Details

Time bar (total: 9.1s)

sample40.0ms

Algorithm
intervals
Results
21.0ms102×body1280valid
5.0ms117×body80valid
4.0ms24×body640valid
1.0ms9×body320valid
0.0ms4×body160valid

simplify3.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.5b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log sqrt-prod flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 66
Calls
4 calls:
12.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
24.0ms
(/ 1.0 (hypot 1.0 x))
12.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series210.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
8.0ms
(/ 1.0 (hypot 1.0 x))
79.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
92.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify60.0ms

Counts
78 → 78

prune262.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
1.1b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
7×pow1
6×associate-*r/ associate-/r* associate-/l* add-log-exp
4×associate--l+
3×sub-neg
2×cbrt-undiv distribute-rgt-in flip3-- frac-2neg distribute-lft-in sqrt-pow1 sqrt-div div-exp clear-num frac-sub flip-- div-inv
1×flip3-+ pow1/2 diff-log pow-prod-down sqrt-prod flip-+
Counts
4 → 85
Calls
4 calls:
19.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
8.0ms
(/ 1.0 (hypot 1.0 x))
8.0ms
(/ 1.0 (hypot 1.0 x))
32.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series170.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
10.0ms
(/ 1.0 (hypot 1.0 x))
8.0ms
(/ 1.0 (hypot 1.0 x))
44.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify111.0ms

Counts
97 → 97

prune319.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 15.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
0.1b
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
1.1b
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
271×associate-*r/
104×frac-add
74×flip3-- associate-/r/ flip--
68×frac-times
47×add-sqr-sqrt
37×*-un-lft-identity
36×times-frac
27×add-cube-cbrt
26×associate-*l/
21×sqr-pow
20×difference-of-squares
17×flip3-+ flip-+
14×add-exp-log add-cbrt-cube
12×associate-/l*
9×cube-div
7×pow1
6×associate-/r* add-log-exp
5×difference-cubes distribute-lft-out--
4×frac-sub associate-/l/
3×cbrt-undiv pow-unpow div-exp pow-exp rem-cube-cbrt
2×pow-pow frac-2neg prod-exp clear-num cbrt-unprod div-inv
1×cube-mult pow-to-exp sub-neg unpow-prod-down diff-log unpow3 div-sub cube-prod pow-prod-down
Counts
4 → 202
Calls
4 calls:
7.0ms
(/ 1.0 (hypot 1.0 x))
187.0ms
(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
16.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
25.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series427.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/ 1.0 (hypot 1.0 x))
265.0ms
(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
40.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
114.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify106.0ms

Counts
214 → 214

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 15.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (+ (sqrt (pow (* 1.0 (- 1.0 0.5)) 3)) (sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))) (/ (- (sqrt (pow (* 1.0 (- 1.0 0.5)) 3)) (sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))))))
1.1b
(- (sqrt (pow (* 1.0 (- 1.0 0.5)) 3)) (sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)))
10.3b
(sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
10.3b
(sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite637.0ms

Algorithm
rewrite-expression-head
Rules
277×associate-*r/
120×associate-*r*
108×frac-add
80×add-sqr-sqrt
74×flip3-- sqrt-prod associate-/r/ flip--
72×frac-times
45×*-un-lft-identity
43×times-frac
36×difference-of-squares
30×associate-*l/
28×sqr-pow
25×add-cube-cbrt
19×flip3-+ flip-+
14×cube-div sqrt-div
9×add-exp-log add-cbrt-cube
8×distribute-lft-out--
6×pow1 add-log-exp
5×associate-*l*
4×rem-sqrt-square
2×cube-mult unpow-prod-down sqrt-pow1 pow1/2 unpow3 cube-prod prod-exp frac-sub cbrt-unprod distribute-lft-out unswap-sqr
1×cbrt-undiv sub-neg diff-log div-exp pow-prod-down *-commutative div-inv
Counts
4 → 214
Calls
4 calls:
568.0ms
(* (+ (sqrt (pow (* 1.0 (- 1.0 0.5)) 3)) (sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))) (/ (- (sqrt (pow (* 1.0 (- 1.0 0.5)) 3)) (sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))))))
39.0ms
(- (sqrt (pow (* 1.0 (- 1.0 0.5)) 3)) (sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)))
3.0ms
(sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
3.0ms
(sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series1.2s

Counts
4 → 12
Calls
4 calls:
687.0ms
(* (+ (sqrt (pow (* 1.0 (- 1.0 0.5)) 3)) (sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))) (/ (- (sqrt (pow (* 1.0 (- 1.0 0.5)) 3)) (sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))))))
242.0ms
(- (sqrt (pow (* 1.0 (- 1.0 0.5)) 3)) (sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)))
123.0ms
(sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
113.0ms
(sqrt (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify99.0ms

Counts
226 → 226

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 15.2b

regimes76.0ms

Accuracy

-0.6% (0.2b remaining)

Error of 14.7b against oracle of 14.4b and baseline of 14.7b

bsearch0.0ms

simplify101.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.2s2830×body1280valid
214.0ms4102×body80valid
158.0ms622×body640valid
70.0ms289×body320valid
14.0ms157×body160valid