Details

Time bar (total: 17.5s)

sample100.0ms

Algorithm
intervals
Results
59.0ms89×body1280valid
17.0ms142×body80valid
7.0ms13×body640valid
4.0ms10×body320valid
0.0ms2×body160valid

simplify37.0ms

Counts
1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.4b

localize48.0ms

Local error

Found 3 expressions with local error:

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

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt
8×sqrt-prod
7×add-log-exp
4×pow1 add-cube-cbrt difference-of-squares
3×add-cbrt-cube add-exp-log insert-posit16 distribute-lft-out distribute-lft-out--
2×flip3-+ sqrt-div flip-+
1×+-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip--
Counts
3 → 50
Calls
3 calls:
Slowest
28.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
17.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
8.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)

series191.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
84.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
72.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
35.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)

simplify2.9s

Counts
59 → 59

prune536.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 9.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.8b
(- 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
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
77×*-un-lft-identity
76×add-sqr-sqrt
44×times-frac
33×distribute-lft-out
20×sqrt-prod
19×add-cube-cbrt
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×insert-posit16
3×flip3-+ flip-+
2×flip3-- sqrt-div associate-/r/ 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 div-inv
Counts
4 → 114
Calls
4 calls:
Slowest
84.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
32.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
17.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
11.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
175.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
73.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
59.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
44.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify1.7s

Counts
126 → 126

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 9.9b

localize60.0ms

Local error

Found 4 expressions with local error:

0.8b
(- 1/2 (/ 1/2 (hypot 1 x)))
0.8b
(- 1/2 (/ 1/2 (hypot 1 x)))
0.2b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.1b
(* (/ 1/2 (hypot 1 x)) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
57×add-cbrt-cube add-exp-log
52×times-frac
43×*-un-lft-identity
39×add-cube-cbrt
26×associate-*l*
25×pow1
22×prod-exp cbrt-unprod
17×cbrt-undiv div-exp
14×associate-*r*
13×swap-sqr
8×add-log-exp
6×frac-times associate-*r/ pow-prod-up unswap-sqr
5×div-inv
4×pow-prod-down associate-*l/ insert-posit16 difference-of-squares
2×pow2 sub-neg pow-plus flip3-- diff-log pow-sqr *-commutative flip-- distribute-lft-out--
1×cube-unmult
Counts
4 → 159
Calls
4 calls:
Slowest
40.0ms
(* (/ 1/2 (hypot 1 x)) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))
34.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
11.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
10.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series184.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
56.0ms
(* (/ 1/2 (hypot 1 x)) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))
54.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
37.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
37.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify695.0ms

Counts
171 → 171

prune2.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 9.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))
0.2b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.0b
(* (+ (/ 1/2 (hypot 1 x)) 1/2) (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1))
0.0b
(+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)

rewrite306.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
46×*-un-lft-identity
40×times-frac
34×add-cube-cbrt
19×associate-*r*
18×add-cbrt-cube add-exp-log
17×associate-*l*
13×pow1 swap-sqr
9×distribute-lft-out
8×add-log-exp
7×flip3-+ flip-+
5×frac-times prod-exp cbrt-unprod unswap-sqr
4×cbrt-undiv div-exp sqrt-prod insert-posit16 div-inv
3×associate-*l/ associate-*r/
2×pow-prod-down *-commutative
1×pow2 distribute-rgt-in +-commutative sum-log sub-neg distribute-lft-in pow-plus flip3-- diff-log pow-sqr pow-prod-up flip-- difference-of-squares
Counts
4 → 130
Calls
4 calls:
Slowest
209.0ms
(* (+ (/ 1/2 (hypot 1 x)) 1/2) (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1))
69.0ms
(+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)
18.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
7.0ms
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

series352.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(* (+ (/ 1/2 (hypot 1 x)) 1/2) (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1))
84.0ms
(+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)
78.0ms
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))
32.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))

simplify1.1s

Counts
142 → 142

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 9.7b

regimes62.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 15.0b and baseline of 15.2b

bsearch4.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.2s2850×body1280valid
480.0ms4021×body80valid
358.0ms607×body640valid
99.0ms348×body320valid
33.0ms174×body160valid