Details

Time bar (total: 59.6s)

sample105.0ms

Algorithm
intervals
Results
60.0ms90×body1280valid
14.0ms130×body80valid
12.0ms24×body640valid
2.0ms6×body320valid
1.0ms6×body160valid

simplify19.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
19.0ms
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize29.0ms

Local error

Found 4 expressions with local error:

1.8b
(- 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))

rewrite68.0ms

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
42.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
10.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
9.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)
7.0ms
(/ 1/2 (hypot 1 x))

series169.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
86.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
47.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
27.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)
8.0ms
(/ 1/2 (hypot 1 x))

simplify1.9s

Counts
61 → 90
Calls
61 calls:
Slowest
324.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
310.0ms
(sqrt (+ (pow (/ 1/2 (hypot 1 x)) 3) (pow 1/2 3)))
150.0ms
(sqrt (- (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* 1/2 1/2)))
52.0ms
(/ (* (cbrt 1/2) (cbrt 1/2)) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))))
48.0ms
(/ (exp 1) (exp (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

prune809.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.1b

localize57.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (* 1 1) (* (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)))
0.0b
(+ 1 (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))))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
48×add-sqr-sqrt
38×sqrt-prod
30×distribute-lft-out
24×times-frac add-cube-cbrt
19×pow1
12×sqrt-div
11×swap-sqr
8×sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ add-log-exp difference-of-squares
7×associate-*r* associate-*l*
6×associate-/r*
5×pow-prod-up
4×frac-times insert-posit16 associate-/l* unswap-sqr
3×pow-prod-down pow-sqr
2×flip3-- associate-*l/ associate-*r/ associate-/r/ flip-- associate-/l/
1×pow2 cbrt-undiv +-commutative clear-num sum-log sub-neg rem-square-sqrt frac-2neg pow-plus sqrt-unprod diff-log div-sub div-exp prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 144
Calls
4 calls:
Slowest
114.0ms
(/ (- (* 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))))
87.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
44.0ms
(- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
36.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(/ (- (* 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))))
54.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
41.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
37.0ms
(- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

simplify11.4s

Counts
165 → 156
Calls
165 calls:
Slowest
671.0ms
(/ (* (* (- (* 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)))))
468.0ms
(- (pow (* 1 1) 3) (pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3))
398.0ms
(* (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))))
373.0ms
(+ (* 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)))))
339.0ms
(* (sqrt (+ (pow (/ 1/2 (hypot 1 x)) 3) (pow 1/2 3))) (sqrt (+ (pow (/ 1/2 (hypot 1 x)) 3) (pow 1/2 3))))

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.6b

localize45.0ms

Local error

Found 4 expressions with local error:

1.3b
(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.0b
(/ 1/2 (hypot 1 x))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
82×add-sqr-sqrt *-un-lft-identity
53×times-frac
32×distribute-lft-out
26×add-cube-cbrt
16×sqrt-prod difference-of-squares
9×associate-/r* associate-/l*
8×add-cbrt-cube add-exp-log distribute-lft-out-- add-log-exp
4×pow1 insert-posit16
2×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-exp associate-/r/ flip-+ div-inv flip-- associate-/l/
1×+-commutative sum-log sub-neg diff-log div-sub
Counts
4 → 125
Calls
4 calls:
Slowest
89.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
17.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
8.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
7.0ms
(/ 1/2 (hypot 1 x))

series229.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
55.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
42.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
6.0ms
(/ 1/2 (hypot 1 x))

simplify7.1s

Counts
138 → 137
Calls
138 calls:
Slowest
453.0ms
(/ (* (* (- 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)))))
419.0ms
(- (pow 1/2 3) (pow (/ 1/2 (hypot 1 x)) 3))
312.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
282.0ms
(+ (* 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)))))
209.0ms
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.6b

localize107.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (pow 1/2 3) (pow (/ 1/2 (hypot 1 x)) 3))
0.1b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.1b
(pow (/ 1/2 (hypot 1 x)) 3)
0.0b
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt
66×times-frac
62×*-un-lft-identity
47×add-cube-cbrt
31×unpow-prod-down cube-prod
24×difference-of-squares
19×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
12×pow1
11×sqr-pow
8×add-log-exp
6×div-inv
5×cbrt-undiv div-exp distribute-lft-out--
4×prod-exp cbrt-unprod insert-posit16 distribute-lft-out unswap-sqr
3×pow-unpow
2×pow-exp sqrt-prod rem-cube-cbrt
1×cube-div pow2 cube-mult frac-times pow-to-exp difference-cubes +-commutative sum-log sub-neg pow-pow flip3-+ pow-plus flip3-- diff-log unpow3 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+ flip--
Counts
4 → 173
Calls
4 calls:
Slowest
29.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
23.0ms
(- (pow 1/2 3) (pow (/ 1/2 (hypot 1 x)) 3))
12.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
4.0ms
(pow (/ 1/2 (hypot 1 x)) 3)

series243.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(- (pow 1/2 3) (pow (/ 1/2 (hypot 1 x)) 3))
60.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
42.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
41.0ms
(pow (/ 1/2 (hypot 1 x)) 3)

simplify27.5s

Counts
188 → 185
Calls
188 calls:
Slowest
674.0ms
(- (pow (sqrt 1/2) 3) (pow (sqrt (/ 1/2 (hypot 1 x))) 3))
528.0ms
(+ (sqrt (pow 1/2 3)) (pow (/ (sqrt 1/2) (sqrt (hypot 1 x))) 3))
520.0ms
(+ (pow 1/2 (/ 3 2)) (pow (/ 1/2 (hypot 1 x)) (/ 3 2)))
496.0ms
(+ (sqrt (pow 1/2 3)) (pow (/ 1/2 (hypot 1 x)) (/ 3 2)))
488.0ms
(* (/ (* (cbrt 1/2) (cbrt 1/2)) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))) (/ (* (cbrt 1/2) (cbrt 1/2)) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))))

prune2.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.4b

regimes161.0ms

Accuracy

0% (0.3b remaining)

Error of 14.8b against oracle of 14.5b and baseline of 14.8b

bsearch2.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.9s2868×body1280valid
660.0ms621×body640valid
468.0ms4056×body80valid
96.0ms306×body320valid
30.0ms149×body160valid