Details

sample117.0ms

Algorithm

intervals

Results

28.0ms	179×	body	80	valid
24.0ms	34×	body	2560	valid
18.0ms	31×	body	1280	valid
11.0ms	82×	body	80	nan
8.0ms	17×	body	640	valid
5.0ms	5×	body	5120	valid
3.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify117.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

116.0ms

(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize40.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (- (* b b) (* (* 3 a) c)))
1.2b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.4b	(- (* b b) (* (* 3 a) c))
0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))

rewrite607.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

Slowest

543.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
44.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
8.0ms	(- (* b b) (* (* 3 a) c))

series423.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
109.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
105.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
68.0ms	(- (* b b) (* (* 3 a) c))

simplify5.0s

Counts

49 → 88

Calls

49 calls:

Slowest

554.0ms	(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
317.0ms	(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
299.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
298.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
229.0ms	(/ (* (* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize39.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (- (* b b) (* (* 3 a) c)))
1.2b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.4b	(- (* b b) (* (* 3 a) c))
0.2b	(* (* 3 a) c)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

Slowest

47.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
32.0ms	(* (* 3 a) c)
16.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
9.0ms	(- (* b b) (* (* 3 a) c))

series284.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
87.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
76.0ms	(- (* b b) (* (* 3 a) c))
21.0ms	(* (* 3 a) c)

simplify3.0s

Counts

34 → 76

Calls

34 calls:

Slowest

399.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
387.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
384.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
227.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
199.0ms	(- b (* 3/2 (/ (* a c) b)))

prune946.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize25.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (+ (* b b) (* (* c -3) a)))
1.2b	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
0.4b	(+ (* b b) (* (* c -3) a))
0.2b	(* (* c -3) a)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `sqrt-div` `flip-+` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-l` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

Slowest

39.0ms	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
15.0ms	(* (* c -3) a)
8.0ms	(+ (* b b) (* (* c -3) a))
7.0ms	(sqrt (+ (* b b) (* (* c -3) a)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

85.0ms	(- (sqrt (+ (* b b) (* (* c -3) a))) b)
79.0ms	(sqrt (+ (* b b) (* (* c -3) a)))
56.0ms	(+ (* b b) (* (* c -3) a))
24.0ms	(* (* c -3) a)

simplify2.6s

Counts

34 → 75

Calls

34 calls:

Slowest

382.0ms	(* (* (* (* c -3) (* c -3)) (* c -3)) (* (* a a) a))
349.0ms	(* (* (* (* c c) c) (* (* -3 -3) -3)) (* (* a a) a))
286.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* c -3) a) (* (* c -3) a))))
244.0ms	(- b (* 3/2 (/ (* a c) b)))
239.0ms	(* (exp (* b b)) (exp (* (* c -3) a)))

prune988.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.1b

localize42.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (- (* b b) (* (* 3 a) c)))
1.2b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.4b	(- (* b b) (* (* 3 a) c))
0.3b	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`associate-r`
19×	`times-frac`
16×	`add-cube-cbrt`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
4×	`insert-posit16` `distribute-lft-out--`
3×	`flip3--` `associate-l` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv`

Counts

4 → 87

Calls

4 calls:

Slowest

93.0ms	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
46.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
15.0ms	(- (* b b) (* (* 3 a) c))
15.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
127.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
77.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
74.0ms	(- (* b b) (* (* 3 a) c))

simplify5.5s

Counts

59 → 99

Calls

59 calls:

Slowest

341.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
280.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
262.0ms	(- b (* 3/2 (/ (* a c) b)))
229.0ms	(* (* (* 1/3 1/3) 1/3) (/ (* (* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (* (* a a) a)))
172.0ms	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.1b

regimes849.0ms

Accuracy

84% (4.4b remaining)

Error of 10.3b against oracle of 5.9b and baseline of 33.6b

bsearch435.0ms

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.4s	1052×	body	2560	valid
1.0s	871×	body	1280	valid
959.0ms	5836×	body	80	valid
437.0ms	2786×	body	80	nan
281.0ms	469×	body	640	valid
121.0ms	124×	body	5120	valid
114.0ms	237×	body	320	valid
27.0ms	108×	body	160	valid