Details

sample177.0ms

Algorithm

intervals

Results

86.0ms	87×	body	1280	valid
32.0ms	51×	body	640	valid
25.0ms	22×	body	320	valid
13.0ms	16×	body	2560	valid
7.0ms	69×	body	80	valid
2.0ms	11×	body	160	valid

simplify20.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize9.0ms

Local error

Found 3 expressions with local error:

2.6b	(log (+ x (hypot 1 x)))
1.6b	(+ x (hypot 1 x))
0.0b	(hypot 1 x)

rewrite10.0ms

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:

Slowest

5.0ms	(+ x (hypot 1 x))
3.0ms	(log (+ x (hypot 1 x)))
0.0ms	(hypot 1 x)

series629.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

502.0ms	(log (+ x (hypot 1 x)))
72.0ms	(+ x (hypot 1 x))
55.0ms	(hypot 1 x)

simplify1.6s

Counts: 56 → 56

prune548.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 3 expressions with local error:

14.4b	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))
0.1b	(* (* x x) x)
0.0b	(fma 3/40 (pow x 5) x)

rewrite36.0ms

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:

Slowest

35.0ms	(* (* x x) x)
0.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))
0.0ms	(fma 3/40 (pow x 5) x)

series279.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

163.0ms	(fma 3/40 (pow x 5) x)
75.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))
40.0ms	(* (* x x) x)

simplify2.1s

Counts: 62 → 62

prune541.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

31.9b	(log (expm1 (log1p (+ x (hypot 1 x)))))
1.6b	(+ x (hypot 1 x))
1.5b	(expm1 (log1p (+ x (hypot 1 x))))
0.0b	(hypot 1 x)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

Slowest

9.0ms	(+ x (hypot 1 x))
1.0ms	(log (expm1 (log1p (+ x (hypot 1 x)))))
0.0ms	(expm1 (log1p (+ x (hypot 1 x))))
0.0ms	(hypot 1 x)

series603.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

273.0ms	(log (expm1 (log1p (+ x (hypot 1 x)))))
196.0ms	(expm1 (log1p (+ x (hypot 1 x))))
76.0ms	(+ x (hypot 1 x))
58.0ms	(hypot 1 x)

simplify876.0ms

Counts: 68 → 68

prune492.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

2.6b	(log (+ x (hypot 1 x)))
1.6b	(+ x (hypot 1 x))
0.0b	(hypot 1 x)

rewrite9.0ms

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:

Slowest

5.0ms	(+ x (hypot 1 x))
3.0ms	(log (+ x (hypot 1 x)))
0.0ms	(hypot 1 x)

series356.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

180.0ms	(log (+ x (hypot 1 x)))
93.0ms	(+ x (hypot 1 x))
83.0ms	(hypot 1 x)

simplify1.7s

Counts: 56 → 56

prune352.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch138.0ms

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.4s	2326×	body	1280	valid
795.0ms	1538×	body	640	valid
504.0ms	790×	body	2560	valid
329.0ms	749×	body	320	valid
166.0ms	2201×	body	80	valid
72.0ms	396×	body	160	valid