Details

sample114.0ms

Algorithm

intervals

Results

67.0ms	90×	body	1280	valid
16.0ms	129×	body	80	valid
9.0ms	18×	body	640	valid
6.0ms	14×	body	320	valid
1.0ms	5×	body	160	valid

simplify82.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	114
6	114
5	111
4	89
3	69
2	43
1	21
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)
1.7b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
21×	`prod-diff`
20×	`sqrt-prod`
10×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow1` `distribute-lft-out`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r` `fma-neg` `associate-/l` `distribute-lft-out--`
2×	`sqrt-div` `hypot-def`
1×	`cbrt-undiv` `rem-sqrt-square` `hypot-udef` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `div-exp` `flip-+` `div-inv` `flip--`

Counts

4 → 108

Calls

4 calls:

20.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
7.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
49.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series362.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
59.0ms	(/ 1/2 (hypot 1 x))
46.0ms	(hypot 1 x)
147.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.4s

Counts

120 → 120

Iterations

Iter	Nodes
done	2022
3	2022
2	1327
1	495
0	212

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)
0.0b	(hypot 1 x)
1.3b	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
3×	`associate-/r` `fma-neg` `associate-/l`
2×	`hypot-udef` `diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `div-exp` `div-inv` `flip--` `associate--r+`

Counts

4 → 88

Calls

4 calls:

6.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
0.0ms	(hypot 1 x)
37.0ms	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

series337.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 1/2 (hypot 1 x))
63.0ms	(hypot 1 x)
77.0ms	(hypot 1 x)
94.0ms	(- 1 (+ (/ 1/2 (hypot 1 x)) 1/2))

simplify1.0s

Counts

100 → 100

Iterations

Iter	Nodes
done	2006
3	2006
2	1029
1	372
0	161

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 x)
0.0b	(hypot 1 x)
0.0b	(* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x))))
1.2b	(- 1 (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt`
6×	`flip3-+` `add-cbrt-cube` `swap-sqr` `add-exp-log` `flip-+` `distribute-lft-out` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`distribute-rgt-in` `hypot-udef` `distribute-lft-in` `associate-l/` `associate-r/` `associate--r+`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

0.0ms	(hypot 1 x)
0.0ms	(hypot 1 x)
42.0ms	(* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x))))
9.0ms	(- 1 (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

series806.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(hypot 1 x)
436.0ms	(hypot 1 x)
75.0ms	(* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x))))
238.0ms	(- 1 (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.3s

Counts

100 → 100

Iterations

Iter	Nodes
done	2019
3	2019
2	1617
1	471
0	155

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (- 1 (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))))
0.0b	(* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x))))
0.1b	(exp (log (- 1 (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))))
1.2b	(- 1 (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
13×	`pow1` `add-cube-cbrt`
7×	`add-exp-log`
6×	`log-prod` `flip3-+` `add-cbrt-cube` `swap-sqr` `flip-+` `distribute-lft-out` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `log-div` `exp-prod` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `exp-sum` `prod-diff` `flip--`
2×	`distribute-rgt-in` `sub-neg` `log1p-def` `distribute-lft-in` `exp-diff` `associate-l/` `associate-r/` `log-pow` `associate--r+`
1×	`pow2` `pow-plus` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 105

Calls

4 calls:

7.0ms	(log (- 1 (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))))
58.0ms	(* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x))))
5.0ms	(exp (log (- 1 (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))))
5.0ms	(- 1 (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

series970.0ms

Counts

4 → 12

Calls

4 calls:

372.0ms	(log (- 1 (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))))
84.0ms	(* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x))))
265.0ms	(exp (log (- 1 (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))))
248.0ms	(- 1 (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	2001
3	2001
2	1661
1	520
0	188

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes161.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.9b

bsearch180.0ms

Steps

Iters	Range		Point
8	0.0042870261776910435	186.95626557948964	0.010372877460017476
9	-0.35383103211093586	-9.60334830165094e-09	-0.010054607689223198

simplify13.0ms

Iterations

Iter	Nodes
done	54
1	54
0	43

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.2s	2863×	body	1280	valid
476.0ms	4051×	body	80	valid
254.0ms	635×	body	640	valid
127.0ms	310×	body	320	valid
26.0ms	141×	body	160	valid