Details

sample124.0ms

Algorithm

intervals

Results

47.0ms	189×	body	80	valid
19.0ms	30×	body	2560	valid
12.0ms	22×	body	1280	valid
11.0ms	95×	body	80	nan
8.0ms	18×	body	640	valid
4.0ms	11×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify137.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

137.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize27.0ms

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))

rewrite160.0ms

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

99.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
40.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
12.0ms	(- (* b b) (* (* 3 a) c))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

150.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
102.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
86.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
59.0ms	(- (* b b) (* (* 3 a) c))

simplify12.9s

Counts

105 → 88

Calls

105 calls:

Slowest

660.0ms	(sqrt (+ (* (* b b) (* b b)) (+ (* (* (* 3 a) c) (* (* 3 a) c)) (* (* b b) (* (* 3 a) c)))))
596.0ms	(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
414.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
401.0ms	(- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c)))
400.0ms	(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

localize43.0ms

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)

rewrite129.0ms

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

71.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
27.0ms	(* (* 3 a) c)
15.0ms	(- (* b b) (* (* 3 a) c))
15.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

104.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
78.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
48.0ms	(- (* b b) (* (* 3 a) c))
27.0ms	(* (* 3 a) c)

simplify10.3s

Counts

84 → 76

Calls

84 calls:

Slowest

592.0ms	(* (* (* (* 3 a) c) (* (* 3 a) c)) (* (* 3 a) c))
590.0ms	(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
586.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
427.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
419.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.5b

localize34.0ms

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)

rewrite72.0ms

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

40.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
14.0ms	(* (* 3 a) c)
9.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
8.0ms	(- (* b b) (* (* 3 a) c))

series294.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

114.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
98.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
58.0ms	(- (* b b) (* (* 3 a) c))
24.0ms	(* (* 3 a) c)

simplify10.2s

Counts

84 → 76

Calls

84 calls:

Slowest

923.0ms	(* (* (* (* 3 a) c) (* (* 3 a) c)) (* (* 3 a) c))
584.0ms	(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
464.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
443.0ms	(- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c)))
415.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))

prune869.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.5b

localize51.0ms

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))

rewrite46.0ms

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

14.0ms	(cbrt (* (* 3 a) c))
13.0ms	(cbrt (* (* 3 a) c))
10.0ms	(cbrt (* (* 3 a) c))
8.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

series554.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

183.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))
127.0ms	(cbrt (* (* 3 a) c))
125.0ms	(cbrt (* (* 3 a) c))
119.0ms	(cbrt (* (* 3 a) c))

simplify7.9s

Counts

61 → 58

Calls

61 calls:

Slowest

692.0ms	(sqrt (- (pow (* b b) 3) (pow (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c))) 3)))
469.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c))) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c))))))
417.0ms	(* (cbrt 3) (exp (* 1/3 (+ (log a) (log c)))))
396.0ms	(* (cbrt 3) (exp (* 1/3 (+ (log a) (log c)))))
390.0ms	(* (cbrt 3) (exp (* 1/3 (+ (log a) (log c)))))

prune822.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.5b

regimes662.0ms

Accuracy

82.3% (4.9b remaining)

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

bsearch151.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.3s	5862×	body	80	valid
1.1s	1056×	body	2560	valid
602.0ms	872×	body	1280	valid
353.0ms	3023×	body	80	nan
254.0ms	476×	body	640	valid
188.0ms	121×	body	5120	valid
88.0ms	241×	body	320	valid
25.0ms	105×	body	160	valid