Details

Time bar (total: 1.0m)

sample83.0ms

Algorithm
intervals
Results
55.0ms101×body1280valid
10.0ms128×body80valid
5.0ms15×body640valid
2.0ms10×body320valid
0.0ms2×body160valid

simplify25.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
24.0ms
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.9b
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(hypot 1 x)
0.0b
(+ (/ 1/2 (hypot 1 x)) 1/2)

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
20×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
6×add-cbrt-cube add-exp-log
4×pow1 sqrt-prod insert-posit16 difference-of-squares
3×associate-/r* associate-/l* distribute-lft-out--
2×distribute-lft-out
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log div-exp flip-+ div-inv flip--
Counts
4 → 69
Calls
4 calls:
Slowest
60.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
16.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)
7.0ms
(/ 1/2 (hypot 1 x))
0.0ms
(hypot 1 x)

series137.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
40.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)
10.0ms
(/ 1/2 (hypot 1 x))
2.0ms
(hypot 1 x)

simplify1.3s

Counts
53 → 81
Calls
53 calls:
Slowest
355.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
71.0ms
(/ (* (cbrt 1/2) (cbrt 1/2)) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))))
52.0ms
(/ (exp 1) (exp (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
46.0ms
(- 1 (sqrt (+ (* 1/2 (/ 1 (hypot 1 x))) 1/2)))
45.0ms
(- 1 (sqrt (+ (* 1/2 (/ 1 (hypot 1 x))) 1/2)))

prune794.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.5b
(- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.0b
(/ (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.0b
(/ 1/2 (hypot 1 x))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
54×add-sqr-sqrt
36×sqrt-prod
33×times-frac
32×add-cube-cbrt
26×distribute-lft-out
19×pow1
12×sqrt-div
11×swap-sqr
10×add-cbrt-cube add-exp-log
9×associate-/r*
8×sqrt-pow1 pow1/2 difference-of-squares
7×flip3-+ associate-*r* associate-*l* flip-+ associate-/l*
6×add-log-exp
5×pow-prod-up
4×frac-times insert-posit16 unswap-sqr
3×pow-prod-down pow-sqr
2×cbrt-undiv clear-num frac-2neg flip3-- div-exp associate-*l/ associate-*r/ associate-/r/ div-inv flip-- associate-/l/
1×pow2 sub-neg rem-square-sqrt pow-plus sqrt-unprod diff-log div-sub prod-exp *-commutative cbrt-unprod
Counts
4 → 157
Calls
4 calls:
Slowest
121.0ms
(/ (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
71.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
21.0ms
(- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
7.0ms
(/ 1/2 (hypot 1 x))

series215.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(/ (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
51.0ms
(- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
34.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
10.0ms
(/ 1/2 (hypot 1 x))

simplify11.9s

Counts
184 → 169
Calls
184 calls:
Slowest
623.0ms
(/ (* (* (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (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)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
421.0ms
(- (pow (* 1 1) 3) (pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3))
401.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
373.0ms
(* (sqrt (+ (pow (/ 1/2 (hypot 1 x)) 3) (pow 1/2 3))) (sqrt (- (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* 1/2 1/2))))
365.0ms
(* (sqrt (- (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* 1/2 1/2))) (sqrt (+ (pow (/ 1/2 (hypot 1 x)) 3) (pow 1/2 3))))

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.5b
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.5b
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.5b
(* (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))

rewrite386.0ms

Algorithm
rewrite-expression-head
Rules
80×sqrt-prod
77×*-un-lft-identity
70×add-sqr-sqrt
51×pow1
36×sqrt-div
33×swap-sqr
30×add-cube-cbrt
27×associate-*l*
24×sqrt-pow1 flip3-+ pow1/2 associate-*r* flip-+
22×distribute-lft-out
16×frac-times
15×pow-prod-up
13×unswap-sqr
12×add-cbrt-cube add-exp-log
10×pow-prod-down
9×pow-sqr
8×associate-*l/ associate-*r/
4×prod-exp *-commutative cbrt-unprod insert-posit16 add-log-exp
3×pow2 rem-square-sqrt pow-plus sqrt-unprod
1×distribute-rgt-in distribute-lft-in
Counts
4 → 221
Calls
4 calls:
Slowest
203.0ms
(* (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
63.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
61.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
57.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(* (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
46.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
39.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
28.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify19.6s

Counts
278 → 233
Calls
278 calls:
Slowest
1.1s
(* (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (* (* 1 1) (* 1 1)) (- (* (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (* (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))))
454.0ms
(* (+ (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)) (+ (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
446.0ms
(* (+ (* 1/2 (/ 1 (hypot 1 x))) 3/2) (+ (sqrt (+ (* 1/2 (/ 1 (hypot 1 x))) 1/2)) 1))
418.0ms
(* (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
401.0ms
(* (+ (* 1 1) (- (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))

prune2.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.5b

localize81.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
0.5b
(/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
0.5b
(/ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
0.5b
(- (/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (/ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))))

rewrite469.0ms

Algorithm
rewrite-expression-head
Rules
289×*-un-lft-identity
177×sqrt-prod
175×times-frac
164×add-sqr-sqrt
110×distribute-lft-out
68×add-cube-cbrt
32×distribute-lft-out--
27×associate-/r*
15×difference-of-squares
14×add-exp-log
10×add-cbrt-cube sqrt-div associate-/r/ div-inv associate-/l*
8×pow1
7×distribute-rgt-out--
6×flip3-+ flip-+ pow-flip add-log-exp
5×div-exp
4×insert-posit16
3×cbrt-undiv clear-num frac-2neg
2×rec-exp sqrt-pow1 pow1/2 1-exp inv-pow associate-/l/
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Counts
4 → 255
Calls
4 calls:
Slowest
310.0ms
(- (/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (/ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))))
65.0ms
(/ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
46.0ms
(/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
36.0ms
(/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))

series661.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
282.0ms
(- (/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (/ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))))
188.0ms
(/ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
99.0ms
(/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
92.0ms
(/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))

simplify14.1s

Counts
358 → 267
Calls
358 calls:
Slowest
524.0ms
(- (* 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (* (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ (/ 1/2 (hypot 1 x)) 1/2)))
376.0ms
(sqrt (+ (* 1 1) (- (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))))
344.0ms
(/ (* (* (+ (/ 1/2 (hypot 1 x)) 1/2) (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (* (* (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))))
335.0ms
(sqrt (+ (* 1 1) (- (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))))
326.0ms
(sqrt (+ (* 1 1) (- (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))))

prune3.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.4b

regimes105.0ms

Accuracy

0% (0.3b remaining)

Error of 15.0b against oracle of 14.7b and baseline of 15.0b

bsearch9.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.1s2785×body1280valid
518.0ms4107×body80valid
374.0ms633×body640valid
92.0ms312×body320valid
34.0ms163×body160valid