Details

sample114.0ms

Algorithm

intervals

Results

40.0ms	40×	body	2560	valid
19.0ms	184×	body	80	valid
16.0ms	31×	body	1280	valid
9.0ms	98×	body	80	nan
6.0ms	16×	body	640	valid
2.0ms	5×	body	320	valid
2.0ms	2×	body	5120	valid
1.0ms	5×	body	160	valid

simplify142.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

142.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize32.0ms

Local error

Found 4 expressions with local error:

22.0b	(sqrt (- (* b b) (* (* 3 a) c)))
0.9b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.8b	(- (* b b) (* (* 3 a) c))
0.2b	(* (* 3 a) c)

rewrite107.0ms

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

58.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
27.0ms	(* (* 3 a) c)
14.0ms	(- (* b b) (* (* 3 a) c))
8.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

105.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
99.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
59.0ms	(- (* b b) (* (* 3 a) c))
30.0ms	(* (* 3 a) c)

simplify3.3s

Counts

34 → 76

Calls

34 calls:

Slowest

432.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
404.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
358.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
266.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
253.0ms	(- b (* 3/2 (/ (* a c) b)))

prune896.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.6b

localize61.0ms

Local error

Found 4 expressions with local error:

22.0b	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
0.9b	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
0.8b	(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))
0.6b	(cbrt c)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `sqrt-prod` `insert-posit16`
3×	`cbrt-prod` `flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `distribute-lft-out--`

Counts

4 → 57

Calls

4 calls:

Slowest

33.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
20.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
7.0ms	(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))
1.0ms	(cbrt c)

series589.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

249.0ms	(cbrt c)
133.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
121.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
86.0ms	(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))

simplify5.3s

Counts

29 → 69

Calls

29 calls:

Slowest

418.0ms	(- (sqrt (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))) (sqrt b))
417.0ms	(/ (exp (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))) (exp b))
416.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
359.0ms	(sqrt (* (cbrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) (cbrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))))
357.0ms	(+ (sqrt (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))) (sqrt b))

prune987.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 12.6b

localize75.0ms

Local error

Found 4 expressions with local error:

22.0b	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))
0.9b	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))) b)
0.8b	(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))
0.6b	(cbrt (* (cbrt c) (cbrt c)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-log-exp`
7×	`*-un-lft-identity`
5×	`pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `sqrt-prod` `insert-posit16`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `distribute-lft-out--`

Counts

4 → 55

Calls

4 calls:

Slowest

55.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))) b)
16.0ms	(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))
7.0ms	(cbrt (* (cbrt c) (cbrt c)))
7.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

571.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))
394.0ms	(cbrt (* (cbrt c) (cbrt c)))
166.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))) b)
102.0ms	(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))

simplify7.1s

Counts

27 → 67

Calls

27 calls:

Slowest

560.0ms	(- (sqrt (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))) (sqrt b))
557.0ms	(sqrt (- (pow (* b b) 3) (pow (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))) 3)))
491.0ms	(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))
487.0ms	(- (sqrt (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))) (sqrt b))
482.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))

prune1.0s

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 12.6b

localize34.0ms

Local error

Found 4 expressions with local error:

22.0b	(sqrt (- (* b b) (* (* 3 a) c)))
22.0b	(sqrt (- (* b b) (* (* 3 a) c)))
0.9b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.9b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

Slowest

48.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
33.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
13.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

110.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
109.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
105.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
97.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.7s

Counts

38 → 76

Calls

38 calls:

Slowest

381.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
366.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
227.0ms	(- b (* 3/2 (/ (* a c) b)))
201.0ms	(- b (* 3/2 (/ (* a c) b)))
167.0ms	(sqrt (- (pow (* b b) 3) (pow (* (* 3 a) c) 3)))

prune1.0s

Pruning

15 alts after pruning (11 fresh and 4 done)

Merged error: 12.6b

regimes815.0ms

Accuracy

86.1% (3.0b remaining)

Error of 14.8b against oracle of 11.8b and baseline of 33.3b

bsearch176.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

987.0ms	1038×	body	2560	valid
953.0ms	5893×	body	80	valid
709.0ms	898×	body	1280	valid
518.0ms	446×	body	640	valid
421.0ms	2895×	body	80	nan
117.0ms	125×	body	5120	valid
93.0ms	259×	body	320	valid
32.0ms	133×	body	160	valid