Details

sample58.0ms

Algorithm

intervals

Results

28.0ms	90×	body	1280	valid
7.0ms	129×	body	80	valid
7.0ms	25×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	5×	body	160	valid

simplify42.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize47.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
2.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 70

Calls

3 calls:

0.0ms	(hypot 1.0 x)
4.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series797.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(hypot 1.0 x)
151.0ms	(/ 1.0 (hypot 1.0 x))
558.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.2s

Counts

79 → 79

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	200	1787
1	483	1416
2	2095	1174
done	5001	1157

prune409.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.4b

localize26.0ms

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))
1.6b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

4.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
4.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series873.0ms

Counts

4 → 12

Calls

4 calls:

391.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
114.0ms	(/ 1.0 (hypot 1.0 x))
185.0ms	(/ 1.0 (hypot 1.0 x))
183.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.5s

Counts

105 → 105

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	194	1548
1	545	1463
2	2673	1330
done	5001	1325

prune687.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (/ 1.0 (hypot 1.0 x)))
0.2b	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
1.6b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x)))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

92×	`sqrt-prod`
84×	`add-sqr-sqrt`
62×	`times-frac`
50×	`*-un-lft-identity` `add-cube-cbrt`
21×	`pow1`
18×	`swap-sqr`
16×	`associate-r` `associate-l`
10×	`sqrt-pow1` `pow1/2`
9×	`unswap-sqr`
6×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `div-inv` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `rem-sqrt-square` `log1p-expm1-u`
3×	`pow-prod-down` `pow-sqr`
2×	`associate--r+`
1×	`pow2` `distribute-rgt-in` `frac-times` `sub-neg` `rem-square-sqrt` `distribute-lft-in` `pow-plus` `flip3--` `fma-neg` `sqrt-unprod` `diff-log` `prod-diff` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `flip--`

Counts

4 → 161

Calls

4 calls:

3.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
3.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
36.0ms	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
6.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x)))))))

series791.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
192.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
204.0ms	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
195.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x)))))))

simplify1.2s

Counts

173 → 173

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	241	3138
1	557	2188
2	2509	2038
done	5002	2004

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (/ 1.0 (hypot 1.0 x)))
0.2b	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
1.6b	(- (* 1.0 (- 1.0 0.5)) (* (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x)))) 0.5))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
92×	`sqrt-prod`
62×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
22×	`associate--l+`
21×	`pow1`
19×	`prod-diff`
18×	`swap-sqr`
16×	`associate-r` `associate-l`
14×	`sqrt-div`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-l/` `associate-r/` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `frac-sub` `div-inv` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `rem-sqrt-square` `flip3--` `log1p-expm1-u` `flip--`
3×	`frac-times` `sub-neg` `pow-prod-down` `pow-sqr`
1×	`pow2` `rem-square-sqrt` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 187

Calls

4 calls:

3.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
3.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
31.0ms	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
42.0ms	(- (* 1.0 (- 1.0 0.5)) (* (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x)))) 0.5))

series921.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
225.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
226.0ms	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
223.0ms	(- (* 1.0 (- 1.0 0.5)) (* (* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x)))) 0.5))

simplify1.8s

Counts

199 → 199

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	299	4016
1	735	2786
2	3397	2565
done	5001	2527

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.4b

regimes200.0ms

Accuracy

0% (0.2b remaining)

Error of 15.0b against oracle of 14.8b and baseline of 15.0b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	34
1	21	34
done	21	34

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.5s	2906×	body	1280	valid
297.0ms	3977×	body	80	valid
262.0ms	646×	body	640	valid
51.0ms	306×	body	320	valid
19.0ms	165×	body	160	valid