Details

sample136.0ms

Algorithm

intervals

Results

75.0ms	76×	body	1280	valid
26.0ms	50×	body	640	valid
10.0ms	15×	body	2560	valid
7.0ms	24×	body	320	valid
6.0ms	71×	body	80	valid
3.0ms	20×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1 x)
1.6b	(+ x (hypot 1 x))
3.8b	(log (+ x (hypot 1 x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

0.0ms	(hypot 1 x)
9.0ms	(+ x (hypot 1 x))
7.0ms	(log (+ x (hypot 1 x)))

series353.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(hypot 1 x)
91.0ms	(+ x (hypot 1 x))
196.0ms	(log (+ x (hypot 1 x)))

simplify1.1s

Counts

56 → 56

Iterations

Iter	Nodes
done	2001
3	2001
2	666
1	244
0	108

prune492.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 3/40 (pow x 5) x)
0.1b	(* (* x x) x)
17.2b	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma 3/40 (pow x 5) x)
14.0ms	(* (* x x) x)
0.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

series287.0ms

Counts

3 → 9

Calls

3 calls:

169.0ms	(fma 3/40 (pow x 5) x)
57.0ms	(* (* x x) x)
61.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

simplify1.2s

Counts

62 → 62

Iterations

Iter	Nodes
done	2003
4	2003
3	1455
2	362
1	133
0	69

prune652.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (hypot 1 x))
0.3b	(* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))
3.8b	(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
9.7b	(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`cbrt-prod`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow1`
7×	`pow1/3` `add-exp-log`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `fma-def`
2×	`log-div` `flip3-+` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip-+`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt (hypot 1 x))
11.0ms	(* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))
3.0ms	(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
5.0ms	(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

series555.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (hypot 1 x))
160.0ms	(* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))
185.0ms	(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
66.0ms	(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

simplify1.0s

Counts

103 → 103

Iterations

Iter	Nodes
done	2000
3	2000
2	1192
1	435
0	184

prune817.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
3.8b	(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x)))
14.6b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
2×	`pow1/3`
1×	`rem-log-exp` `log-pow` `fma-udef`

Counts

4 → 54

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x)))
0.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))

series740.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(cbrt x)
207.0ms	(cbrt x)
145.0ms	(log (fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x)))
148.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (hypot 1 x))

simplify1.3s

Counts

66 → 66

Iterations

Iter	Nodes
done	2007
4	2007
3	1172
2	460
1	183
0	90

prune472.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes43.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch141.0ms

Steps

Iters	Range		Point
8	0.0042870261776910435	186.95626557948964	0.009904032332962092
9	-24078.920296370652	-0.35383103211093586	-1.061520745717705

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	32

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.3s	2354×	body	1280	valid
860.0ms	1532×	body	640	valid
532.0ms	784×	body	2560	valid
263.0ms	784×	body	320	valid
220.0ms	2135×	body	80	valid
94.0ms	411×	body	160	valid