Details

sample132.0ms

Algorithm

intervals

Results

45.0ms	35×	body	2560	valid
26.0ms	182×	body	80	valid
21.0ms	29×	body	1280	valid
12.0ms	97×	body	80	nan
7.0ms	13×	body	640	valid
2.0ms	5×	body	320	valid
2.0ms	2×	body	5120	valid
1.0ms	2×	body	160	valid

simplify82.0ms

Calls

1 calls:

Slowest

82.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize49.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (- (* b_2 b_2) (* a c)))
0.8b	(- (* b_2 b_2) (* a c))
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `prod-diff`
21×	`add-cube-cbrt`
17×	`sqrt-prod`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`associate-/l*`
5×	`fma-neg`
4×	`expm1-log1p-u` `pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`sub-neg` `sqrt-div` `diff-log` `distribute-lft-out--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `pow1/2` `div-sub` `div-inv`

Calls

4 calls:

Slowest

28.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(- (* b_2 b_2) (* a c))

series372.0ms

Calls

4 calls:

Slowest

142.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))
91.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
47.0ms	(- (* b_2 b_2) (* a c))

simplify5.8s

Calls

84 calls:

Slowest

348.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
342.0ms	(- (* (- b_2) (- b_2)) (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))))
243.0ms	(- (pow (- b_2) 3) (pow (sqrt (- (* b_2 b_2) (* a c))) 3))
228.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
189.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

localize23.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (- (* b_2 b_2) (* a c)))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))
0.8b	(- (* b_2 b_2) (* a c))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Calls

4 calls:

Slowest

8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))
5.0ms	(- (* b_2 b_2) (* a c))

series323.0ms

Calls

4 calls:

Slowest

100.0ms	(sqrt (- (* b_2 b_2) (* a c)))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))
49.0ms	(- (* b_2 b_2) (* a c))

simplify3.1s

Calls

33 calls:

Slowest

384.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
351.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
341.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
263.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
245.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize16.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (- (* b_2 b_2) (* a c)))
5.7b	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
0.8b	(- (* b_2 b_2) (* a c))
0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
17×	`prod-diff`
16×	`add-cube-cbrt`
12×	`div-inv`
8×	`add-log-exp`
6×	`sqrt-prod` `associate-/l*`
5×	`fma-neg`
4×	`expm1-log1p-u` `pow1` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-rgt-out--` `pow1/2` `div-sub` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Calls

4 calls:

Slowest

15.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
6.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
2.0ms	(- (* b_2 b_2) (* a c))

series444.0ms

Calls

4 calls:

Slowest

137.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
135.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))
68.0ms	(- (* b_2 b_2) (* a c))

simplify6.1s

Calls

73 calls:

Slowest

363.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
352.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
242.0ms	(fma (- b_2) (/ 1 a) (- (* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c))))))
219.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
209.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.8b

localize12.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (- (* b_2 b_2) (* a c)))
9.6b	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
0.8b	(- (* b_2 b_2) (* a c))
0.3b	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `frac-sub` `sqrt-prod`
5×	`fma-neg` `prod-diff`
4×	`expm1-log1p-u` `frac-times` `associate-r` `associate-*l/` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`associate-*r/` `un-div-inv`
2×	`sub-neg` `diff-log` `sub-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-out--` `pow1/2` `div-sub` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

11.0ms	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
8.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))
2.0ms	(- (* b_2 b_2) (* a c))

series432.0ms

Calls

4 calls:

Slowest

153.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
125.0ms	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(- (* b_2 b_2) (* a c))

simplify6.3s

Calls

68 calls:

Slowest

448.0ms	(* (sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3))) (/ 1 a))
432.0ms	(* (* (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (- (* b_2 b_2) (* a c)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
382.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
296.0ms	(* (sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3))) 1)
295.0ms	(- (* (- b_2) (* (sqrt (+ (* b_2 b_2) (* a c))) a)) (* a (* (sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c)))) 1)))

prune879.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.8b

regimes474.0ms

Accuracy

82.6% (5.0b remaining)

Error of 10.5b against oracle of 5.5b and baseline of 34.2b

bsearch142.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.0s	5836×	body	80	valid
793.0ms	1092×	body	2560	valid
604.0ms	925×	body	1280	valid
322.0ms	2941×	body	80	nan
161.0ms	424×	body	640	valid
107.0ms	105×	body	5120	valid
99.0ms	233×	body	320	valid
23.0ms	120×	body	160	valid