Details

sample107.0ms

Algorithm

intervals

Results

65.0ms	95×	body	1280	valid
17.0ms	133×	body	80	valid
8.0ms	15×	body	640	valid
2.0ms	8×	body	160	valid
2.0ms	5×	body	320	valid

simplify74.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize13.0ms

Local error

Found 4 expressions with local error:

2.1b	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b	(+ (/ 1/2 (hypot 1 x)) 1/2)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

Slowest

41.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
11.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)
10.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
4.0ms	(/ 1/2 (hypot 1 x))

series371.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

139.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
87.0ms	(/ 1/2 (hypot 1 x))
84.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
61.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)

simplify1.5s

Counts: 137 → 137

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

1.6b	(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

Slowest

28.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
7.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
4.0ms	(/ 1/2 (hypot 1 x))
3.0ms	(/ 1/2 (hypot 1 x))

series352.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

132.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
81.0ms	(/ 1/2 (hypot 1 x))
75.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
64.0ms	(/ 1/2 (hypot 1 x))

simplify1.3s

Counts: 152 → 152

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

1.5b	(- 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	(/ (- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))) (fma (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2) 1/4))
0.0b	(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

Slowest

104.0ms	(/ (- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))) (fma (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2) 1/4))
43.0ms	(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))
28.0ms	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
27.0ms	(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))

series587.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

260.0ms	(/ (- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))) (fma (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2) 1/4))
138.0ms	(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))
105.0ms	(* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))
84.0ms	(/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))

simplify1.0s

Counts: 152 → 152

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

1.6b	(log (exp (- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)))))
1.5b	(- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)))
0.3b	(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
0.1b	(/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
175×	`add-sqr-sqrt`
163×	`*-un-lft-identity`
159×	`add-cube-cbrt`
150×	`prod-diff`
80×	`log-prod`
77×	`exp-sum`
30×	`div-inv`
18×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/l*`
8×	`log-pow`
7×	`cbrt-undiv` `exp-prod` `div-exp`
6×	`add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`clear-num` `sub-neg` `frac-2neg` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--` `associate-/l/`

Counts

4 → 272

Calls

4 calls:

Slowest

40.0ms	(log (exp (- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)))))
23.0ms	(/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))
17.0ms	(- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)))
13.0ms	(/ 1/8 (* (hypot 1 x) (hypot 1 x)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

145.0ms	(log (exp (- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)))))
113.0ms	(- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)))
102.0ms	(/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))
100.0ms	(/ 1/8 (* (hypot 1 x) (hypot 1 x)))

simplify988.0ms

Counts: 284 → 284

prune4.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes195.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch282.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.3s	2901×	body	1280	valid
465.0ms	4028×	body	80	valid
328.0ms	613×	body	640	valid
92.0ms	296×	body	320	valid
36.0ms	162×	body	160	valid