Details

sample159.0ms

Algorithm

intervals

Results

48.0ms	199×	body	80	valid
31.0ms	32×	body	2560	valid
20.0ms	26×	body	1280	valid
15.0ms	97×	body	80	nan
10.0ms	16×	body	640	valid
9.0ms	7×	body	5120	valid
3.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify194.0ms

Counts: 1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize39.0ms

Local error

Found 4 expressions with local error:

23.0b	(sqrt (- (* b b) (* 4 (* a c))))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.8b	(- (* b b) (* 4 (* a c)))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`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 → 161

Calls

4 calls:

Slowest

83.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
19.0ms	(sqrt (- (* b b) (* 4 (* a c))))
9.0ms	(- (* b b) (* 4 (* a c)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

144.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
140.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
89.0ms	(sqrt (- (* b b) (* 4 (* a c))))
81.0ms	(- (* b b) (* 4 (* a c)))

simplify783.0ms

Counts: 173 → 173

prune2.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize37.0ms

Local error

Found 4 expressions with local error:

23.0b	(sqrt (- (* b b) (* 4 (* a c))))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.8b	(- (* b b) (* 4 (* a c)))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`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 → 161

Calls

4 calls:

Slowest

65.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
21.0ms	(- (* b b) (* 4 (* a c)))
19.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

127.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
121.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
96.0ms	(sqrt (- (* b b) (* 4 (* a c))))
59.0ms	(- (* b b) (* 4 (* a c)))

simplify723.0ms

Counts: 173 → 173

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.0b

localize78.0ms

Local error

Found 4 expressions with local error:

23.0b	(sqrt (- (* b b) (* 4 (* a c))))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.8b	(- (* b b) (* 4 (* a c)))
0.2b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
68×	`add-cube-cbrt`
67×	`times-frac`
61×	`prod-diff`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
25×	`add-exp-log`
21×	`distribute-lft-neg-in`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 209

Calls

4 calls:

Slowest

38.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
19.0ms	(sqrt (- (* b b) (* 4 (* a c))))
9.0ms	(- (* b b) (* 4 (* a c)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
121.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
96.0ms	(sqrt (- (* b b) (* 4 (* a c))))
80.0ms	(- (* b b) (* 4 (* a c)))

simplify1.2s

Counts: 221 → 221

prune3.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.9b

localize72.0ms

Local error

Found 4 expressions with local error:

23.0b	(sqrt (- (* b b) (* 4 (* a c))))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.8b	(- (* b b) (* 4 (* a c)))
0.2b	(* (/ 1 (* 2 a)) (- (- b) (sqrt (- (* b b) (* 4 (* a c))))))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
136×	`add-sqr-sqrt`
133×	`*-un-lft-identity`
125×	`add-cube-cbrt`
95×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
23×	`add-exp-log`
19×	`neg-mul-1`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `associate-*r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 292

Calls

4 calls:

Slowest

121.0ms	(* (/ 1 (* 2 a)) (- (- b) (sqrt (- (* b b) (* 4 (* a c))))))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
25.0ms	(sqrt (- (* b b) (* 4 (* a c))))
17.0ms	(- (* b b) (* 4 (* a c)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

155.0ms	(* (/ 1 (* 2 a)) (- (- b) (sqrt (- (* b b) (* 4 (* a c))))))
120.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
109.0ms	(sqrt (- (* b b) (* 4 (* a c))))
59.0ms	(- (* b b) (* 4 (* a c)))

simplify1.6s

Counts: 304 → 304

prune5.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.9b

regimes381.0ms

Accuracy

82.5% (5.0b remaining)

Error of 10.5b against oracle of 5.5b and baseline of 34.0b

bsearch229.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.6s	953×	body	1280	valid
1.2s	1139×	body	2560	valid
1.1s	5730×	body	80	valid
428.0ms	2788×	body	80	nan
283.0ms	402×	body	640	valid
120.0ms	215×	body	320	valid
101.0ms	96×	body	5120	valid
44.0ms	149×	body	160	valid