Details

sample125.0ms

Algorithm

intervals

Results

26.0ms	189×	body	80	valid
23.0ms	30×	body	2560	valid
21.0ms	95×	body	80	nan
14.0ms	22×	body	1280	valid
9.0ms	18×	body	640	valid
4.0ms	11×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify142.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize22.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b b) (* (* 3 a) c)))
1.8b	(- (* b b) (* (* 3 a) c))
1.5b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))

rewrite122.0ms

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

73.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
34.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
7.0ms	(- (* b b) (* (* 3 a) c))

series335.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

103.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
100.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
84.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
48.0ms	(- (* b b) (* (* 3 a) c))

simplify351.0ms

Counts: 105 → 88

prune699.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

localize24.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b b) (* (* 3 a) c)))
1.8b	(- (* b b) (* (* 3 a) c))
1.5b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.2b	(* (* 3 a) c)

rewrite62.0ms

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

33.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
14.0ms	(* (* 3 a) c)
7.0ms	(- (* b b) (* (* 3 a) c))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
98.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
74.0ms	(- (* b b) (* (* 3 a) c))
29.0ms	(* (* 3 a) c)

simplify293.0ms

Counts: 84 → 76

prune793.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.5b

localize37.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b b) (* (* 3 a) c)))
1.8b	(- (* b b) (* (* 3 a) c))
1.5b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.2b	(* (* 3 a) c)

rewrite113.0ms

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

59.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
25.0ms	(* (* 3 a) c)
13.0ms	(- (* b b) (* (* 3 a) c))
13.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

104.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
95.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
45.0ms	(- (* b b) (* (* 3 a) c))
29.0ms	(* (* 3 a) c)

simplify357.0ms

Counts: 84 → 76

prune927.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.5b

localize66.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))
16.2b	(cbrt (* (* 3 a) c))
16.2b	(cbrt (* (* 3 a) c))
16.2b	(cbrt (* (* 3 a) c))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 46

Calls

4 calls:

Slowest

25.0ms	(cbrt (* (* 3 a) c))
18.0ms	(cbrt (* (* 3 a) c))
17.0ms	(cbrt (* (* 3 a) c))
14.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

series603.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

169.0ms	(cbrt (* (* 3 a) c))
159.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))
145.0ms	(cbrt (* (* 3 a) c))
131.0ms	(cbrt (* (* 3 a) c))

simplify704.0ms

Counts: 61 → 58

prune891.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.5b

regimes744.0ms

Accuracy

82.3% (4.9b remaining)

Error of 10.7b against oracle of 5.8b and baseline of 33.6b

bsearch148.0ms

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.3s	5862×	body	80	valid
1.0s	872×	body	1280	valid
807.0ms	1056×	body	2560	valid
426.0ms	3023×	body	80	nan
250.0ms	476×	body	640	valid
106.0ms	121×	body	5120	valid
82.0ms	241×	body	320	valid
56.0ms	105×	body	160	valid