Details

Time bar (total: 27.7s)

sample93.0ms

Algorithm
intervals
Results
48.0ms92×body1280valid
21.0ms132×body80valid
9.0ms19×body640valid
2.0ms7×body320valid
1.0ms6×body160valid

simplify30.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize17.0ms

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)

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
22×add-sqr-sqrt
13×add-cube-cbrt
9×times-frac
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log
5×pow1
4×insert-posit16 difference-of-squares
3×associate-/r* distribute-lft-out associate-/l* distribute-lft-out--
2×flip3-+ sqrt-div flip-+
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log div-exp div-inv flip--
Counts
4 → 78
Calls
4 calls:
Slowest
55.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
18.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
8.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)
6.0ms
(/ 1/2 (hypot 1 x))

series164.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
66.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
59.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
34.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)
6.0ms
(/ 1/2 (hypot 1 x))

simplify2.1s

Counts
90 → 90

prune950.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.6b

localize62.0ms

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))))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
107×*-un-lft-identity
79×add-sqr-sqrt
50×times-frac
37×distribute-lft-out
24×distribute-lft-out--
22×sqrt-prod
20×add-cube-cbrt
16×difference-of-squares
11×add-log-exp
7×associate-/l*
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×flip3-- frac-sub insert-posit16 flip-- associate-/l/
3×flip3-+ diff-log flip-+
2×sub-neg sqrt-div associate--l+ associate-/r/
1×associate--l- cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 130
Calls
4 calls:
Slowest
126.0ms
(/ (- (- 1 1/2) (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
28.0ms
(- (- 1 1/2) (/ 1/2 (hypot 1 x)))
17.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
17.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(/ (- (- 1 1/2) (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
65.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
57.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
43.0ms
(- (- 1 1/2) (/ 1/2 (hypot 1 x)))

simplify1.7s

Counts
142 → 142

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.6b

localize89.0ms

Local error

Found 4 expressions with local error:

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

rewrite360.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
15×add-log-exp
13×add-sqr-sqrt
10×associate--l+
7×pow1 add-cube-cbrt
6×add-cbrt-cube add-exp-log sqrt-prod distribute-lft-out
5×diff-log
4×sub-neg associate-*r* insert-posit16
3×distribute-rgt-in distribute-lft-in flip3-+ associate-*l* flip-+
2×sum-log sqrt-div associate-*r/
1×associate--l- +-commutative rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-- difference-of-squares unswap-sqr
Counts
4 → 79
Calls
4 calls:
Slowest
257.0ms
(- (- (* (hypot 1 x) (- 1 (* 1/2 (* 1/2 1/2)))) (+ (* 1/2 (* 1/2 1/2)) 1/2)) (* 1/2 1/2))
52.0ms
(* (hypot 1 x) (+ (+ 1/2 (* 1/2 1/2)) 1))
33.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
17.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

series154.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
52.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
49.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
34.0ms
(- (- (* (hypot 1 x) (- 1 (* 1/2 (* 1/2 1/2)))) (+ (* 1/2 (* 1/2 1/2)) 1/2)) (* 1/2 1/2))
19.0ms
(* (hypot 1 x) (+ (+ 1/2 (* 1/2 1/2)) 1))

simplify1.9s

Counts
91 → 91

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.5b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite477.0ms

Algorithm
rewrite-expression-head
Rules
1469×*-un-lft-identity
1444×sqrt-prod
986×add-sqr-sqrt
910×times-frac
412×distribute-lft-out
360×distribute-lft-out--
276×swap-sqr
258×add-cube-cbrt
120×difference-of-squares
96×associate-*r* associate-*l*
25×unswap-sqr
18×add-cbrt-cube add-exp-log
14×sqrt-div add-log-exp
11×pow1
10×associate-/r/ associate-/l*
9×associate-/r*
6×flip3-- diff-log frac-sub flip--
5×cbrt-undiv sqrt-undiv flip3-+ div-exp flip-+ div-inv
4×sub-neg prod-exp associate--l+ cbrt-unprod insert-posit16 associate-/l/
2×associate--l-
1×pow2 frac-times clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 695
Calls
4 calls:
Slowest
294.0ms
(* (/ (sqrt (- (- 1 1/2) (/ 1/2 (hypot 1 x)))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (/ (sqrt (- (- 1 1/2) (/ 1/2 (hypot 1 x)))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))))
79.0ms
(/ (sqrt (- (- 1 1/2) (/ 1/2 (hypot 1 x)))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
40.0ms
(- (- 1 1/2) (/ 1/2 (hypot 1 x)))
29.0ms
(- (- 1 1/2) (/ 1/2 (hypot 1 x)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(/ (sqrt (- (- 1 1/2) (/ 1/2 (hypot 1 x)))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
144.0ms
(* (/ (sqrt (- (- 1 1/2) (/ 1/2 (hypot 1 x)))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (/ (sqrt (- (- 1 1/2) (/ 1/2 (hypot 1 x)))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))))
49.0ms
(- (- 1 1/2) (/ 1/2 (hypot 1 x)))
46.0ms
(- (- 1 1/2) (/ 1/2 (hypot 1 x)))

simplify1.0s

Counts
707 → 707

prune11.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.5b

regimes142.0ms

Accuracy

0% (0.0b remaining)

Error of 14.9b against oracle of 14.8b and baseline of 14.9b

bsearch5.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.9s2893×body1280valid
502.0ms3985×body80valid
358.0ms634×body640valid
139.0ms327×body320valid
33.0ms161×body160valid