Details

Time bar (total: 18.4s)

sample112.0ms

Algorithm
intervals
Results
66.0ms92×body1280valid
16.0ms132×body80valid
10.0ms19×body640valid
2.0ms7×body320valid
2.0ms6×body160valid

simplify37.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

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
72.0ms
(- 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)
4.0ms
(/ 1/2 (hypot 1 x))

series426.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
109.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
82.0ms
(/ 1/2 (hypot 1 x))
77.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)

simplify1.3s

Counts
137 → 137

prune1.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite253.0ms

Algorithm
rewrite-expression-head
Rules
212×*-un-lft-identity
189×add-sqr-sqrt
105×times-frac
87×prod-diff
83×add-cube-cbrt
44×difference-of-squares
38×distribute-lft-out--
37×distribute-lft-out
22×sqrt-prod
11×associate--l+ add-log-exp
7×div-inv associate-/l*
6×associate-/r* add-cbrt-cube fma-neg add-exp-log
5×pow1
4×expm1-log1p-u flip3-- frac-sub insert-posit16 log1p-expm1-u flip-- associate-/l/
3×fma-def flip3-+ diff-log flip-+
2×sub-neg sqrt-div associate-/r/ hypot-def
1×associate--l- cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-sub div-exp
Counts
4 → 236
Calls
4 calls:
Slowest
174.0ms
(/ (- (- 1 1/2) (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
35.0ms
(- (- 1 1/2) (/ 1/2 (hypot 1 x)))
20.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
19.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

series656.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
375.0ms
(/ (- (- 1 1/2) (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
105.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
88.0ms
(- (- 1 1/2) (/ 1/2 (hypot 1 x)))
87.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

simplify1.5s

Counts
248 → 248

prune2.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
126×*-un-lft-identity
125×add-sqr-sqrt
87×prod-diff
72×add-cube-cbrt
56×times-frac
30×difference-of-squares
17×distribute-lft-out--
11×associate--l+
10×add-log-exp
9×log-pow
8×sqrt-prod
7×pow1 exp-prod
6×log-prod fma-neg div-inv
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u distribute-lft-out
3×associate-+r+ fma-def diff-log
2×sub-neg flip3-+ flip3-- sqrt-div frac-sub flip-+ hypot-def flip--
1×associate--l- +-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp
Counts
4 → 183
Calls
4 calls:
Slowest
66.0ms
(+ 1 (log (exp (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
47.0ms
(- (- 1 1/2) (/ 1/2 (hypot 1 x)))
20.0ms
(log (exp (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
18.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

series410.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(+ 1 (log (exp (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
101.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
99.0ms
(- (- 1 1/2) (/ 1/2 (hypot 1 x)))
85.0ms
(log (exp (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

simplify923.0ms

Counts
195 → 195

prune2.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 3 expressions with local error:

19.6b
(- (fma 1/8 (* x x) (* (pow x 6) 69/1024)) (* 11/128 (pow x 4)))
0.1b
(* (pow x 6) 69/1024)
0.1b
(* 11/128 (pow x 4))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
13×add-exp-log
11×*-un-lft-identity add-cube-cbrt
10×associate-*r* associate-*l*
8×unpow-prod-down
7×add-cbrt-cube
6×prod-exp unswap-sqr
5×add-log-exp
4×sqr-pow
3×expm1-log1p-u pow1 fma-neg prod-diff insert-posit16 log1p-expm1-u
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×sub-neg flip3-- diff-log associate--l+ fma-udef flip--
Counts
3 → 78
Calls
3 calls:
Slowest
11.0ms
(* 11/128 (pow x 4))
9.0ms
(* (pow x 6) 69/1024)
5.0ms
(- (fma 1/8 (* x x) (* (pow x 6) 69/1024)) (* 11/128 (pow x 4)))

series218.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
85.0ms
(- (fma 1/8 (* x x) (* (pow x 6) 69/1024)) (* 11/128 (pow x 4)))
77.0ms
(* (pow x 6) 69/1024)
56.0ms
(* 11/128 (pow x 4))

simplify981.0ms

Counts
87 → 87

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes83.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch177.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.3s2893×body1280valid
436.0ms3985×body80valid
266.0ms634×body640valid
125.0ms327×body320valid
31.0ms161×body160valid