Details

sample119.0ms

Algorithm

intervals

Results

73.0ms	104×	body	1280	valid
15.0ms	121×	body	80	valid
9.0ms	17×	body	640	valid
3.0ms	8×	body	320	valid
2.0ms	6×	body	160	valid

simplify48.0ms

Counts: 1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize49.0ms

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

rewrite75.0ms

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

48.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
13.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
9.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)
4.0ms	(/ 1/2 (hypot 1 x))

series402.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

169.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
81.0ms	(/ 1/2 (hypot 1 x))
77.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
75.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)

simplify1.4s

Counts: 137 → 137

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

1.4b	(- 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))

rewrite72.0ms

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

39.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
13.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
8.0ms	(/ 1/2 (hypot 1 x))
7.0ms	(/ 1/2 (hypot 1 x))

series368.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
90.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
80.0ms	(/ 1/2 (hypot 1 x))
73.0ms	(/ 1/2 (hypot 1 x))

simplify932.0ms

Counts: 152 → 152

prune1.6s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

3.4b	(log (exp (/ 1/2 (hypot 1 x))))
1.4b	(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(+ 1 (sqrt (+ (log (exp (/ 1/2 (hypot 1 x)))) 1/2)))
0.0b	(/ 1/2 (hypot 1 x))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 139

Calls

4 calls:

Slowest

65.0ms	(+ 1 (sqrt (+ (log (exp (/ 1/2 (hypot 1 x)))) 1/2)))
14.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
7.0ms	(log (exp (/ 1/2 (hypot 1 x))))
4.0ms	(/ 1/2 (hypot 1 x))

series393.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(+ 1 (sqrt (+ (log (exp (/ 1/2 (hypot 1 x)))) 1/2)))
100.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
91.0ms	(log (exp (/ 1/2 (hypot 1 x))))
78.0ms	(/ 1/2 (hypot 1 x))

simplify958.0ms

Counts: 151 → 151

prune1.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

15.4b	(fma 69/1024 (* (* x x) (* (* x x) (* x x))) (fma 1/8 (* x x) (* (* (* x x) (* x x)) -11/128)))
12.8b	(fma 1/8 (* x x) (* (* (* x x) (* x x)) -11/128))
0.5b	(* (* (* x x) (* x x)) -11/128)
0.1b	(* (* x x) (* x x))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

133×	`pow1`
36×	`pow-prod-down` `pow-prod-up`
34×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
21×	`prod-exp` `cbrt-unprod`
18×	`pow-plus`
13×	`pow2`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-l` `*-commutative` `fma-udef` `unswap-sqr`
1×	`swap-sqr`

Counts

4 → 119

Calls

4 calls:

Slowest

107.0ms	(* (* (* x x) (* x x)) -11/128)
47.0ms	(* (* x x) (* x x))
1.0ms	(fma 69/1024 (* (* x x) (* (* x x) (* x x))) (fma 1/8 (* x x) (* (* (* x x) (* x x)) -11/128)))
0.0ms	(fma 1/8 (* x x) (* (* (* x x) (* x x)) -11/128))

series319.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

131.0ms	(fma 1/8 (* x x) (* (* (* x x) (* x x)) -11/128))
71.0ms	(fma 69/1024 (* (* x x) (* (* x x) (* x x))) (fma 1/8 (* x x) (* (* (* x x) (* x x)) -11/128)))
69.0ms	(* (* (* x x) (* x x)) -11/128)
47.0ms	(* (* x x) (* x x))

simplify1.1s

Counts: 131 → 131

prune1.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.6b

bsearch204.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.4s	2857×	body	1280	valid
452.0ms	4102×	body	80	valid
291.0ms	611×	body	640	valid
91.0ms	279×	body	320	valid
33.0ms	151×	body	160	valid