Details

sample335.0ms

Algorithm

intervals

Results

187.0ms	32×	body	2560	valid
47.0ms	27×	body	1280	valid
20.0ms	194×	body	80	valid
8.0ms	95×	body	80	nan
5.0ms	5×	body	5120	valid
3.0ms	8×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	7×	body	160	valid

simplify91.0ms

Calls

1 calls:

Slowest

90.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize32.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b_2 b_2) (* a c)))
2.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite66.0ms

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

33.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
17.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(- (* b_2 b_2) (* a c))

series351.0ms

Calls

4 calls:

Slowest

138.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
87.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
50.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Calls

31 calls:

Slowest

545.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
536.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
201.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
199.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
195.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune954.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize11.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b_2 b_2) (* a c)))
2.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

31.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
16.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(- (* b_2 b_2) (* a c))

series170.0ms

Calls

4 calls:

Slowest

71.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
43.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
36.0ms	(sqrt (- (* b_2 b_2) (* a c)))
20.0ms	(- (* b_2 b_2) (* a c))

simplify4.3s

Calls

41 calls:

Slowest

523.0ms	(* (* (* (- (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)))
409.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
389.0ms	(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) 1)
379.0ms	(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) (/ 1 a))
372.0ms	(* (+ (* (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)

prune993.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.4b

localize11.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b_2 b_2) (* a c)))
13.1b	(/ (- 0 (* a c)) a)
1.1b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

22.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms	(/ (- 0 (* a c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(- (* b_2 b_2) (* a c))

series148.0ms

Calls

4 calls:

Slowest

66.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
38.0ms	(sqrt (- (* b_2 b_2) (* a c)))
33.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ (- 0 (* a c)) a)

simplify2.3s

Calls

32 calls:

Slowest

384.0ms	(- (pow 0 3) (pow (* a c) 3))
376.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
264.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
234.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
223.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune950.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.4b

localize9.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
6×	`fma-def` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `neg-mul-1` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*`
2×	`flip3-+` `flip3--` `sqrt-div` `associate-/r/` `flip-+` `flip--`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `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

15.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(- (* b_2 b_2) (* a c))

series228.0ms

Calls

4 calls:

Slowest

115.0ms	(/ (- c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
44.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms	(sqrt (- (* b_2 b_2) (* a c)))
28.0ms	(- (* b_2 b_2) (* a c))

simplify3.8s

Calls

61 calls:

Slowest

866.0ms	(+ (* (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)))
440.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
255.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
219.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
194.0ms	(/ (* (* (- c) (- c)) (- c)) (* (* (+ (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)))

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.4b

regimes353.0ms

Accuracy

95% (1.2b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 29.1b

bsearch283.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

934.0ms	876×	body	1280	valid
858.0ms	5801×	body	80	valid
763.0ms	1119×	body	2560	valid
318.0ms	2891×	body	80	nan
201.0ms	470×	body	640	valid
162.0ms	216×	body	320	valid
160.0ms	118×	body	5120	valid
26.0ms	128×	body	160	valid