Details

sample59.0ms

Algorithm

intervals

Results

31.0ms	98×	body	1280	valid
7.0ms	123×	body	80	valid
4.0ms	18×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	5×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	26	12
3	32	12
4	34	12
5	40	12
6	42	12
done	42	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
2.3b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-neg` `associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `hypot-udef` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

0.0ms	(hypot 1.0 x)
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

95.0ms	(hypot 1.0 x)
385.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
136.0ms	(/ 1.0 (hypot 1.0 x))
512.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.0s

Counts

97 → 97

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	225	2149
1	536	1724
2	1590	1489
done	5000	1355

prune381.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.8b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r` `associate-/l`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `fma-neg` `diff-log` `prod-diff` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 91

Calls

4 calls:

7.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
5.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series1.0s

Counts

4 → 12

Calls

4 calls:

492.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
157.0ms	(/ 1.0 (hypot 1.0 x))
156.0ms	(/ 1.0 (hypot 1.0 x))
208.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.3s

Counts

103 → 103

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	190	1534
1	492	1450
2	1662	1311
done	5000	1302

prune490.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))
0.0b	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
1.7b	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
56×	`prod-diff`
53×	`add-cube-cbrt`
45×	`unpow-prod-down`
42×	`sqr-pow`
39×	`times-frac`
30×	`difference-of-squares`
13×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
8×	`cube-mult` `unpow3` `cube-prod`
7×	`pow1` `fma-neg`
6×	`associate-/r*` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow`
2×	`cbrt-undiv` `cube-div` `flip3--` `pow-pow` `frac-2neg` `div-exp` `associate-*l/` `pow-exp` `clear-num` `flip--` `div-inv` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `flip3-+` `diff-log` `div-sub` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 199

Calls

4 calls:

11.0ms	(/ 1.0 (hypot 1.0 x))
76.0ms	(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))
28.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
36.0ms	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

series3.4s

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ 1.0 (hypot 1.0 x))
2.5s	(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))
301.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
474.0ms	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

simplify1.1s

Counts

211 → 211

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	522	11139
1	1373	8703
done	5000	7567

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
0.0b	(* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))
0.0b	(/ (- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))) (* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))
1.7b	(- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`pow1` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `times-frac` `associate-r/` `associate-r` `log1p-expm1-u` `associate-/l`
3×	`pow-unpow` `flip3-+` `associate-l` `prod-exp` `cbrt-unprod` `flip-+` `difference-of-squares`
2×	`cbrt-undiv` `cube-div` `flip3--` `pow-pow` `div-exp` `pow-prod-down` `associate-*l/` `pow-exp` `associate-/r/` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `frac-2neg` `distribute-lft-in` `fma-neg` `diff-log` `unpow3` `div-sub` `cube-prod` `prod-diff` `clear-num` `associate-/r` `-commutative` `div-inv` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 98

Calls

4 calls:

33.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
66.0ms	(* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))
62.0ms	(/ (- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))) (* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))
40.0ms	(- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))

series19.6s

Counts

4 → 12

Calls

4 calls:

369.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
1.3s	(* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))
16.2s	(/ (- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))) (* (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)) (+ (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))
1.6s	(- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))

simplify1.3s

Counts

110 → 110

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	634	10170
1	2012	8596
done	5000	7047

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

regimes477.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.8b

bsearch608.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	0.002129030310090778
8	-9.640722949014248e-05	-1.9918553488737634e-08	-9.494777107334508e-05

simplify11.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	60	259
1	67	259
done	67	259

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s	2834×	body	1280	valid
287.0ms	4075×	body	80	valid
159.0ms	609×	body	640	valid
116.0ms	327×	body	320	valid
18.0ms	155×	body	160	valid