Details

sample139.0ms

Algorithm

intervals

Results

32.0ms	33×	body	2560	valid
28.0ms	176×	body	80	valid
26.0ms	34×	body	1280	valid
11.0ms	76×	body	80	nan
8.0ms	12×	body	640	valid
5.0ms	4×	body	5120	valid
3.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify173.0ms

Counts: 1 → 1

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize22.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (- (* b b) (* (* 3 a) c)))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.2b	(- (* b b) (* (* 3 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

rewrite122.0ms

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

61.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
34.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
11.0ms	(- (* b b) (* (* 3 a) c))

series425.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

157.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
121.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
78.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
69.0ms	(- (* b b) (* (* 3 a) c))

simplify2.2s

Counts: 106 → 106

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.4b

localize37.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (fma (* a c) -3 (* b b)))
1.2b	(- (sqrt (fma (* a c) -3 (* b b))) b)
0.3b	(fma (* a c) -3 (* b b))
0.2b	(/ (/ (- (sqrt (fma (* a c) -3 (* b b))) b) 3) a)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 179

Calls

4 calls:

Slowest

26.0ms	(/ (/ (- (sqrt (fma (* a c) -3 (* b b))) b) 3) a)
13.0ms	(- (sqrt (fma (* a c) -3 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -3 (* b b)))
0.0ms	(fma (* a c) -3 (* b b))

series426.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

144.0ms	(/ (/ (- (sqrt (fma (* a c) -3 (* b b))) b) 3) a)
120.0ms	(- (sqrt (fma (* a c) -3 (* b b))) b)
90.0ms	(sqrt (fma (* a c) -3 (* b b)))
72.0ms	(fma (* a c) -3 (* b b))

simplify797.0ms

Counts: 191 → 191

prune2.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

localize41.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (fma a (* -3 c) (* b b)))
1.2b	(- (sqrt (fma a (* -3 c) (* b b))) b)
0.2b	(/ (/ (- (sqrt (fma a (* -3 c) (* b b))) b) 3) a)
0.1b	(/ (- (sqrt (fma a (* -3 c) (* b b))) b) 3)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
156×	`times-frac`
127×	`*-un-lft-identity`
93×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
28×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 213

Calls

4 calls:

Slowest

16.0ms	(/ (/ (- (sqrt (fma a (* -3 c) (* b b))) b) 3) a)
16.0ms	(/ (- (sqrt (fma a (* -3 c) (* b b))) b) 3)
15.0ms	(- (sqrt (fma a (* -3 c) (* b b))) b)
2.0ms	(sqrt (fma a (* -3 c) (* b b)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

167.0ms	(/ (/ (- (sqrt (fma a (* -3 c) (* b b))) b) 3) a)
117.0ms	(sqrt (fma a (* -3 c) (* b b)))
114.0ms	(- (sqrt (fma a (* -3 c) (* b b))) b)
99.0ms	(/ (- (sqrt (fma a (* -3 c) (* b b))) b) 3)

simplify821.0ms

Counts: 225 → 225

prune2.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.3b

localize34.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (fma a (* -3 c) (* b b)))
1.2b	(- (sqrt (fma a (* -3 c) (* b b))) b)
0.3b	(/ (- (sqrt (fma a (* -3 c) (* b b))) b) (cbrt 3))
0.2b	(* (/ 1 (* (cbrt 3) (cbrt 3))) (/ (/ (- (sqrt (fma a (* -3 c) (* b b))) b) (cbrt 3)) a))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

290×	`times-frac`
280×	`add-sqr-sqrt`
196×	`*-un-lft-identity`
140×	`add-cube-cbrt`
124×	`associate-r`
84×	`add-exp-log`
78×	`cbrt-prod`
52×	`difference-of-squares`
41×	`sqrt-prod`
34×	`div-exp`
32×	`add-cbrt-cube`
30×	`prod-exp`
26×	`distribute-lft-out--`
18×	`prod-diff`
16×	`cbrt-undiv`
12×	`cbrt-unprod` `unswap-sqr`
7×	`pow1` `associate-l`
6×	`rec-exp` `associate-/r` `fma-neg` `1-exp` `div-inv` `associate-/l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`flip3--` `flip--` `associate-/l/`
1×	`frac-times` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 312

Calls

4 calls:

Slowest

81.0ms	(* (/ 1 (* (cbrt 3) (cbrt 3))) (/ (/ (- (sqrt (fma a (* -3 c) (* b b))) b) (cbrt 3)) a))
17.0ms	(/ (- (sqrt (fma a (* -3 c) (* b b))) b) (cbrt 3))
8.0ms	(- (sqrt (fma a (* -3 c) (* b b))) b)
1.0ms	(sqrt (fma a (* -3 c) (* b b)))

series997.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

485.0ms	(/ (- (sqrt (fma a (* -3 c) (* b b))) b) (cbrt 3))
301.0ms	(* (/ 1 (* (cbrt 3) (cbrt 3))) (/ (/ (- (sqrt (fma a (* -3 c) (* b b))) b) (cbrt 3)) a))
121.0ms	(- (sqrt (fma a (* -3 c) (* b b))) b)
90.0ms	(sqrt (fma a (* -3 c) (* b b)))

simplify975.0ms

Counts: 324 → 324

prune4.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.3b

regimes629.0ms

Accuracy

84.5% (4.3b remaining)

Error of 10.2b against oracle of 5.9b and baseline of 33.6b

bsearch461.0ms

end0.0ms

sample4.0s

Algorithm

intervals

Results

849.0ms	5799×	body	80	valid
803.0ms	1090×	body	2560	valid
672.0ms	921×	body	1280	valid
508.0ms	124×	body	5120	valid
460.0ms	2992×	body	80	nan
272.0ms	438×	body	640	valid
73.0ms	226×	body	320	valid
28.0ms	125×	body	160	valid