Details

sample112.0ms

Algorithm

intervals

Results

25.0ms	196×	body	80	valid
20.0ms	32×	body	1280	valid
19.0ms	26×	body	2560	valid
10.0ms	83×	body	80	nan
7.0ms	12×	body	640	valid
6.0ms	7×	body	5120	valid
2.0ms	6×	body	160	valid
0.0ms	1×	body	320	valid

simplify177.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

177.0ms

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.9b

localize26.0ms

Local error

Found 4 expressions with local error:

24.0b	(sqrt (- (* b b) (* (* 3 a) c)))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.8b	(- (* b b) (* (* 3 a) c))
0.4b	(* (* 3 a) c)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `pow1` `fma-def` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`sum-log` `flip3--` `sqrt-div` `flip--` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `neg-mul-1` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `associate-+l-` `flip-+`

Counts

4 → 84

Calls

4 calls:

Slowest

26.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
15.0ms	(* (* 3 a) c)
12.0ms	(- (* b b) (* (* 3 a) c))

series280.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
98.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
61.0ms	(- (* b b) (* (* 3 a) c))
21.0ms	(* (* 3 a) c)

simplify3.6s

Counts

41 → 96

Calls

41 calls:

Slowest

482.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
466.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
384.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
264.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
263.0ms	(- b (* 3/2 (/ (* a c) b)))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.5b

localize38.0ms

Local error

Found 4 expressions with local error:

24.0b	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))
15.8b	(cbrt (* (* 3 a) c))
15.8b	(cbrt (* (* 3 a) c))
15.8b	(cbrt (* (* 3 a) c))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `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 → 54

Calls

4 calls:

Slowest

15.0ms	(cbrt (* (* 3 a) c))
10.0ms	(cbrt (* (* 3 a) c))
9.0ms	(cbrt (* (* 3 a) c))
9.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

series667.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

203.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))
158.0ms	(cbrt (* (* 3 a) c))
154.0ms	(cbrt (* (* 3 a) c))
151.0ms	(cbrt (* (* 3 a) c))

simplify5.0s

Counts

22 → 66

Calls

22 calls:

Slowest

561.0ms	(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))))))
446.0ms	(sqrt (- (pow (* b b) 3) (pow (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c))) 3)))
412.0ms	(* (cbrt 3) (exp (* 1/3 (+ (log a) (log c)))))
383.0ms	(* (exp (* -1/3 (+ (log (/ -1 c)) (log (/ -1 a))))) (cbrt 3))
365.0ms	(* (exp (* -1/3 (+ (log (/ -1 c)) (log (/ -1 a))))) (cbrt 3))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.5b

localize37.0ms

Local error

Found 4 expressions with local error:

24.0b	(sqrt (- (* b b) (* (* 3 a) c)))
1.5b	(+ (- b) (fabs (sqrt (- (* b b) (* (* 3 a) c)))))
0.8b	(- (* b b) (* (* 3 a) c))
0.4b	(* (* 3 a) c)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `pow1` `fma-def` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`sum-log` `flip3--` `sqrt-div` `flip--` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `neg-mul-1` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `associate-+l-` `flip-+`

Counts

4 → 84

Calls

4 calls:

Slowest

25.0ms	(* (* 3 a) c)
16.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
8.0ms	(- (* b b) (* (* 3 a) c))
7.0ms	(+ (- b) (fabs (sqrt (- (* b b) (* (* 3 a) c)))))

series185.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

87.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
57.0ms	(- (* b b) (* (* 3 a) c))
24.0ms	(* (* 3 a) c)
16.0ms	(+ (- b) (fabs (sqrt (- (* b b) (* (* 3 a) c)))))

simplify3.8s

Counts

41 → 96

Calls

41 calls:

Slowest

445.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
442.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
400.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
318.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
250.0ms	(- b (* 3/2 (/ (* a c) b)))

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 9.5b

localize42.0ms

Local error

Found 4 expressions with local error:

24.0b	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt 3) (cbrt (* a c))))))
15.8b	(cbrt (* a c))
15.8b	(cbrt (* (* 3 a) c))
15.8b	(cbrt (* (* 3 a) c))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `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 → 54

Calls

4 calls:

Slowest

18.0ms	(cbrt (* (* 3 a) c))
18.0ms	(cbrt (* (* 3 a) c))
9.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt 3) (cbrt (* a c))))))
3.0ms	(cbrt (* a c))

series556.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

187.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt 3) (cbrt (* a c))))))
129.0ms	(cbrt (* (* 3 a) c))
120.0ms	(cbrt (* (* 3 a) c))
120.0ms	(cbrt (* a c))

simplify4.8s

Counts

22 → 66

Calls

22 calls:

Slowest

411.0ms	(* (exp (* -1/3 (+ (log (/ -1 c)) (log (/ -1 a))))) (cbrt 3))
388.0ms	(* (exp (* -1/3 (+ (log (/ -1 c)) (log (/ -1 a))))) (cbrt 3))
388.0ms	(* (cbrt 3) (exp (* 1/3 (+ (log a) (log c)))))
382.0ms	(sqrt (- (pow (* b b) 3) (pow (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (* (cbrt 3) (cbrt (* a c)))) 3)))
358.0ms	(* (exp (* -1/3 (+ (log (/ 1 a)) (log (/ 1 c))))) (cbrt 3))

prune1.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 9.5b

regimes638.0ms

Accuracy

86.6% (3.0b remaining)

Error of 13.8b against oracle of 10.8b and baseline of 33.3b

bsearch234.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	5871×	body	80	valid
1.0s	1083×	body	2560	valid
557.0ms	862×	body	1280	valid
394.0ms	2988×	body	80	nan
277.0ms	415×	body	640	valid
122.0ms	245×	body	320	valid
95.0ms	110×	body	5120	valid
30.0ms	126×	body	160	valid