Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	37×	body	2560	valid
7.0ms	195×	body	80	valid
4.0ms	21×	body	1280	valid
3.0ms	81×	body	80	nan
3.0ms	19×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
55.0ms	(- (* b b) (* (* 4.0 a) c))
90.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify755.0ms

Counts

82 → 82

Iterations

Useful iterations: done (752.0ms)

Iter	Nodes	Cost
0	154	1565
1	406	1461
2	1359	1245
done	5000	1235

prune267.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
5×	`associate-l`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

56.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
61.0ms	(- (* b b) (* (* 4.0 a) c))
104.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify948.0ms

Counts

92 → 92

Iterations

Useful iterations: done (945.0ms)

Iter	Nodes	Cost
0	181	1881
1	480	1671
2	1649	1400
done	5000	1399

prune283.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) (/ (cbrt 1) a))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
28×	`add-cube-cbrt`
22×	`associate-r` `associate-l`
16×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`cbrt-prod`
8×	`add-log-exp` `difference-of-squares` `unswap-sqr`
7×	`pow1` `sqrt-prod`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 114

Calls

4 calls:

65.0ms	(* (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) (/ (cbrt 1) a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
19.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) (/ (cbrt 1) a))
57.0ms	(- (* b b) (* (* 4.0 a) c))
102.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

126 → 126

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	239	2735
1	679	2428
2	1794	2178
done	5000	2177

prune372.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
19.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(cbrt a)
214.0ms	(cbrt a)
92.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

64 → 64

Iterations

Useful iterations: 3 (458.0ms)

Iter	Nodes	Cost
0	103	754
1	227	674
2	675	628
3	2178	618
done	5000	618

prune256.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.6b

regimes212.0ms

Accuracy

83.3% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.3b

bsearch172.0ms

Steps

Iters	Range		Point
10	3.056596725548563e-78	7.076105677608322e-63	3.446447862996811e-75
10	-1.852183237050365e+100	-1.9127319211193897e+86	-4.123103533644211e+95

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	41
1	36	41
done	36	41

end0.0ms

sample1.2s

Algorithm

intervals

Results

256.0ms	1096×	body	2560	valid
234.0ms	5880×	body	80	valid
167.0ms	852×	body	1280	valid
108.0ms	2945×	body	80	nan
68.0ms	471×	body	640	valid
31.0ms	109×	body	5120	valid
23.0ms	211×	body	320	valid
8.0ms	107×	body	160	valid