Details

sample181.0ms

Algorithm

intervals

Results

53.0ms	64×	body	80	nan
17.0ms	31×	body	2560	valid
17.0ms	35×	body	1280	valid
17.0ms	183×	body	80	valid
6.0ms	18×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	3×	body	160	valid

simplify79.0ms

Calls

1 calls:

Slowest

78.0ms

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize35.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite94.0ms

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

60.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
17.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(- (* b_2 b_2) (* a c))

series206.0ms

Calls

4 calls:

Slowest

73.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))
46.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
26.0ms	(- (* b_2 b_2) (* a c))

simplify2.4s

Calls

31 calls:

Slowest

492.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
377.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
218.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
215.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
193.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune933.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize6.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

34.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(/ 1 (/ a (- (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))

series254.0ms

Calls

4 calls:

Slowest

92.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
67.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))
35.0ms	(- (* b_2 b_2) (* a c))

simplify1.9s

Calls

34 calls:

Slowest

405.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
287.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
242.0ms	(+ (* (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)))
206.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
125.0ms	(- (* 1/2 (/ (* a c) b_2)) (* 2 b_2))

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.8b

localize6.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite68.0ms

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))
30.0ms	(- (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))

series211.0ms

Calls

4 calls:

Slowest

78.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
60.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
53.0ms	(sqrt (- (* b_2 b_2) (* a c)))
21.0ms	(- (* b_2 b_2) (* a c))

simplify4.2s

Calls

41 calls:

Slowest

430.0ms	(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) 1)
403.0ms	(* (* (* (- (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)))
392.0ms	(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) (/ 1 a))
388.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
341.0ms	(* (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2)) 1)

prune901.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.8b

localize11.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (- (* b_2 b_2) (* a c)))
13.2b	(/ (- 0 (* a c)) a)
1.0b	(- (* b_2 b_2) (* a c))
0.8b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite34.0ms

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

21.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(/ (- 0 (* a c)) a)

series131.0ms

Calls

4 calls:

Slowest

43.0ms	(sqrt (- (* b_2 b_2) (* a c)))
41.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
37.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ (- 0 (* a c)) a)

simplify2.1s

Calls

32 calls:

Slowest

375.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
301.0ms	(- (pow 0 3) (pow (* a c) 3))
262.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
234.0ms	(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
212.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune947.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.8b

regimes357.0ms

Accuracy

96.1% (0.9b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.1b

bsearch241.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.2s	1088×	body	2560	valid
889.0ms	5810×	body	80	valid
750.0ms	2844×	body	80	nan
660.0ms	923×	body	1280	valid
260.0ms	459×	body	640	valid
112.0ms	97×	body	5120	valid
110.0ms	222×	body	320	valid
24.0ms	110×	body	160	valid