Details

Time bar (total: 1.6m)

sample91.0ms

Algorithm
intervals
Results
49.0ms90×body1280valid
13.0ms132×body80valid
11.0ms24×body640valid
3.0ms9×body320valid
0.0ms1×body160valid

simplify71.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
71.0ms
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize28.0ms

Local error

Found 3 expressions with local error:

1.7b
(- 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))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
40×add-sqr-sqrt
26×add-cube-cbrt
21×prod-diff
20×sqrt-prod
10×times-frac
5×add-cbrt-cube add-exp-log distribute-lft-out add-log-exp
4×pow1 difference-of-squares
3×expm1-log1p-u associate-/r* fma-neg insert-posit16 log1p-expm1-u associate-/l* distribute-lft-out--
2×sqrt-div hypot-def
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log div-exp flip-+ div-inv flip--
Counts
3 → 97
Calls
3 calls:
Slowest
71.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
21.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
7.0ms
(/ 1/2 (hypot 1 x))

series341.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
163.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
90.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
88.0ms
(/ 1/2 (hypot 1 x))

simplify10.1s

Counts
145 → 106
Calls
145 calls:
Slowest
544.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
399.0ms
(- (+ (* 1/8 (pow x 2)) (* 69/1024 (pow x 6))) (* 11/128 (pow x 4)))
392.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
363.0ms
(- (+ (* 3/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))) (* 1/4 (/ 1 (pow x 3))))
362.0ms
(* (* (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

prune945.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.2b
(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.0b
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
117×add-sqr-sqrt
113×*-un-lft-identity
72×times-frac
55×add-cube-cbrt
39×prod-diff
33×distribute-lft-out
20×sqrt-prod
16×difference-of-squares
8×distribute-lft-out-- add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log associate-/l*
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv
3×fma-def flip3-+ fma-neg flip-+
2×flip3-- sqrt-div associate-/r/ hypot-def flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp
Counts
4 → 169
Calls
4 calls:
Slowest
84.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
23.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
19.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
19.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series737.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
426.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
121.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
96.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
93.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify30.5s

Counts
262 → 181
Calls
262 calls:
Slowest
705.0ms
(* (* (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
634.0ms
(+ (* 1/8 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 3) (pow (sqrt 1/2) 2))))) (+ (* 1/8 (/ 1 (* x (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (pow (sqrt 1/2) 3))))) (+ (* 1/2 (/ 1 (* x (+ (sqrt 1/2) 1)))) (* 1/2 (/ 1 (+ (sqrt 1/2) 1))))))))
606.0ms
(- (+ (* 1/8 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 3) (pow (sqrt 1/2) 2))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (pow (sqrt 1/2) 3))))) (* 1/2 (/ 1 (+ (sqrt 1/2) 1)))))) (+ (* 1/8 (/ 1 (* x (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (* 1/2 (/ 1 (* x (+ (sqrt 1/2) 1))))))
592.0ms
(/ (* (* (- 1/2 (/ 1/2 (hypot 1 x))) (- 1/2 (/ 1/2 (hypot 1 x)))) (- 1/2 (/ 1/2 (hypot 1 x)))) (* (* (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
510.0ms
(* (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ 1/2 (/ 1/2 (hypot 1 x))))

prune1.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

1.2b
(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x)))))
0.0b
(log1p (- 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(/ (expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x))))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity
63×add-sqr-sqrt
50×add-cube-cbrt
46×times-frac
39×prod-diff
16×distribute-lft-out
8×sqrt-prod
6×associate-/r* add-cbrt-cube add-exp-log add-log-exp
5×expm1-log1p-u
4×pow1 insert-posit16 log1p-expm1-u div-inv
3×fma-neg associate-/l*
2×associate-/r/ expm1-udef difference-of-squares
1×cbrt-undiv log1p-udef expm1-log1p clear-num sub-neg frac-2neg flip3-+ flip3-- diff-log div-sub div-exp log1p-expm1 flip-+ flip-- distribute-lft-out--
Counts
4 → 129
Calls
4 calls:
Slowest
45.0ms
(/ (expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x))))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
14.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
1.0ms
(log1p (- 1/2 (/ 1/2 (hypot 1 x))))
0.0ms
(expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
573.0ms
(/ (expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x))))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
259.0ms
(expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x)))))
207.0ms
(log1p (- 1/2 (/ 1/2 (hypot 1 x))))
97.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify26.6s

Counts
202 → 141
Calls
202 calls:
Slowest
913.0ms
(fma (- (/ (cbrt 1/2) (cbrt (hypot 1 x)))) (/ (* (cbrt 1/2) (cbrt 1/2)) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))) (* (/ (cbrt 1/2) (cbrt (hypot 1 x))) (/ (* (cbrt 1/2) (cbrt 1/2)) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))))))
634.0ms
(/ (* (* (expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x))))) (expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x)))))) (expm1 (log1p (- 1/2 (/ 1/2 (hypot 1 x)))))) (* (* (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
633.0ms
(fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1/2 (cbrt (hypot 1 x))) (/ 1 (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))))))
597.0ms
(+ (* 1/8 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 3) (pow (sqrt 1/2) 2))))) (+ (* 1/8 (/ 1 (* x (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (pow (sqrt 1/2) 3))))) (+ (* 1/2 (/ 1 (* x (+ (sqrt 1/2) 1)))) (* 1/2 (/ 1 (+ (sqrt 1/2) 1))))))))
566.0ms
(- (+ (* 1/8 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 3) (pow (sqrt 1/2) 2))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (pow (sqrt 1/2) 3))))) (* 1/2 (/ 1 (+ (sqrt 1/2) 1)))))) (+ (* 1/8 (/ 1 (* x (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (* 1/2 (/ 1 (* x (+ (sqrt 1/2) 1))))))

prune1.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) 69/1024)
0.1b
(* (* x x) (- (* (* x x) 69/1024) 11/128))
0.0b
(* (* x x) (+ 1/8 (* (* x x) (- (* (* x x) 69/1024) 11/128))))
0.0b
(- (* (* x x) 69/1024) 11/128)

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 add-cbrt-cube add-exp-log
13×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×associate-*r* prod-diff pow-prod-down prod-exp cbrt-unprod
6×distribute-rgt-in distribute-lft-in add-log-exp
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u
3×sub-neg associate-*l* *-commutative unswap-sqr
2×flip3-- flip--
1×flip3-+ fma-neg diff-log flip-+
Counts
4 → 101
Calls
4 calls:
Slowest
96.0ms
(* (* x x) (- (* (* x x) 69/1024) 11/128))
35.0ms
(- (* (* x x) 69/1024) 11/128)
29.0ms
(* (* x x) (+ 1/8 (* (* x x) (- (* (* x x) 69/1024) 11/128))))
22.0ms
(* (* x x) 69/1024)

series376.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(* (* x x) (- (* (* x x) 69/1024) 11/128))
101.0ms
(* (* x x) (+ 1/8 (* (* x x) (- (* (* x x) 69/1024) 11/128))))
66.0ms
(- (* (* x x) 69/1024) 11/128)
50.0ms
(* (* x x) 69/1024)

simplify18.2s

Counts
130 → 113
Calls
130 calls:
Slowest
819.0ms
(* (* (* (* x x) (- (* (* x x) 69/1024) 11/128)) (* (* x x) (- (* (* x x) 69/1024) 11/128))) (* (* x x) (- (* (* x x) 69/1024) 11/128)))
716.0ms
(* (* x x) (- (* 1/8 1/8) (* (* (* x x) (- (* (* x x) 69/1024) 11/128)) (* (* x x) (- (* (* x x) 69/1024) 11/128)))))
619.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (- (* (* x x) 69/1024) 11/128) (- (* (* x x) 69/1024) 11/128)) (- (* (* x x) 69/1024) 11/128)))
558.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (- (* (* x x) 69/1024) 11/128) (- (* (* x x) 69/1024) 11/128)) (- (* (* x x) 69/1024) 11/128)))
498.0ms
(* (* (* (* x x) (+ 1/8 (* (* x x) (- (* (* x x) 69/1024) 11/128)))) (* (* x x) (+ 1/8 (* (* x x) (- (* (* x x) 69/1024) 11/128))))) (* (* x x) (+ 1/8 (* (* x x) (- (* (* x x) 69/1024) 11/128)))))

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes85.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.9b

bsearch210.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.4s2891×body1280valid
452.0ms4006×body80valid
324.0ms614×body640valid
98.0ms334×body320valid
29.0ms155×body160valid