Details

sample138.0ms

Algorithm

intervals

Results

14.0ms	200×	body	80	valid
13.0ms	34×	body	1280	valid
9.0ms	22×	body	2560	valid
7.0ms	104×	body	80	nan
3.0ms	11×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify71.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

70.0ms

(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize19.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (- (* b_2 b_2) (* a c)))
1.4b	(- (* b_2 b_2) (* a c))
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
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`

Counts

4 → 88

Calls

4 calls:

Slowest

60.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
40.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

series799.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

305.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
194.0ms	(- (* b_2 b_2) (* a c))
157.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
142.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.9s

Counts

73 → 100

Calls

73 calls:

Slowest

379.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
310.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
308.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
259.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
218.0ms	(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))

prune963.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize40.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (- (* b_2 b_2) (* a c)))
1.4b	(- (* b_2 b_2) (* a c))
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

Slowest

131.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
41.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(- (* b_2 b_2) (* a c))

series379.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

162.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))
82.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms	(- (* b_2 b_2) (* a c))

simplify5.3s

Counts

62 → 101

Calls

62 calls:

Slowest

469.0ms	(* (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
446.0ms	(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) 1)
433.0ms	(* (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2)) 1)
349.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
263.0ms	(* (+ (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (+ (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

localize41.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (- (* b_2 b_2) (* a c)))
14.4b	(/ (- 0 (* a c)) a)
1.4b	(- (* b_2 b_2) (* a c))
0.7b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`insert-posit16`
3×	`associate-/r` `flip3--` `sqrt-prod` `flip--` `associate-/l`
2×	`sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-sub` `div-exp` `distribute-frac-neg` `flip-+` `div-inv` `distribute-lft-out` `sub0-neg`

Counts

4 → 74

Calls

4 calls:

Slowest

41.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(/ (- 0 (* a c)) a)
9.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

119.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))
42.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ (- 0 (* a c)) a)

simplify4.2s

Counts

50 → 86

Calls

50 calls:

Slowest

1.3s	(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
305.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
261.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
227.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
221.0ms	(- (pow 0 3) (pow (* a c) 3))

prune879.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.9b

localize18.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (- (* b_2 b_2) (* a c)))
1.4b	(- (* b_2 b_2) (* a c))
0.7b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.3b	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
40×	`times-frac`
32×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
15×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`distribute-lft-out`
10×	`associate-/l*`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `neg-mul-1`
4×	`associate-/r*` `insert-posit16`
3×	`sqrt-prod`
2×	`flip3-+` `flip3--` `sqrt-div` `associate-/r/` `flip-+` `flip--`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `distribute-frac-neg` `div-inv`

Counts

4 → 113

Calls

4 calls:

Slowest

61.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
50.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

266.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
148.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))
52.0ms	(- (* b_2 b_2) (* a c))

simplify4.8s

Counts

119 → 125

Calls

119 calls:

Slowest

317.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
294.0ms	(+ (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (- (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) b_2)))
241.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
216.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
201.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.9b

regimes320.0ms

Accuracy

81% (4.4b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 29.1b

bsearch227.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	1113×	body	2560	valid
770.0ms	5763×	body	80	valid
482.0ms	885×	body	1280	valid
375.0ms	2953×	body	80	nan
222.0ms	485×	body	640	valid
86.0ms	115×	body	5120	valid
67.0ms	229×	body	320	valid
23.0ms	117×	body	160	valid