Details

sample121.0ms

Algorithm

intervals

Results

63.0ms	88×	body	1280	valid
19.0ms	42×	body	640	valid
18.0ms	29×	body	2560	valid
5.0ms	69×	body	80	valid
4.0ms	15×	body	320	valid
2.0ms	13×	body	160	valid

simplify12.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize10.0ms

Local error

Found 2 expressions with local error:

2.7b	(log (+ x (hypot 1 x)))
1.5b	(+ x (hypot 1 x))

rewrite9.0ms

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:

Slowest

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

series288.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

186.0ms	(log (+ x (hypot 1 x)))
102.0ms	(+ x (hypot 1 x))

simplify1.5s

Counts: 42 → 42

prune370.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

22.7b	(fma (pow x 5) 3/40 (fma x (* x (* -1/6 x)) x))
0.4b	(* -1/6 x)
0.1b	(* x (* -1/6 x))
0.0b	(fma x (* x (* -1/6 x)) x)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `fma-udef`
1×	`unswap-sqr`

Counts

4 → 64

Calls

4 calls:

Slowest

26.0ms	(* x (* -1/6 x))
12.0ms	(* -1/6 x)
0.0ms	(fma x (* x (* -1/6 x)) x)
0.0ms	(fma (pow x 5) 3/40 (fma x (* x (* -1/6 x)) x))

series252.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

117.0ms	(fma x (* x (* -1/6 x)) x)
88.0ms	(fma (pow x 5) 3/40 (fma x (* x (* -1/6 x)) x))
29.0ms	(* x (* -1/6 x))
18.0ms	(* -1/6 x)

simplify3.6s

Counts: 76 → 76

prune608.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

2.5b	(log (* (* (cbrt (+ x (hypot 1 x))) (cbrt (+ x (hypot 1 x)))) (cbrt (+ x (hypot 1 x)))))
1.5b	(+ x (hypot 1 x))
1.5b	(+ x (hypot 1 x))
1.5b	(+ x (hypot 1 x))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`log-div`
24×	`pow1`
15×	`log-pow`
14×	`associate-*l/`
13×	`*-un-lft-identity`
10×	`add-exp-log` `add-log-exp`
9×	`fma-def` `pow1/3` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`+-commutative` `sum-log` `rem-log-exp` `prod-exp` `pow-sqr` `distribute-lft-out`
2×	`pow2`
1×	`log-prod` `pow3`

Counts

4 → 109

Calls

4 calls:

Slowest

89.0ms	(log (* (* (cbrt (+ x (hypot 1 x))) (cbrt (+ x (hypot 1 x)))) (cbrt (+ x (hypot 1 x)))))
9.0ms	(+ x (hypot 1 x))
9.0ms	(+ x (hypot 1 x))
8.0ms	(+ x (hypot 1 x))

series373.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

163.0ms	(log (* (* (cbrt (+ x (hypot 1 x))) (cbrt (+ x (hypot 1 x)))) (cbrt (+ x (hypot 1 x)))))
78.0ms	(+ x (hypot 1 x))
68.0ms	(+ x (hypot 1 x))
64.0ms	(+ x (hypot 1 x))

simplify673.0ms

Counts: 121 → 121

prune972.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

2.7b	(log (+ x (hypot 1 x)))
1.5b	(+ x (hypot 1 x))

rewrite8.0ms

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:

Slowest

4.0ms	(+ x (hypot 1 x))
3.0ms	(log (+ x (hypot 1 x)))

series258.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

188.0ms	(log (+ x (hypot 1 x)))
71.0ms	(+ x (hypot 1 x))

simplify1.3s

Counts: 42 → 42

prune380.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes76.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.0b

bsearch150.0ms

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.2s	2321×	body	1280	valid
1.3s	1541×	body	640	valid
608.0ms	789×	body	2560	valid
347.0ms	770×	body	320	valid
215.0ms	2140×	body	80	valid
95.0ms	439×	body	160	valid