Details

sample81.0ms

Algorithm

intervals

Results

18.0ms	44×	body	2560	valid
12.0ms	167×	body	80	valid
11.0ms	32×	body	1280	valid
7.0ms	100×	body	80	nan
4.0ms	14×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify121.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	76	16
4	96	16
5	104	16
done	104	16

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 3.0 a) c)
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

34.0ms	(* (* 3.0 a) c)
37.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
13.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* 3.0 a) c)
100.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
78.0ms	(- (* b b) (* (* 3.0 a) c))
110.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.1s

Counts

72 → 72

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	122	1001
1	328	907
2	1722	805
done	5000	799

prune306.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.8b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.4b	(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.3b	(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
139.0ms	(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
110.0ms	(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series608.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 3.0 a) c))
189.0ms	(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
264.0ms	(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
106.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.6s

Counts

160 → 160

Iterations

Useful iterations: 2 (751.0ms)

Iter	Nodes	Cost
0	250	4912
1	662	4366
2	4260	4036
done	5000	4036

prune543.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.4b

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.4b	(/ (/ (* (* a c) 3.0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
11.3b	(/ (* (* a c) 3.0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

11.0ms	(- (* b b) (* (* 3.0 a) c))
106.0ms	(/ (/ (* (* a c) 3.0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
59.0ms	(/ (* (* a c) 3.0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b b) (* (* 3.0 a) c))
178.0ms	(/ (/ (* (* a c) 3.0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
225.0ms	(/ (* (* a c) 3.0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
78.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.1s

Counts

146 → 146

Iterations

Useful iterations: 2 (601.0ms)

Iter	Nodes	Cost
0	254	4073
1	702	3835
2	4284	3439
done	5000	3439

prune687.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.4b

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.4b	(/ (* (* a c) (/ 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
11.3b	(* (* a c) (/ 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-cbrt-cube`
31×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`associate-r`
24×	`times-frac`
18×	`add-cube-cbrt`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
9×	`cbrt-undiv` `div-exp`
6×	`sqrt-prod` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`flip3--` `distribute-rgt-neg-in` `pow-prod-down` `associate-/r*` `flip--`
2×	`sqrt-div` `associate-*r/` `associate-/r/` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 102

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
48.0ms	(/ (* (* a c) (/ 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
124.0ms	(* (* a c) (/ 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series718.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b b) (* (* 3.0 a) c))
234.0ms	(/ (* (* a c) (/ 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
311.0ms	(* (* a c) (/ 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
110.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify365.0ms

Counts

114 → 114

Iterations

Useful iterations: done (360.0ms)

Iter	Nodes	Cost
0	213	2538
1	648	2421
done	5000	1973

prune489.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.1b

regimes799.0ms

Accuracy

93.3% (1.4b remaining)

Error of 12.0b against oracle of 10.6b and baseline of 32.1b

bsearch223.0ms

Steps

Iters	Range	Point
8	7.396244385895765e+122	8.016899727942974e+125	2.39445321165085e+124
10	-8.138706044250008e-279	-2.4810350231976038e-293	-5.602943297867931e-285
4	-5.365119720024443e+91	-2.969789614895389e+91	-3.938820754703496e+91

Iters

Range

Point

7.396244385895765e+122

8.016899727942974e+125

2.39445321165085e+124

-8.138706044250008e-279

-2.4810350231976038e-293

-5.602943297867931e-285

-5.365119720024443e+91

-2.969789614895389e+91

-3.938820754703496e+91

simplify9.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	45	92
1	56	90
2	57	90
done	57	90

end0.0ms

sample3.1s

Algorithm

intervals

Results

834.0ms	1127×	body	2560	valid
601.0ms	2902×	body	80	nan
486.0ms	5718×	body	80	valid
449.0ms	936×	body	1280	valid
133.0ms	448×	body	640	valid
54.0ms	111×	body	5120	valid
42.0ms	223×	body	320	valid
13.0ms	111×	body	160	valid