Details

sample162.0ms

Algorithm

intervals

Results

81.0ms	75×	body	1280	valid
32.0ms	57×	body	640	valid
18.0ms	24×	body	2560	valid
10.0ms	26×	body	320	valid
6.0ms	59×	body	80	valid
4.0ms	15×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.7b

localize16.0ms

Local error

Found 2 expressions with local error:

1.0b	(+ x (hypot 1 x))
2.7b	(log (+ x (hypot 1 x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `log-prod` `add-cube-cbrt` `add-log-exp`
3×	`pow1` `fma-def` `add-exp-log`
2×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `sum-log` `rem-log-exp` `log-pow`

Counts

2 → 36

Calls

2 calls:

22.0ms	(+ x (hypot 1 x))
4.0ms	(log (+ x (hypot 1 x)))

series234.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(+ x (hypot 1 x))
156.0ms	(log (+ x (hypot 1 x)))

simplify2.5s

Counts

42 → 42

Iterations

Iter	Nodes
done	5000
3	3951
2	730
1	215
0	93

prune196.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 3/40 (pow x 5) x)
0.1b	(* x (* x x))
16.3b	(fma (* x (* x x)) -1/6 (fma 3/40 (pow x 5) x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt` `pow-prod-up`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `unswap-sqr`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma 3/40 (pow x 5) x)
23.0ms	(* x (* x x))
0.0ms	(fma (* x (* x x)) -1/6 (fma 3/40 (pow x 5) x))

series297.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms	(fma 3/40 (pow x 5) x)
42.0ms	(* x (* x x))
97.0ms	(fma (* x (* x x)) -1/6 (fma 3/40 (pow x 5) x))

simplify797.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	644
1	138
0	70

prune204.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1/16 (pow x 5))
0.2b	(/ 1/8 (* x (* x x)))
14.6b	(log (- (/ 1/8 (* x (* x x))) (- (/ 1/16 (pow x 5)) (/ -1/2 x))))
19.2b	(- (/ 1/8 (* x (* x x))) (- (/ 1/16 (pow x 5)) (/ -1/2 x)))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

648×	`times-frac`
587×	`add-sqr-sqrt`
467×	`*-un-lft-identity`
416×	`prod-diff`
415×	`add-cube-cbrt`
327×	`associate--r+`
143×	`unpow-prod-down`
58×	`difference-of-squares`
57×	`sqr-pow`
54×	`div-inv`
20×	`distribute-lft-out--`
19×	`add-exp-log`
15×	`add-cbrt-cube`
9×	`add-log-exp`
8×	`associate-/r*` `frac-sub`
7×	`fma-neg`
6×	`log-prod` `div-exp` `associate-/l*`
5×	`pow1` `log-div`
4×	`expm1-log1p-u` `cbrt-undiv` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`diff-log` `prod-exp` `cbrt-unprod`
2×	`clear-num` `sub-neg` `frac-2neg`
1×	`pow-to-exp` `rem-log-exp` `pow-exp` `log-pow` `associate--r-`

Counts

4 → 545

Calls

4 calls:

5.0ms	(/ 1/16 (pow x 5))
13.0ms	(/ 1/8 (* x (* x x)))
131.0ms	(log (- (/ 1/8 (* x (* x x))) (- (/ 1/16 (pow x 5)) (/ -1/2 x))))
123.0ms	(- (/ 1/8 (* x (* x x))) (- (/ 1/16 (pow x 5)) (/ -1/2 x)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ 1/16 (pow x 5))
66.0ms	(/ 1/8 (* x (* x x)))
119.0ms	(log (- (/ 1/8 (* x (* x x))) (- (/ 1/16 (pow x 5)) (/ -1/2 x))))
53.0ms	(- (/ 1/8 (* x (* x x))) (- (/ 1/16 (pow x 5)) (/ -1/2 x)))

simplify2.1s

Counts

557 → 557

Iterations

Iter	Nodes
done	5000
1	2813
0	1109

prune3.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (+ x (hypot 1 x))) (sqrt (+ x (hypot 1 x))))
1.0b	(+ x (hypot 1 x))
1.0b	(+ x (hypot 1 x))
2.7b	(log (* (sqrt (+ x (hypot 1 x))) (sqrt (+ x (hypot 1 x)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

35×	`pow1`
32×	`*-un-lft-identity`
26×	`add-sqr-sqrt` `sqrt-prod`
24×	`sqrt-div`
16×	`sqrt-pow1` `pow1/2`
14×	`flip3-+` `log-pow` `add-cube-cbrt` `flip-+`
11×	`swap-sqr`
10×	`pow-prod-up`
9×	`add-exp-log`
8×	`frac-times` `log-div` `distribute-lft-out` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`fma-def` `add-cbrt-cube` `pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
2×	`pow2` `+-commutative` `sum-log` `pow-plus` `rem-log-exp` `prod-exp`
1×	`log-prod` `rem-square-sqrt` `sqrt-unprod` `*-commutative` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

35.0ms	(* (sqrt (+ x (hypot 1 x))) (sqrt (+ x (hypot 1 x))))
9.0ms	(+ x (hypot 1 x))
7.0ms	(+ x (hypot 1 x))
14.0ms	(log (* (sqrt (+ x (hypot 1 x))) (sqrt (+ x (hypot 1 x)))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sqrt (+ x (hypot 1 x))) (sqrt (+ x (hypot 1 x))))
103.0ms	(+ x (hypot 1 x))
95.0ms	(+ x (hypot 1 x))
183.0ms	(log (* (sqrt (+ x (hypot 1 x))) (sqrt (+ x (hypot 1 x)))))

simplify1.3s

Counts

148 → 148

Iterations

Iter	Nodes
done	5000
2	1580
1	358
0	160

prune420.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch115.0ms

Steps

Iters	Range		Point
10	4.3052657707541446e-11	1.874259372897972	0.009515787017106168
9	-209901990.47645873	-0.28008678268591264	-1.0468290506388152

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	30

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.7s	2308×	body	1280	valid
1.1s	1548×	body	640	valid
570.0ms	822×	body	2560	valid
217.0ms	779×	body	320	valid
202.0ms	2129×	body	80	valid
96.0ms	414×	body	160	valid