Details

sample80.0ms

Algorithm

intervals

Results

46.0ms	96×	body	1280	valid
11.0ms	122×	body	80	valid
9.0ms	26×	body	640	valid
2.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify51.0ms

Counts: 1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize21.0ms

Local error

Found 3 expressions with local error:

1.3b	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
21×	`prod-diff`
16×	`sqrt-prod`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`distribute-lft-out` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `associate-/r` `fma-neg` `insert-posit16` `log1p-expm1-u` `associate-/l` `distribute-lft-out--`
1×	`cbrt-undiv` `hypot-udef` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--`

Counts

3 → 87

Calls

3 calls:

Slowest

47.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
8.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)

series299.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

168.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
74.0ms	(/ 1/2 (hypot 1 x))
57.0ms	(hypot 1 x)

simplify998.0ms

Counts: 96 → 96

prune962.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

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

19.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
11.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
7.0ms	(/ 1/2 (hypot 1 x))
6.0ms	(/ 1/2 (hypot 1 x))

series419.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

141.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
110.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
90.0ms	(/ 1/2 (hypot 1 x))
78.0ms	(/ 1/2 (hypot 1 x))

simplify685.0ms

Counts: 152 → 152

prune1.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

2.5b	(log (exp (/ 1/2 (hypot 1 x))))
0.8b	(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

Slowest

12.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
7.0ms	(/ 1/2 (hypot 1 x))
7.0ms	(log (exp (/ 1/2 (hypot 1 x))))
4.0ms	(/ 1/2 (hypot 1 x))

series285.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

85.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
73.0ms	(/ 1/2 (hypot 1 x))
68.0ms	(log (exp (/ 1/2 (hypot 1 x))))
58.0ms	(/ 1/2 (hypot 1 x))

simplify2.3s

Counts: 160 → 160

prune2.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

18.2b	(fma (* (* (* x x) (* x x)) (* x x)) 5/32 (fma (* x x) 1/4 (* -3/16 (* (* x x) (* x x)))))
15.3b	(fma (* x x) 1/4 (* -3/16 (* (* x x) (* x x))))
2.5b	(log (exp (/ 1/2 (hypot 1 x))))
0.3b	(* -3/16 (* (* x x) (* x x)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
22×	`add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt` `log-pow`
13×	`exp-prod` `*-un-lft-identity` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
9×	`times-frac`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `associate-l`
2×	`fma-udef`
1×	`rem-log-exp` `associate-r` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

Slowest

69.0ms	(* -3/16 (* (* x x) (* x x)))
20.0ms	(log (exp (/ 1/2 (hypot 1 x))))
0.0ms	(fma (* (* (* x x) (* x x)) (* x x)) 5/32 (fma (* x x) 1/4 (* -3/16 (* (* x x) (* x x)))))
0.0ms	(fma (* x x) 1/4 (* -3/16 (* (* x x) (* x x))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

144.0ms	(fma (* x x) 1/4 (* -3/16 (* (* x x) (* x x))))
113.0ms	(log (exp (/ 1/2 (hypot 1 x))))
87.0ms	(* -3/16 (* (* x x) (* x x)))
63.0ms	(fma (* (* (* x x) (* x x)) (* x x)) 5/32 (fma (* x x) 1/4 (* -3/16 (* (* x x) (* x x)))))

simplify1.4s

Counts: 93 → 93

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes84.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.2b

bsearch259.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.3s	2832×	body	1280	valid
405.0ms	4083×	body	80	valid
265.0ms	605×	body	640	valid
83.0ms	295×	body	320	valid
35.0ms	185×	body	160	valid