Details

sample75.0ms

Algorithm

intervals

Results

13.0ms	98×	body	80	nan
13.0ms	38×	body	2560	valid
13.0ms	192×	body	80	valid
8.0ms	25×	body	1280	valid
3.0ms	15×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify66.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

113.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
125.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
83.0ms	(- (* b b) (* 4.0 (* a c)))
115.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify784.0ms

Counts: 82 → 82

prune305.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.9b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
45×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `flip3-+` `flip-+` `div-inv`
3×	`rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 114

Calls

4 calls:

83.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
30.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
118.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
59.0ms	(- (* b b) (* 4.0 (* a c)))
125.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts: 126 → 126

prune461.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

localize38.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

13.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* b b) (* 4.0 (* a c)))
122.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
105.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
102.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts: 69 → 69

prune512.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize59.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series479.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
114.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
135.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
116.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts: 72 → 72

prune611.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.6b

regimes395.0ms

Accuracy

83.3% (4.7b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 33.6b

bsearch136.0ms

Steps

Iters	Range		Point
6	3.2999883719107076e-115	1.481810096151352e-114	5.81843322574321e-115
8	-1.3549447721302977e+118	-2.218977696437643e+113	-1.2609617020890706e+118

simplify208.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

716.0ms	857×	body	1280	valid
692.0ms	5956×	body	80	valid
503.0ms	1036×	body	2560	valid
286.0ms	2895×	body	80	nan
201.0ms	458×	body	640	valid
103.0ms	101×	body	5120	valid
60.0ms	117×	body	160	valid
51.0ms	247×	body	320	valid