Details

sample221.0ms

Algorithm

intervals

Results

21.0ms	44×	body	2560	valid
16.0ms	167×	body	80	valid
13.0ms	32×	body	1280	valid
8.0ms	100×	body	80	nan
4.0ms	14×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify62.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

96.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
42.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
136.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(- (* b_2 b_2) (* a c))
132.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

112 → 112

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	164	1638
1	405	1539
2	1677	1355
done	5000	1344

prune426.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.3b	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.3b	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 210

Calls

4 calls:

11.0ms	(- (* b_2 b_2) (* a c))
148.0ms	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
63.0ms	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (* b_2 b_2) (* a c))
248.0ms	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
280.0ms	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

222 → 222

Iterations

Useful iterations: 2 (823.0ms)

Iter	Nodes	Cost
0	315	6355
1	805	5507
2	4695	5301
done	5000	5301

prune865.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize35.0ms

Local error

Found 4 expressions with local error:

8.4b	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
10.4b	(/ (+ 0 (* c a)) (- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite126.0ms

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:

24.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
58.0ms	(/ (+ 0 (* c a)) (- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
284.0ms	(/ (+ 0 (* c a)) (- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
114.0ms	(sqrt (- (* b_2 b_2) (* a c)))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

120 → 120

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	186	3553
1	473	2093
2	2620	1972
done	5001	1955

prune543.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma b_2 b_2 (- (* c a)))
3.3b	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (fma b_2 b_2 (- (* c a)))))) a)
11.3b	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (fma b_2 b_2 (- (* c a))))))
25.3b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
6×	`div-inv`
5×	`pow1` `flip3--` `flip--`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `fma-udef`

Counts

4 → 202

Calls

4 calls:

1.0ms	(fma b_2 b_2 (- (* c a)))
98.0ms	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (fma b_2 b_2 (- (* c a)))))) a)
55.0ms	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (fma b_2 b_2 (- (* c a))))))
2.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series662.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(fma b_2 b_2 (- (* c a)))
264.0ms	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (fma b_2 b_2 (- (* c a)))))) a)
258.0ms	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (fma b_2 b_2 (- (* c a))))))
87.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.1s

Counts

214 → 214

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	294	6207
1	714	5384
2	3728	5189
done	5000	5186

prune802.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

regimes444.0ms

Accuracy

88.1% (3.2b remaining)

Error of 8.8b against oracle of 5.6b and baseline of 32.8b

bsearch234.0ms

Steps

Iters	Range		Point
7	517946.10598021303	17102963.46615162	4173650.6547572073
7	1.743450368345407e-128	9.096741835583034e-127	1.769241967981359e-128
8	-1.471055469501053e+100	-2.16094220789435e+96	-1.8069356592732734e+98

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	36	62
1	41	60
done	41	60

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	936×	body	1280	valid
606.0ms	1131×	body	2560	valid
470.0ms	5719×	body	80	valid
209.0ms	446×	body	640	valid
180.0ms	2902×	body	80	nan
55.0ms	111×	body	5120	valid
41.0ms	224×	body	320	valid
13.0ms	110×	body	160	valid