Details

sample128.0ms

Algorithm

intervals

Results

36.0ms	197×	body	80	valid
29.0ms	36×	body	2560	valid
18.0ms	28×	body	1280	valid
11.0ms	93×	body	80	nan
9.0ms	15×	body	640	valid
3.0ms	6×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	2×	body	160	valid

simplify279.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize22.0ms

Local error

Found 4 expressions with local error:

24.8b	(sqrt (- (* b b) (* 4 (* a c))))
1.4b	(- (* b b) (* 4 (* a c)))
0.4b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 81

Calls

4 calls:

Slowest

41.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
19.0ms	(- (* b b) (* 4 (* a c)))
18.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
114.0ms	(sqrt (- (* b b) (* 4 (* a c))))
97.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
64.0ms	(- (* b b) (* 4 (* a c)))

simplify1.7s

Counts: 93 → 93

prune954.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize48.0ms

Local error

Found 4 expressions with local error:

24.8b	(sqrt (- (* b b) (* 4 (* a c))))
1.4b	(- (* b b) (* 4 (* a c)))
0.4b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.1b	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
13×	`associate-r` `add-cube-cbrt`
10×	`times-frac` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

Slowest

99.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
22.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
16.0ms	(- (* b b) (* 4 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
120.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
89.0ms	(sqrt (- (* b b) (* 4 (* a c))))
68.0ms	(- (* b b) (* 4 (* a c)))

simplify2.2s

Counts: 101 → 101

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.6b

localize39.0ms

Local error

Found 4 expressions with local error:

24.8b	(sqrt (- (* b b) (* 4 (* a c))))
21.0b	(- (* b b) (* b b))
9.6b	(/ (+ (- (* b b) (* b b)) (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b))
3.2b	(/ (/ (+ (- (* b b) (* b b)) (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b)) (* 2 a))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
77×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
21×	`difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
13×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`insert-posit16` `div-inv`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `prod-exp` `associate-+l-` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out--` `pow1/2` `+-inverses` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

Slowest

187.0ms	(/ (/ (+ (- (* b b) (* b b)) (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b)) (* 2 a))
93.0ms	(/ (+ (- (* b b) (* b b)) (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b))
12.0ms	(sqrt (- (* b b) (* 4 (* a c))))
7.0ms	(- (* b b) (* b b))

series491.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

227.0ms	(/ (+ (- (* b b) (* b b)) (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b))
164.0ms	(/ (/ (+ (- (* b b) (* b b)) (* 4 (* a c))) (- (sqrt (- (* b b) (* 4 (* a c)))) b)) (* 2 a))
97.0ms	(sqrt (- (* b b) (* 4 (* a c))))
2.0ms	(- (* b b) (* b b))

simplify737.0ms

Counts: 160 → 160

prune1.9s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.6b

localize34.0ms

Local error

Found 4 expressions with local error:

24.8b	(sqrt (- (* b b) (* 4 (* a c))))
16.0b	(* (/ (* 4 (* a c)) 2) (/ (/ 1 (- (sqrt (- (* b b) (* 4 (* a c)))) b)) a))
1.4b	(- (* b b) (* 4 (* a c)))
1.0b	(- (sqrt (- (* b b) (* 4 (* a c)))) b)

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
115×	`add-sqr-sqrt`
94×	`add-exp-log`
83×	`*-un-lft-identity`
76×	`associate-r`
62×	`add-cube-cbrt`
58×	`add-cbrt-cube`
39×	`div-exp`
35×	`prod-exp`
21×	`cbrt-undiv` `cbrt-unprod`
20×	`difference-of-squares`
13×	`sqrt-prod`
10×	`distribute-lft-out--`
8×	`add-log-exp`
7×	`pow1` `associate-l`
6×	`flip3--` `associate-/r/` `flip--`
5×	`div-inv`
4×	`rec-exp` `1-exp` `insert-posit16` `unswap-sqr`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 177

Calls

4 calls:

Slowest

151.0ms	(* (/ (* 4 (* a c)) 2) (/ (/ 1 (- (sqrt (- (* b b) (* 4 (* a c)))) b)) a))
54.0ms	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
12.0ms	(- (* b b) (* 4 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series500.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

252.0ms	(* (/ (* 4 (* a c)) 2) (/ (/ 1 (- (sqrt (- (* b b) (* 4 (* a c)))) b)) a))
101.0ms	(- (sqrt (- (* b b) (* 4 (* a c)))) b)
85.0ms	(sqrt (- (* b b) (* 4 (* a c))))
62.0ms	(- (* b b) (* 4 (* a c)))

simplify2.3s

Counts: 189 → 189

prune2.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.6b

regimes570.0ms

Accuracy

84.3% (4.2b remaining)

Error of 9.9b against oracle of 5.7b and baseline of 32.5b

bsearch197.0ms

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.2s	895×	body	1280	valid
992.0ms	1077×	body	2560	valid
932.0ms	5902×	body	80	valid
465.0ms	2917×	body	80	nan
303.0ms	465×	body	640	valid
119.0ms	106×	body	5120	valid
90.0ms	229×	body	320	valid
24.0ms	96×	body	160	valid