Details

Time bar (total: 3.3m)

sample124.0ms

Algorithm
intervals
Results
69.0ms105×body1280valid
27.0ms126×body80valid
7.0ms12×body640valid
4.0ms11×body320valid
1.0ms2×body160valid

simplify28.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
28.0ms
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize13.0ms

Local error

Found 1 expressions with local error:

1.1b
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity
4×sqrt-prod difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt insert-posit16 flip-- distribute-lft-out
Counts
1 → 20
Calls
1 calls:
Slowest
62.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series85.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
85.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify402.0ms

Counts
17 → 23
Calls
17 calls:
Slowest
62.0ms
(/ (exp 1) (exp (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
40.0ms
(- 1 (sqrt (+ (* 1/2 (/ 1 (hypot 1 x))) 1/2)))
37.0ms
(- 1 (sqrt (+ (* 1/2 (/ 1 (hypot 1 x))) 1/2)))
32.0ms
(- 1 (sqrt (+ (* 1/2 (/ 1 (hypot 1 x))) 1/2)))
30.0ms
(- 1 (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

prune207.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.1b

localize26.0ms

Local error

Found 2 expressions with local error:

1.1b
(log (exp (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
1.1b
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×*-un-lft-identity
11×log-pow
10×exp-prod
8×sqrt-prod difference-of-squares
6×distribute-lft-out--
5×log-prod
4×add-cube-cbrt add-log-exp
3×pow1
2×sub-neg add-cbrt-cube exp-sum add-exp-log insert-posit16 distribute-lft-out
1×log-div flip3-- exp-diff diff-log rem-log-exp flip--
Counts
2 → 46
Calls
2 calls:
Slowest
182.0ms
(log (exp (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
56.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series151.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
83.0ms
(log (exp (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
68.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify871.0ms

Counts
36 → 52
Calls
36 calls:
Slowest
67.0ms
(log (* (cbrt (exp (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (cbrt (exp (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))))
49.0ms
(/ (exp 1) (exp (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
47.0ms
(log (sqrt (exp (- 1 (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)))

prune573.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 14.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
0.5b
(pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)
0.5b
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(+ (* (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))))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
85×add-sqr-sqrt
70×*-un-lft-identity
54×sqrt-div sqrt-prod
43×unpow-prod-down cube-prod
36×difference-of-squares
28×flip3-+ flip-+
22×associate-*r/
21×pow1
17×add-cube-cbrt
16×frac-add
14×distribute-lft-out--
13×sqr-pow
12×frac-times distribute-lft-out
11×swap-sqr
9×sqrt-pow1 pow1/2
8×add-log-exp
7×add-cbrt-cube associate-*r* associate-*l* add-exp-log
6×associate-*l/
5×pow-prod-up
4×insert-posit16 unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr
2×cube-div cube-mult
1×pow2 pow-to-exp difference-cubes +-commutative sum-log sub-neg rem-square-sqrt pow-plus distribute-rgt-out flip3-- sqrt-unprod diff-log unpow3 pow-exp prod-exp *-commutative cbrt-unprod sqrt-pow2 flip-- rem-cube-cbrt
Counts
4 → 193
Calls
4 calls:
Slowest
88.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
45.0ms
(+ (* (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))))
41.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
25.0ms
(pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)

series400.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
121.0ms
(+ (* (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))))
92.0ms
(pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)
44.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify45.9s

Counts
252 → 205
Calls
252 calls:
Slowest
658.0ms
(+ (pow (sqrt 1) 3) (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3))
634.0ms
(* (* (sqrt (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) 1/2)))) (sqrt (- (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (- (/ 1/2 (hypot 1 x)) 1/2)))
628.0ms
(pow (* (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) 3)
537.0ms
(+ (* (* (sqrt (+ (pow (/ 1/2 (hypot 1 x)) 3) (pow 1/2 3))) (sqrt (+ (pow (/ 1/2 (hypot 1 x)) 3) (pow 1/2 3)))) (sqrt (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) 1/2))))) (* (* (sqrt (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) 1/2)))) (sqrt (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) 1/2))))) (* 1 (sqrt (+ (pow (/ 1/2 (hypot 1 x)) 3) (pow 1/2 3))))))
510.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (/ 3 2)))

prune2.8s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 13.6b

localize73.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
0.6b
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
0.6b
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
0.5b
(* (* (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))) (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)))) (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))))

rewrite846.0ms

Algorithm
rewrite-expression-head
Rules
232×add-sqr-sqrt
146×*-un-lft-identity
144×unpow-prod-down cube-prod difference-of-squares
80×sqrt-prod
57×associate-*r*
56×distribute-lft-out--
55×cbrt-prod
54×cbrt-div
48×sqr-pow
30×flip3-- flip--
28×frac-times
23×pow1
16×distribute-lft-out
14×associate-*l/
10×add-log-exp
9×pow1/3 add-exp-log pow-prod-up
8×associate-*r/
6×pow-plus add-cube-cbrt
5×add-cbrt-cube pow-prod-down
4×cube-mult difference-cubes insert-posit16
3×sub-neg diff-log prod-exp pow-sqr cbrt-unprod
2×pow2 unswap-sqr
1×associate-*l* pow3 *-commutative
Counts
4 → 305
Calls
4 calls:
Slowest
646.0ms
(* (* (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))) (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)))) (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))))
81.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
53.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
48.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))

series463.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
118.0ms
(* (* (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))) (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)))) (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))))
102.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
101.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))

simplify2.2m

Counts
443 → 317
Calls
443 calls:
Slowest
883.0ms
(cbrt (- (pow (sqrt 1) 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (/ 3 2))))
839.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
789.0ms
(- (pow 1 (/ 3 2)) (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3))
780.0ms
(- (pow 1 (/ 3 2)) (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3))
589.0ms
(- (pow 1 (/ 3 2)) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (/ 3 2)))

prune6.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 13.6b

regimes93.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.2s2850×body1280valid
506.0ms4056×body80valid
291.0ms635×body640valid
95.0ms303×body320valid
61.0ms156×body160valid