Details

sample68.0ms

Algorithm

intervals

Results

38.0ms	101×	body	1280	valid
9.0ms	124×	body	80	valid
5.0ms	17×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify50.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize23.0ms

Local error

Found 4 expressions with local error:

1.9b	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)
0.0b	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

rewrite72.0ms

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:

Slowest

39.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
23.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
8.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)

series374.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

149.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
98.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
74.0ms	(/ 1/2 (hypot 1 x))
53.0ms	(hypot 1 x)

simplify576.0ms

Counts: 159 → 120

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

1.4b	(- 1 (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

Slowest

50.0ms	(- 1 (+ 1/2 (/ 1/2 (hypot 1 x))))
8.0ms	(/ 1/2 (hypot 1 x))
4.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)

series337.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

93.0ms	(- 1 (+ 1/2 (/ 1/2 (hypot 1 x))))
86.0ms	(/ 1/2 (hypot 1 x))
84.0ms	(/ 1/2 (hypot 1 x))
74.0ms	(hypot 1 x)

simplify421.0ms

Counts: 155 → 119

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

1.4b	(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
55×	`add-cube-cbrt`
46×	`times-frac`
39×	`prod-diff`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `difference-of-squares`
1×	`hypot-udef` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 131

Calls

4 calls:

Slowest

13.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
4.0ms	(/ 1/2 (hypot 1 x))
4.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)

series348.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

109.0ms	(/ 1/2 (hypot 1 x))
93.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
91.0ms	(/ 1/2 (hypot 1 x))
55.0ms	(hypot 1 x)

simplify1.0s

Counts: 206 → 143

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

1.3b	(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))
0.1b	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
0.0b	(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))
0.0b	(* (hypot 1 x) (hypot 1 x))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `pow1`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
21×	`prod-diff`
20×	`add-cbrt-cube` `add-exp-log`
12×	`times-frac`
7×	`hypot-udef` `pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`pow2` `cbrt-undiv` `fma-neg` `sqrt-unprod` `swap-sqr` `div-exp` `pow-sqr` `associate-/l*`
2×	`*-commutative` `unswap-sqr`
1×	`clear-num` `associate-/r*` `sub-neg` `rem-square-sqrt` `frac-2neg` `flip3--` `diff-log` `pow3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 129

Calls

4 calls:

Slowest

38.0ms	(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))
24.0ms	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
18.0ms	(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))
7.0ms	(* (hypot 1 x) (hypot 1 x))

series556.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

224.0ms	(* (hypot 1 x) (hypot 1 x))
134.0ms	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
104.0ms	(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))
94.0ms	(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))

simplify801.0ms

Counts: 169 → 141

prune1.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes143.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.0b

bsearch152.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.3s	2933×	body	1280	valid
506.0ms	4014×	body	80	valid
339.0ms	591×	body	640	valid
94.0ms	303×	body	320	valid
34.0ms	159×	body	160	valid