Details

sample142.0ms

Algorithm

intervals

Results

51.0ms	179×	body	80	valid
34.0ms	44×	body	2560	valid
19.0ms	31×	body	1280	valid
10.0ms	92×	body	80	nan
7.0ms	11×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify159.0ms

Counts: 1 → 1

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize27.0ms

Local error

Found 4 expressions with local error:

25.5b	(sqrt (- (* b b) (* 4 (* a c))))
1.4b	(- (* b b) (* 4 (* a c)))
1.0b	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

rewrite143.0ms

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

82.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
28.0ms	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
23.0ms	(- (* b b) (* 4 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series443.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

144.0ms	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
135.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
96.0ms	(sqrt (- (* b b) (* 4 (* a c))))
68.0ms	(- (* b b) (* 4 (* a c)))

simplify2.0s

Counts: 106 → 106

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize46.0ms

Local error

Found 4 expressions with local error:

25.5b	(sqrt (- (* b b) (* 4 (* a c))))
1.4b	(- (* b b) (* 4 (* a c)))
1.0b	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

Slowest

63.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
21.0ms	(sqrt (- (* b b) (* 4 (* a c))))
15.0ms	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms	(- (* b b) (* 4 (* a c)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

173.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
94.0ms	(sqrt (- (* b b) (* 4 (* a c))))
91.0ms	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
60.0ms	(- (* b b) (* 4 (* a c)))

simplify674.0ms

Counts: 116 → 116

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.7b

localize61.0ms

Local error

Found 4 expressions with local error:

25.5b	(sqrt (- (* b b) (* 4 (* a c))))
25.5b	(sqrt (- (* b b) (* 4 (* a c))))
1.4b	(- (* b b) (* 4 (* a c)))
1.4b	(- (* b b) (* 4 (* a c)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

Calls

4 calls:

Slowest

20.0ms	(- (* b b) (* 4 (* a c)))
18.0ms	(- (* b b) (* 4 (* a c)))
15.0ms	(sqrt (- (* b b) (* 4 (* a c))))
9.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series348.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

127.0ms	(sqrt (- (* b b) (* 4 (* a c))))
99.0ms	(sqrt (- (* b b) (* 4 (* a c))))
73.0ms	(- (* b b) (* 4 (* a c)))
48.0ms	(- (* b b) (* 4 (* a c)))

simplify658.0ms

Counts: 82 → 82

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.7b

localize28.0ms

Local error

Found 4 expressions with local error:

25.5b	(sqrt (fma a (* -4 c) (* b b)))
1.0b	(- (sqrt (fma a (* -4 c) (* b b))) b)
0.3b	(fma a (* -4 c) (* b b))
0.1b	(/ (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2) a)

rewrite57.0ms

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

35.0ms	(/ (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2) a)
15.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
3.0ms	(sqrt (fma a (* -4 c) (* b b)))
0.0ms	(fma a (* -4 c) (* b b))

series483.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

158.0ms	(/ (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2) a)
120.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
118.0ms	(sqrt (fma a (* -4 c) (* b b)))
87.0ms	(fma a (* -4 c) (* b b))

simplify754.0ms

Counts: 191 → 191

prune2.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.7b

regimes519.0ms

Accuracy

84.8% (4.3b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 33.7b

bsearch155.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.3s	1094×	body	2560	valid
863.0ms	5828×	body	80	valid
638.0ms	903×	body	1280	valid
414.0ms	234×	body	320	valid
347.0ms	2909×	body	80	nan
255.0ms	466×	body	640	valid
131.0ms	122×	body	5120	valid
23.0ms	99×	body	160	valid