Details

sample131.0ms

Algorithm

intervals

Results

37.0ms	41×	body	2560	valid
28.0ms	191×	body	80	valid
23.0ms	28×	body	1280	valid
12.0ms	93×	body	80	nan
6.0ms	12×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify144.0ms

Counts: 1 → 1

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize43.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (- (* b b) (* (* 4 a) c)))
1.0b	(- (* b b) (* (* 4 a) c))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

Slowest

70.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
17.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(- (* b b) (* (* 4 a) c))

series395.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

145.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
91.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
90.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
69.0ms	(- (* b b) (* (* 4 a) c))

simplify2.4s

Counts: 106 → 106

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.6b

localize41.0ms

Local error

Found 3 expressions with local error:

23.1b	(sqrt (fma c (* -4 a) (* b b)))
0.8b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
134×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
81×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
18×	`prod-diff`
13×	`distribute-lft-out--`
8×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg`
5×	`div-inv` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `div-exp` `insert-posit16` `log1p-expm1-u`
2×	`div-sub`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `associate-/l/`

Counts

3 → 168

Calls

3 calls:

Slowest

19.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
16.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms	(sqrt (fma c (* -4 a) (* b b)))

series354.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

122.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
120.0ms	(sqrt (fma c (* -4 a) (* b b)))
112.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

simplify1.2s

Counts: 177 → 177

prune2.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.6b

localize26.0ms

Local error

Found 3 expressions with local error:

23.1b	(sqrt (fma c (* a -4) (* b b)))
0.8b	(- (sqrt (fma c (* a -4) (* b b))) b)
0.2b	(* (- (sqrt (fma c (* a -4) (* b b))) b) (/ 1/2 a))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r`
10×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `fma-neg` `associate-l`
5×	`add-log-exp`
4×	`difference-of-squares`
3×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`frac-times` `associate-*l/` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv`

Counts

3 → 100

Calls

3 calls:

Slowest

25.0ms	(* (- (sqrt (fma c (* a -4) (* b b))) b) (/ 1/2 a))
8.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
1.0ms	(sqrt (fma c (* a -4) (* b b)))

series364.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

148.0ms	(* (- (sqrt (fma c (* a -4) (* b b))) b) (/ 1/2 a))
118.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
98.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.8s

Counts: 109 → 109

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.6b

localize65.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (fma c (* -4 a) (* b b)))
23.1b	(sqrt (fma c (* -4 a) (* b b)))
0.8b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.8b	(- (sqrt (fma c (* -4 a) (* b b))) b)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

Slowest

9.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
8.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series508.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

145.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
125.0ms	(sqrt (fma c (* -4 a) (* b b)))
121.0ms	(sqrt (fma c (* -4 a) (* b b)))
116.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify3.0s

Counts: 128 → 128

prune2.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.6b

regimes462.0ms

Accuracy

84.5% (4.3b remaining)

Error of 9.9b against oracle of 5.5b and baseline of 33.7b

bsearch172.0ms

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.5s	1143×	body	2560	valid
1.2s	5839×	body	80	valid
768.0ms	888×	body	1280	valid
701.0ms	450×	body	640	valid
452.0ms	2933×	body	80	nan
123.0ms	115×	body	5120	valid
86.0ms	203×	body	320	valid
30.0ms	108×	body	160	valid