Details

sample102.0ms

Algorithm

intervals

Results

24.0ms	34×	body	2560	valid
19.0ms	190×	body	80	valid
19.0ms	38×	body	1280	valid
10.0ms	88×	body	80	nan
5.0ms	6×	body	5120	valid
4.0ms	12×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify133.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

133.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize21.0ms

Local error

Found 4 expressions with local error:

23.9b	(sqrt (- (* b b) (* (* 3 a) c)))
0.8b	(- (* b b) (* (* 3 a) c))
0.7b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.5b	(* (* 3 a) c)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity`
10×	`pow1`
8×	`add-cube-cbrt`
6×	`times-frac` `associate-/l*` `add-log-exp`
5×	`sqrt-prod`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `difference-of-squares`
3×	`flip3--` `associate-r` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `distribute-lft-out--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-l` `-commutative` `div-inv`

Counts

4 → 79

Calls

4 calls:

Slowest

73.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
15.0ms	(* (* 3 a) c)
14.0ms	(- (* b b) (* (* 3 a) c))
12.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

163.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
119.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
62.0ms	(- (* b b) (* (* 3 a) c))
32.0ms	(* (* 3 a) c)

simplify6.3s

Counts

51 → 91

Calls

51 calls:

Slowest

618.0ms	(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
485.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
413.0ms	(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
412.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
406.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize47.0ms

Local error

Found 4 expressions with local error:

23.9b	(sqrt (- (* b b) (* (* 3 a) c)))
0.8b	(- (* b b) (* (* 3 a) c))
0.5b	(* (* 3 a) c)
0.3b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) 3)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
18×	`times-frac`
17×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
8×	`difference-of-squares`
7×	`sqrt-prod`
6×	`associate-/l*` `add-log-exp`
4×	`insert-posit16` `distribute-lft-out--`
3×	`associate-/r` `flip3--` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `associate-l` `*-commutative` `div-inv`

Counts

4 → 91

Calls

4 calls:

Slowest

61.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) 3)
26.0ms	(* (* 3 a) c)
16.0ms	(- (* b b) (* (* 3 a) c))
14.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

151.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) 3)
112.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
57.0ms	(- (* b b) (* (* 3 a) c))
36.0ms	(* (* 3 a) c)

simplify7.1s

Counts

75 → 103

Calls

75 calls:

Slowest

462.0ms	(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
422.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
420.0ms	(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
373.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
367.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize44.0ms

Local error

Found 4 expressions with local error:

23.9b	(sqrt (- (* b b) (* 3 (* a c))))
0.8b	(- (* b b) (* 3 (* a c)))
0.3b	(/ (- (sqrt (- (* b b) (* 3 (* a c)))) b) 3)
0.3b	(* 3 (* a c))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
18×	`times-frac`
17×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
8×	`difference-of-squares`
7×	`sqrt-prod`
6×	`associate-/l*` `add-log-exp`
4×	`insert-posit16` `distribute-lft-out--`
3×	`associate-/r` `flip3--` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `associate-r` `*-commutative` `div-inv`

Counts

4 → 91

Calls

4 calls:

Slowest

104.0ms	(/ (- (sqrt (- (* b b) (* 3 (* a c)))) b) 3)
26.0ms	(* 3 (* a c))
8.0ms	(- (* b b) (* 3 (* a c)))
7.0ms	(sqrt (- (* b b) (* 3 (* a c))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(/ (- (sqrt (- (* b b) (* 3 (* a c)))) b) 3)
83.0ms	(sqrt (- (* b b) (* 3 (* a c))))
64.0ms	(- (* b b) (* 3 (* a c)))
31.0ms	(* 3 (* a c))

simplify8.0s

Counts

75 → 103

Calls

75 calls:

Slowest

548.0ms	(* (* (* 3 3) 3) (* (* (* a c) (* a c)) (* a c)))
548.0ms	(- (* (sqrt (- (* b b) (* 3 (* a c)))) (sqrt (- (* b b) (* 3 (* a c))))) (* b b))
447.0ms	(* (* (* 3 3) 3) (* (* (* a a) a) (* (* c c) c)))
389.0ms	(- (pow (sqrt (- (* b b) (* 3 (* a c)))) 3) (pow b 3))
331.0ms	(sqrt (- (* (* b b) (* b b)) (* (* 3 (* a c)) (* 3 (* a c)))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize29.0ms

Local error

Found 4 expressions with local error:

23.9b	(sqrt (- (* b b) (* (* 3 a) c)))
0.8b	(- (* b b) (* (* 3 a) c))
0.5b	(* (* 3 a) c)
0.4b	(* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (/ 1 3))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
18×	`add-exp-log`
17×	`*-un-lft-identity`
16×	`associate-r`
14×	`add-cbrt-cube` `add-cube-cbrt`
12×	`pow1`
11×	`times-frac`
7×	`associate-l` `prod-exp`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`flip3--` `pow-prod-down` `sqrt-prod` `insert-posit16` `flip--`
3×	`unswap-sqr`
2×	`frac-times` `sqrt-div` `div-exp` `associate-l/` `-commutative` `difference-of-squares`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `associate-*r/` `un-div-inv` `div-inv` `distribute-lft-out--`

Counts

4 → 92

Calls

4 calls:

Slowest

167.0ms	(* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (/ 1 3))
27.0ms	(* (* 3 a) c)
10.0ms	(- (* b b) (* (* 3 a) c))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
109.0ms	(* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (/ 1 3))
54.0ms	(- (* b b) (* (* 3 a) c))
28.0ms	(* (* 3 a) c)

simplify7.4s

Counts

64 → 104

Calls

64 calls:

Slowest

648.0ms	(* (- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b)) 1)
539.0ms	(* (* (* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (/ (* (* 1 1) 1) (* (* 3 3) 3)))
463.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
403.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
374.0ms	(* (+ (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (+ (* b b) (* (sqrt (- (* b b) (* (* 3 a) c))) b))) 3)

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.6b

regimes402.0ms

Accuracy

83.2% (4.5b remaining)

Error of 10.0b against oracle of 5.5b and baseline of 32.0b

bsearch187.0ms

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.3s	1060×	body	2560	valid
1.3s	5962×	body	80	valid
710.0ms	879×	body	1280	valid
465.0ms	2934×	body	80	nan
302.0ms	430×	body	640	valid
147.0ms	119×	body	5120	valid
108.0ms	216×	body	320	valid
27.0ms	110×	body	160	valid