Details

sample181.0ms

Algorithm

intervals

Results

45.0ms	27×	body	1280	valid
45.0ms	41×	body	2560	valid
33.0ms	179×	body	80	valid
16.0ms	95×	body	80	nan
9.0ms	12×	body	640	valid
5.0ms	4×	body	5120	valid
4.0ms	8×	body	320	valid
1.0ms	3×	body	160	valid

simplify150.0ms

Calls

1 calls:

Slowest

150.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize28.0ms

Local error

Found 4 expressions with local error:

25.6b	(sqrt (- (* b b) (* (* 4 a) c)))
1.8b	(- (* b b) (* (* 4 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.1b	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

200×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
72×	`times-frac`
58×	`difference-of-squares`
43×	`unswap-sqr`
39×	`associate-l` `add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-lft-out--`
21×	`associate-r`
13×	`*-commutative`
12×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`swap-sqr` `associate-/l*`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Calls

4 calls:

Slowest

665.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))
355.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
70.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
46.0ms	(- (* b b) (* (* 4 a) c))

series444.0ms

Calls

4 calls:

Slowest

179.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))
107.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
97.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
60.0ms	(- (* b b) (* (* 4 a) c))

simplify20.7s

Calls

247 calls:

Slowest

631.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* (sqrt 2) (sqrt a)))
516.0ms	(- (* (sqrt (- (* b b) (* (* 4 a) c))) (sqrt (- (* b b) (* (* 4 a) c)))) (* b b))
437.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
393.0ms	(- (pow (sqrt (- (* b b) (* (* 4 a) c))) 3) (pow b 3))
288.0ms	(/ (exp (* b b)) (exp (* (* 4 a) c)))

prune2.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.5b

localize43.0ms

Local error

Found 4 expressions with local error:

25.6b	(sqrt (- (* b b) (* (* 4 a) c)))
1.8b	(- (* b b) (* (* 4 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.4b	(* (sqrt 2) a)

rewrite503.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
38×	`unswap-sqr`
34×	`*-un-lft-identity`
32×	`difference-of-squares`
29×	`sqrt-prod`
24×	`associate-l`
13×	`distribute-lft-out--`
8×	`add-cube-cbrt` `add-log-exp`
7×	`pow1` `*-commutative`
6×	`add-cbrt-cube` `swap-sqr` `add-exp-log`
4×	`insert-posit16`
3×	`flip3--` `associate-r` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `cbrt-unprod`

Calls

4 calls:

Slowest

338.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
90.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
65.0ms	(- (* b b) (* (* 4 a) c))
7.0ms	(* (sqrt 2) a)

series308.0ms

Calls

4 calls:

Slowest

97.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
95.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
61.0ms	(- (* b b) (* (* 4 a) c))
55.0ms	(* (sqrt 2) a)

simplify4.8s

Calls

97 calls:

Slowest

485.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
310.0ms	(/ (exp (* b b)) (exp (* (* 4 a) c)))
290.0ms	(- b (* 2 (/ (* a c) b)))
189.0ms	(* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a a) a))
179.0ms	(sqrt (- (pow (* b b) 3) (pow (* (* 4 a) c) 3)))

prune1.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.5b

localize62.0ms

Local error

Found 4 expressions with local error:

25.6b	(sqrt (- (* b b) (* (* 4 a) c)))
1.8b	(- (* b b) (* (* 4 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.3b	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (sqrt 2))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

149×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
53×	`sqrt-prod`
46×	`difference-of-squares`
36×	`times-frac` `unswap-sqr`
26×	`add-cube-cbrt`
20×	`distribute-lft-out--`
18×	`associate-l`
8×	`add-log-exp`
6×	`associate-/r` `add-cbrt-cube` `swap-sqr` `add-exp-log` `-commutative` `associate-/l*`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Calls

4 calls:

Slowest

578.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (sqrt 2))
342.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
61.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
42.0ms	(- (* b b) (* (* 4 a) c))

series536.0ms

Calls

4 calls:

Slowest

244.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (sqrt 2))
121.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
108.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
64.0ms	(- (* b b) (* (* 4 a) c))

simplify12.5s

Calls

170 calls:

Slowest

602.0ms	(- (* (sqrt (- (* b b) (* (* 4 a) c))) (sqrt (- (* b b) (* (* 4 a) c)))) (* b b))
400.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
372.0ms	(- (pow (sqrt (- (* b b) (* (* 4 a) c))) 3) (pow b 3))
265.0ms	(- b (* 2 (/ (* a c) b)))
262.0ms	(/ (* (* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (- (sqrt (- (* b b) (* (* 4 a) c))) b)) (- (sqrt (- (* b b) (* (* 4 a) c))) b)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune2.5s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 5.5b

localize65.0ms

Local error

Found 4 expressions with local error:

25.6b	(sqrt (- (* b b) (* (* 4 a) c)))
1.8b	(- (* b b) (* (* 4 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.3b	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) a))

rewrite606.0ms

Algorithm

rewrite-expression-head

Rules

147×	`add-sqr-sqrt`
67×	`sqrt-prod`
60×	`unswap-sqr`
39×	`*-un-lft-identity`
36×	`associate-l`
32×	`difference-of-squares`
23×	`associate-r`
13×	`add-cube-cbrt` `distribute-lft-out--`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-commutative` `add-log-exp`
6×	`swap-sqr`
4×	`insert-posit16`
3×	`flip3--` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Calls

4 calls:

Slowest

413.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
73.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
67.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) a))
48.0ms	(- (* b b) (* (* 4 a) c))

series353.0ms

Calls

4 calls:

Slowest

124.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
91.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
80.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) a))
58.0ms	(- (* b b) (* (* 4 a) c))

simplify5.8s

Calls

139 calls:

Slowest

431.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
280.0ms	(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) a) (* (sqrt (sqrt 2)) a)) (* (sqrt (sqrt 2)) a)))
251.0ms	(/ (exp (* b b)) (exp (* (* 4 a) c)))
251.0ms	(- b (* 2 (/ (* a c) b)))
229.0ms	(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* a a) a)))

prune2.4s

Pruning

18 alts after pruning (15 fresh and 3 done)

Merged error: 5.5b

regimes693.0ms

Accuracy

80.8% (5.4b remaining)

Error of 11.3b against oracle of 5.9b and baseline of 34.2b

bsearch540.0ms

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.7s	1070×	body	2560	valid
1.2s	889×	body	1280	valid
1.0s	5855×	body	80	valid
548.0ms	3022×	body	80	nan
266.0ms	452×	body	640	valid
100.0ms	245×	body	320	valid
100.0ms	101×	body	5120	valid
28.0ms	106×	body	160	valid