Details

sample198.0ms

Algorithm

intervals

Results

45.0ms	23×	body	1280	valid
20.0ms	38×	body	2560	valid
17.0ms	180×	body	80	valid
9.0ms	19×	body	640	valid
9.0ms	106×	body	80	nan
2.0ms	4×	body	5120	valid
1.0ms	5×	body	160	valid
1.0ms	2×	body	320	valid

simplify88.0ms

Calls

1 calls:

Slowest

88.0ms

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize49.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

44.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
23.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(- (* b_2 b_2) (* a c))

series274.0ms

Calls

4 calls:

Slowest

88.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))
69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
34.0ms	(- (* b_2 b_2) (* a c))

simplify2.6s

Calls

31 calls:

Slowest

476.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
471.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
257.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
234.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
201.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune849.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize2.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

28.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(- (* b_2 b_2) (* a c))

series201.0ms

Calls

4 calls:

Slowest

68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
41.0ms	(sqrt (- (* b_2 b_2) (* a c)))
33.0ms	(- (* b_2 b_2) (* a c))

simplify2.5s

Calls

31 calls:

Slowest

522.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
346.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
288.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
238.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
173.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune837.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize10.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (- (* b_2 b_2) (* a c)))
14.1b	(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.6b	(- (* b_2 b_2) (* a c))
0.5b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`fma-def` `times-frac` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `flip3--` `sqrt-div` `associate-*r/` `associate-/r/` `flip-+` `flip--`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `distribute-frac-neg` `div-inv`

Calls

4 calls:

Slowest

12.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(- (* b_2 b_2) (* a c))

series266.0ms

Calls

4 calls:

Slowest

133.0ms	(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
55.0ms	(sqrt (- (* b_2 b_2) (* a c)))
43.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
35.0ms	(- (* b_2 b_2) (* a c))

simplify5.1s

Calls

48 calls:

Slowest

1.5s	(/ (* (* (- (* a c)) (- (* a c))) (- (* a c))) (* (* (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
483.0ms	(+ (* (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)))
452.0ms	(- (log (- (* a c))) (log (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
393.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
326.0ms	(/ (* a c) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize7.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (- (* b_2 b_2) (* a c)))
0.6b	(- (* b_2 b_2) (* a c))
0.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
0.1b	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `sqrt-prod`
2×	`flip3-+` `flip3--` `sqrt-div` `associate-/r/` `flip-+` `flip--`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `pow1/2` `fma-neg` `diff-log` `prod-diff` `div-inv`

Calls

4 calls:

Slowest

3.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(- (* b_2 b_2) (* a c))
2.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
2.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))

series293.0ms

Calls

4 calls:

Slowest

147.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
70.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
41.0ms	(sqrt (- (* b_2 b_2) (* a c)))
35.0ms	(- (* b_2 b_2) (* a c))

simplify2.1s

Calls

26 calls:

Slowest

396.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
385.0ms	(+ (* b_2 b_2) (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 (sqrt (- (* b_2 b_2) (* a c))))))
275.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
239.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
183.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

regimes353.0ms

Accuracy

83% (4.5b remaining)

Error of 9.7b against oracle of 5.2b and baseline of 31.5b

bsearch184.0ms

end0.0ms

sample3.8s

Algorithm

intervals

Results

748.0ms	1030×	body	2560	valid
743.0ms	5797×	body	80	valid
717.0ms	918×	body	1280	valid
520.0ms	217×	body	320	valid
358.0ms	2862×	body	80	nan
286.0ms	488×	body	640	valid
133.0ms	123×	body	5120	valid
23.0ms	108×	body	160	valid