Details

sample76.0ms

Algorithm

intervals

Results

14.0ms	36×	body	2560	valid
12.0ms	176×	body	80	valid
10.0ms	33×	body	1280	valid
5.0ms	79×	body	80	nan
5.0ms	19×	body	640	valid
3.0ms	6×	body	5120	valid
2.0ms	10×	body	320	valid
0.0ms	3×	body	160	valid

simplify134.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	156
6	156
5	152
4	142
3	115
2	64
1	28
0	14

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
0.2b	(- (* b b) (* a (* 4.0 c)))
1.6b	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
24.4b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

92.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
6.0ms	(- (* b b) (* a (* 4.0 c)))
18.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
7.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
78.0ms	(- (* b b) (* a (* 4.0 c)))
108.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
79.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify640.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1700
1	416
0	157

prune947.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.7b

localize30.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
5.2b	(/ (/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b)) (* 2.0 a))
6.9b	(/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
24.4b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
22×	`difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
14×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 141

Calls

4 calls:

52.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
127.0ms	(/ (/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b)) (* 2.0 a))
80.0ms	(/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
7.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series791.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
257.0ms	(/ (/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b)) (* 2.0 a))
294.0ms	(/ (+ 0 (* a (* 4.0 c))) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b))
102.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.9s

Counts

153 → 153

Iterations

Iter	Nodes
done	5001
2	3716
1	649
0	251

prune907.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* a (* 4.0 c)))
0.7b	(/ (/ 1 1) (* (/ (/ (* a 2.0) (* a 4.0)) c) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b)))
1.3b	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
24.4b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

228×	`add-exp-log`
140×	`div-exp`
77×	`add-cbrt-cube`
70×	`prod-exp`
39×	`cbrt-undiv`
35×	`1-exp`
31×	`times-frac`
24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`cbrt-unprod`
19×	`add-cube-cbrt`
14×	`rec-exp`
13×	`associate-/l*`
8×	`add-log-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`sqrt-prod`
3×	`div-inv`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `associate-*r/` `difference-of-squares`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `distribute-lft-out--` `associate-/l/`

Counts

4 → 148

Calls

4 calls:

7.0ms	(- (* b b) (* a (* 4.0 c)))
105.0ms	(/ (/ 1 1) (* (/ (/ (* a 2.0) (* a 4.0)) c) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b)))
57.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
7.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series518.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* a (* 4.0 c)))
252.0ms	(/ (/ 1 1) (* (/ (/ (* a 2.0) (* a 4.0)) c) (- (sqrt (- (* b b) (* a (* 4.0 c)))) b)))
117.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
99.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify558.0ms

Counts

160 → 160

Iterations

Iter	Nodes
done	5001
1	1158
0	324

prune540.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 1 (/ 2.0 4.0)) c))
0.2b	(- (* b b) (* 4.0 (* c a)))
1.3b	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
24.4b	(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-exp-log`
33×	`times-frac` `div-exp`
26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`add-cbrt-cube`
12×	`1-exp` `prod-exp`
8×	`cbrt-undiv` `add-log-exp`
7×	`associate-/r*`
6×	`pow1` `rec-exp`
5×	`div-inv`
4×	`sqrt-prod`
3×	`flip3--` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `cbrt-unprod` `difference-of-squares`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/r/` `pow-flip` `distribute-lft-out--` `inv-pow`

Counts

4 → 108

Calls

4 calls:

17.0ms	(/ 1 (/ (* 1 (/ 2.0 4.0)) c))
6.0ms	(- (* b b) (* 4.0 (* c a)))
48.0ms	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
7.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1 (/ (* 1 (/ 2.0 4.0)) c))
61.0ms	(- (* b b) (* 4.0 (* c a)))
112.0ms	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
110.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))

simplify1.7s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	3339
1	604
0	221

prune487.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

regimes481.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.5b against oracle of 5.3b and baseline of 30.1b

bsearch403.0ms

Steps

Iters	Range		Point
9	2.1340360609407003e+79	6.102484722804822e+84	1.1809135573683298e+84
10	8.852475844905406e-209	2.711563690867585e-195	8.958852798091287e-209
7	-3.845605078781637e+76	-5.978906984153912e+74	-2.453262666864976e+76

simplify7.0ms

Iterations

Iter	Nodes
done	61
2	61
1	58
0	45

end0.0ms

sample3.1s

Algorithm

intervals

Results

701.0ms	2883×	body	80	nan
590.0ms	5799×	body	80	valid
568.0ms	1065×	body	2560	valid
440.0ms	921×	body	1280	valid
166.0ms	455×	body	640	valid
54.0ms	239×	body	320	valid
48.0ms	86×	body	5120	valid
16.0ms	111×	body	160	valid