Details

sample102.0ms

Algorithm

intervals

Results

15.0ms	187×	body	80	valid
13.0ms	29×	body	2560	valid
12.0ms	4×	body	160	valid
10.0ms	25×	body	1280	valid
9.0ms	103×	body	80	nan
5.0ms	16×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid

simplify140.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	119	16
5	128	16
done	128	16

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
20.0ms	(- (* b b) (* 4.0 (* a c)))
44.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
60.0ms	(- (* b b) (* 4.0 (* a c)))
100.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
99.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	165	1697
1	448	1588
2	1860	1361
done	5000	1352

prune579.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize47.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.8b	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.7b	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

47.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
136.0ms	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
75.0ms	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
30.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series720.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
245.0ms	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
263.0ms	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
98.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify633.0ms

Counts

244 → 244

Iterations

Useful iterations: done (623.0ms)

Iter	Nodes	Cost
0	337	10067
1	856	7629
done	5000	6649

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize44.0ms

Local error

Found 4 expressions with local error:

9.5b	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
9.8b	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod` `add-cbrt-cube`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `associate-/r*` `flip--` `log1p-expm1-u`
3×	`associate-/l*`
2×	`neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 108

Calls

4 calls:

59.0ms	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
27.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
33.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series650.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
121.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
135.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
106.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.8s

Counts

120 → 120

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	189	4229
1	489	2527
2	3109	2380
done	5001	2379

prune857.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.2b	(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
22.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
152×	`times-frac`
150×	`*-un-lft-identity`
109×	`add-cube-cbrt`
94×	`add-exp-log`
85×	`associate-r`
61×	`prod-diff`
58×	`add-cbrt-cube`
43×	`sqrt-prod`
39×	`div-exp`
35×	`prod-exp`
31×	`distribute-rgt-neg-in`
21×	`cbrt-undiv` `distribute-lft-neg-in` `cbrt-unprod`
20×	`distribute-lft-out--` `difference-of-squares`
11×	`fma-neg`
10×	`add-log-exp`
7×	`pow1` `neg-mul-1` `associate-l`
6×	`flip3--` `associate-/r/` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `unswap-sqr`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `*-commutative`

Counts

4 → 265

Calls

4 calls:

14.0ms	(- (* b b) (* 4.0 (* a c)))
39.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
203.0ms	(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* b b) (* 4.0 (* a c)))
107.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
227.0ms	(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
105.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify827.0ms

Counts

277 → 277

Iterations

Useful iterations: done (817.0ms)

Iter	Nodes	Cost
0	440	10426
1	1428	8091
done	5001	6692

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

regimes392.0ms

Accuracy

86.7% (3.5b remaining)

Error of 8.8b against oracle of 5.2b and baseline of 32.0b

bsearch420.0ms

Steps

Iters	Range	Point
9	5.2308229534737164e+20	4.4914796769937245e+27	3.3627913932282257e+22
10	2.3120063448528447e-114	6.389619675209379e-102	2.3448135958717817e-114
9	-1.6867412280479856e+126	-2.8600599763572115e+119	-1.6733539759872003e+120

Iters

Range

Point

5.2308229534737164e+20

4.4914796769937245e+27

3.3627913932282257e+22

2.3120063448528447e-114

6.389619675209379e-102

2.3448135958717817e-114

-1.6867412280479856e+126

-2.8600599763572115e+119

-1.6733539759872003e+120

simplify15.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	41	82
1	50	80
2	51	80
done	51	80

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.2s	5854×	body	80	valid
660.0ms	1075×	body	2560	valid
420.0ms	918×	body	1280	valid
266.0ms	2889×	body	80	nan
178.0ms	457×	body	640	valid
97.0ms	210×	body	320	valid
63.0ms	110×	body	5120	valid
15.0ms	108×	body	160	valid