Details

sample289.0ms

Algorithm

intervals

Results

130.0ms	28×	body	1280	valid
32.0ms	97×	body	80	nan
29.0ms	38×	body	2560	valid
19.0ms	178×	body	80	valid
9.0ms	20×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	valid

simplify117.0ms

Calls

1 calls:

Slowest

116.0ms

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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize37.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (- (* b_2 b_2) (* a c)))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
0.3b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite132.0ms

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

58.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
46.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

series315.0ms

Calls

4 calls:

Slowest

113.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))
76.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms	(- (* b_2 b_2) (* a c))

simplify3.7s

Calls

73 calls:

Slowest

335.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
324.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
303.0ms	(/ (* (* (- (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))
244.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
200.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune969.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.4b

localize35.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (- (* b_2 b_2) (* a c)))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
0.5b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite192.0ms

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

133.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
35.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

series391.0ms

Calls

4 calls:

Slowest

128.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
108.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))
64.0ms	(- (* b_2 b_2) (* a c))

simplify5.2s

Calls

62 calls:

Slowest

537.0ms	(* (* (* (- (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)))
450.0ms	(* (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2)) 1)
391.0ms	(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) 1)
332.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
242.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.4b

localize25.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (- (* b_2 b_2) (* a c)))
18.5b	(/ (- 0 (* a c)) a)
0.8b	(- (* b_2 b_2) (* a c))
0.5b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)

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

44.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(/ (- 0 (* a c)) a)
13.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series259.0ms

Calls

4 calls:

Slowest

99.0ms	(sqrt (- (* b_2 b_2) (* a c)))
90.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
55.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(/ (- 0 (* a c)) a)

simplify4.7s

Calls

50 calls:

Slowest

1.7s	(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
333.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
248.0ms	(- (pow 0 3) (pow (* a c) 3))
246.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
203.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune870.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.4b

localize40.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (- (* b_2 b_2) (* a c)))
0.8b	(- (* b_2 b_2) (* a c))
0.5b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
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

62.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
44.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
14.0ms	(- (* b_2 b_2) (* a c))

series496.0ms

Calls

4 calls:

Slowest

234.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
107.0ms	(sqrt (- (* b_2 b_2) (* a c)))
95.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
61.0ms	(- (* b_2 b_2) (* a c))

simplify4.9s

Calls

119 calls:

Slowest

302.0ms	(+ (* (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)))
255.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
247.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
220.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
189.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.4b

regimes298.0ms

Accuracy

93.1% (1.7b remaining)

Error of 7.1b against oracle of 5.5b and baseline of 29.4b

bsearch293.0ms

end0.0ms

sample3.8s

Algorithm

intervals

Results

954.0ms	920×	body	1280	valid
878.0ms	1095×	body	2560	valid
812.0ms	5800×	body	80	valid
459.0ms	2941×	body	80	nan
229.0ms	451×	body	640	valid
120.0ms	110×	body	5120	valid
112.0ms	243×	body	320	valid
24.0ms	116×	body	160	valid