Details

sample86.0ms

Algorithm

intervals

Results

51.0ms	89×	body	1280	valid
14.0ms	142×	body	80	valid
5.0ms	13×	body	640	valid
3.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify43.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.4b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
21×	`prod-diff`
20×	`sqrt-prod`
13×	`fma-def`
10×	`times-frac`
7×	`add-log-exp`
6×	`distribute-lft-out`
4×	`pow1` `difference-of-squares`
3×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`flip3-+` `sqrt-div` `flip-+` `hypot-def`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `div-inv` `flip--`

Counts

3 → 95

Calls

3 calls:

Slowest

54.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
16.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
9.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)

series265.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

130.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
78.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
57.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)

simplify1.3s

Counts: 104 → 104

prune827.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.8b	(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b	(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.0b	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
72×	`times-frac`
55×	`add-cube-cbrt`
39×	`prod-diff`
33×	`distribute-lft-out`
20×	`sqrt-prod`
16×	`difference-of-squares`
8×	`distribute-lft-out--` `add-log-exp`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-def` `flip3-+` `fma-neg` `flip-+`
2×	`flip3--` `sqrt-div` `associate-/r/` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp`

Counts

4 → 169

Calls

4 calls:

Slowest

78.0ms	(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
34.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
18.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
17.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

series752.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

398.0ms	(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
139.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
118.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
96.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

simplify1.9s

Counts: 181 → 181

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.8b	(- 1/2 (/ 1/2 (hypot 1 x)))
0.1b	(sqrt (/ 1/2 (hypot 1 x)))
0.0b	(+ 1 (hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2)))
0.0b	(hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
39×	`prod-diff`
38×	`times-frac`
13×	`sqrt-prod`
8×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-def` `fma-neg`
2×	`rem-sqrt-square` `difference-of-squares`
1×	`+-commutative` `hypot-udef` `sum-log` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `sqrt-div` `diff-log` `flip-+` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 117

Calls

4 calls:

Slowest

13.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
8.0ms	(+ 1 (hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2)))
4.0ms	(sqrt (/ 1/2 (hypot 1 x)))
0.0ms	(hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2))

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

562.0ms	(hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2))
553.0ms	(+ 1 (hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2)))
153.0ms	(sqrt (/ 1/2 (hypot 1 x)))
116.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify848.0ms

Counts: 129 → 129

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.8b	(- 1/2 (/ 1/2 (hypot 1 x)))
0.1b	(sqrt (/ 1/2 (hypot 1 x)))
0.0b	(+ 1 (hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2)))
0.0b	(hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
39×	`prod-diff`
38×	`times-frac`
13×	`sqrt-prod`
8×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-def` `fma-neg`
2×	`rem-sqrt-square` `difference-of-squares`
1×	`+-commutative` `hypot-udef` `sum-log` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `sqrt-div` `diff-log` `flip-+` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 117

Calls

4 calls:

Slowest

8.0ms	(sqrt (/ 1/2 (hypot 1 x)))
7.0ms	(+ 1 (hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2)))
7.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
0.0ms	(hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2))

series1.7s

Counts

4 → 12

Calls

4 calls:

Slowest

930.0ms	(hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2))
554.0ms	(+ 1 (hypot (sqrt (/ 1/2 (hypot 1 x))) (sqrt 1/2)))
153.0ms	(sqrt (/ 1/2 (hypot 1 x)))
79.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify920.0ms

Counts: 129 → 129

prune1.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes123.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch215.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.1s	2850×	body	1280	valid
503.0ms	4021×	body	80	valid
319.0ms	607×	body	640	valid
102.0ms	348×	body	320	valid
32.0ms	174×	body	160	valid