Details

sample118.0ms

Algorithm

intervals

Results

30.0ms	34×	body	2560	valid
24.0ms	185×	body	80	valid
18.0ms	32×	body	1280	valid
12.0ms	100×	body	80	nan
8.0ms	16×	body	640	valid
4.0ms	5×	body	5120	valid
2.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify125.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

125.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize22.0ms

Local error

Found 4 expressions with local error:

24.4b	(sqrt (- (* b b) (* (* 3 a) c)))
1.0b	(- (* b b) (* (* 3 a) c))
0.9b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))

rewrite167.0ms

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

87.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
64.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
7.0ms	(- (* b b) (* (* 3 a) c))

series457.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

164.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
118.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
112.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
63.0ms	(- (* b b) (* (* 3 a) c))

simplify5.3s

Counts

49 → 88

Calls

49 calls:

Slowest

565.0ms	(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
403.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
374.0ms	(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
323.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
244.0ms	(- b (* 3/2 (/ (* a c) b)))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.3b

localize31.0ms

Local error

Found 4 expressions with local error:

24.4b	(sqrt (- (* b b) (* (* 3 a) c)))
1.0b	(- (* b b) (* (* 3 a) c))
0.9b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.2b	(* (* 3 a) c)

rewrite79.0ms

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

36.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
27.0ms	(* (* 3 a) c)
7.0ms	(- (* b b) (* (* 3 a) c))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

116.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
100.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
63.0ms	(- (* b b) (* (* 3 a) c))
33.0ms	(* (* 3 a) c)

simplify3.3s

Counts

34 → 76

Calls

34 calls:

Slowest

426.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
414.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
389.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
300.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
232.0ms	(- b (* 3/2 (/ (* a c) b)))

prune928.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.3b

localize42.0ms

Local error

Found 4 expressions with local error:

24.4b	(sqrt (- (* b b) (* 3 (* a c))))
1.0b	(- (* b b) (* 3 (* a c)))
0.9b	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
0.2b	(* 3 (* a c))

rewrite79.0ms

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-l` `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-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

Slowest

37.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
25.0ms	(* 3 (* a c))
8.0ms	(- (* b b) (* 3 (* a c)))
7.0ms	(sqrt (- (* b b) (* 3 (* a c))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(sqrt (- (* b b) (* 3 (* a c))))
119.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
56.0ms	(- (* b b) (* 3 (* a c)))
39.0ms	(* 3 (* a c))

simplify3.6s

Counts

34 → 76

Calls

34 calls:

Slowest

564.0ms	(* (* (* 3 3) 3) (* (* (* a c) (* a c)) (* a c)))
429.0ms	(* (* (* 3 3) 3) (* (* (* a a) a) (* (* c c) c)))
352.0ms	(sqrt (- (* (* b b) (* b b)) (* (* 3 (* a c)) (* 3 (* a c)))))
352.0ms	(/ (exp (* b b)) (exp (* 3 (* a c))))
216.0ms	(- b (* 3/2 (/ (* a c) b)))

prune954.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.3b

localize46.0ms

Local error

Found 4 expressions with local error:

24.4b	(sqrt (- (* b b) (* (* 3 a) c)))
1.0b	(- (* b b) (* (* 3 a) c))
0.9b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.2b	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))

rewrite161.0ms

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))
51.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
8.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
7.0ms	(- (* b b) (* (* 3 a) c))

series458.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
132.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
119.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
68.0ms	(- (* b b) (* (* 3 a) c))

simplify6.2s

Counts

59 → 99

Calls

59 calls:

Slowest

539.0ms	(sqrt (- (pow (* b b) 3) (pow (* (* 3 a) c) 3)))
416.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
298.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
243.0ms	(- b (* 3/2 (/ (* a c) b)))
240.0ms	(* (* (* 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)))

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.3b

regimes608.0ms

Accuracy

83.6% (4.6b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 33.8b

bsearch144.0ms

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.2s	910×	body	1280	valid
817.0ms	1049×	body	2560	valid
815.0ms	5850×	body	80	valid
397.0ms	2774×	body	80	nan
282.0ms	442×	body	640	valid
131.0ms	120×	body	5120	valid
82.0ms	241×	body	320	valid
26.0ms	108×	body	160	valid