88.0ms	(sqrt (fma c (* -4 a) (* b b)))
87.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify12.4s

Calls

272 calls:

Slowest

386.0ms	(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
295.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
241.0ms	(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
175.0ms	(/ (* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b)) (* (* 2 2) 2))
147.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))

prune2.0s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 33.2b

regimes322.0ms

Accuracy

94.3% (0.3b remaining)

Error of 29.2b against oracle of 28.9b and baseline of 33.8b

bsearch92.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

980.0ms	5797×	body	80	valid
770.0ms	1093×	body	2560	valid
560.0ms	453×	body	640	valid
473.0ms	916×	body	1280	valid
386.0ms	2941×	body	80	nan
121.0ms	110×	body	5120	valid
118.0ms	240×	body	320	valid
23.0ms	120×	body	160	valid