Details

sample208.0ms

Algorithm

intervals

Results

63.0ms	92×	body	80	nan
31.0ms	38×	body	2560	valid
24.0ms	186×	body	80	valid
17.0ms	27×	body	1280	valid
7.0ms	13×	body	640	valid
4.0ms	9×	body	320	valid
2.0ms	2×	body	5120	valid
1.0ms	4×	body	160	valid

simplify84.0ms

Calls

1 calls:

Slowest

83.0ms

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

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize30.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite159.0ms

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`

Calls

4 calls:

Slowest

77.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
61.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

series399.0ms

Calls

4 calls:

Slowest

133.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
112.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))
56.0ms	(- (* b_2 b_2) (* a c))

simplify4.3s

Calls

73 calls:

Slowest

371.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
343.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
285.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
248.0ms	(/ (* (* (- (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))
217.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize42.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite256.0ms

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`

Calls

4 calls:

Slowest

176.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
56.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

series370.0ms

Calls

4 calls:

Slowest

133.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))
94.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
44.0ms	(- (* b_2 b_2) (* a c))

simplify5.6s

Calls

62 calls:

Slowest

553.0ms	(* (* (* (- (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)))
510.0ms	(* (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 (sqrt a)))
447.0ms	(* (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2)) 1)
390.0ms	(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) 1)
347.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize21.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (- (* b_2 b_2) (* a c)))
14.2b	(/ (- 0 (* a c)) a)
1.1b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))

rewrite80.0ms

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`

Calls

4 calls:

Slowest

39.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(/ (- 0 (* a c)) a)
16.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series306.0ms

Calls

4 calls:

Slowest

121.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))
61.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(/ (- 0 (* a c)) a)

simplify4.1s

Calls

50 calls:

Slowest

1.3s	(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
346.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
251.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
217.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
215.0ms	(- (pow 0 3) (pow (* a c) 3))

prune918.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize17.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))

rewrite137.0ms

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`

Calls

4 calls:

Slowest

59.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
43.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series508.0ms

Calls

4 calls:

Slowest

284.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
96.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))
46.0ms	(- (* b_2 b_2) (* a c))

simplify4.8s

Calls

119 calls:

Slowest

303.0ms	(+ (* (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)))
294.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
265.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
231.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
195.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

regimes307.0ms

Accuracy

94.3% (1.4b remaining)

Error of 6.9b against oracle of 5.5b and baseline of 29.6b

bsearch299.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	1063×	body	2560	valid
866.0ms	5881×	body	80	valid
492.0ms	913×	body	1280	valid
358.0ms	2865×	body	80	nan
183.0ms	413×	body	640	valid
128.0ms	123×	body	5120	valid
70.0ms	229×	body	320	valid
21.0ms	104×	body	160	valid