Details

Time bar (total: 6.9s)

sample23.0ms

Algorithm
intervals
Results
9.0ms249×body80valid
1.0ms3×body1280valid
0.0ms3×body640valid
0.0ms1×body160valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
078
1108
2118
done118

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ x (/ (fabs (- y x)) 2.0))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
4×*-un-lft-identity
3×fma-def add-log-exp
2×add-sqr-sqrt add-cube-cbrt
1×pow1 add-exp-log +-commutative expm1-log1p-u flip3-+ sum-log add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
Counts
1 → 17
Calls
1 calls:
6.0ms
(+ x (/ (fabs (- y x)) 2.0))

series17.0ms

Counts
1 → 3
Calls
1 calls:
17.0ms
(+ x (/ (fabs (- y x)) 2.0))

simplify1.6s

Counts
20 → 20
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
033213
189204
2199185
3478185
41245185
53767185
done5000185

prune44.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (/ (fabs (- y x)) 2.0))
0.0b
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.0b
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.4b
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
35×*-un-lft-identity
34×sqrt-prod
21×pow1
16×sqrt-div
15×add-cube-cbrt
11×swap-sqr
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-up
4×expm1-log1p-u frac-times hypot-def log1p-expm1-u unswap-sqr
3×fma-def pow-prod-down pow-sqr
2×rem-sqrt-square times-frac associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 121
Calls
4 calls:
6.0ms
(+ x (/ (fabs (- y x)) 2.0))
11.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
12.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
51.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series132.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ x (/ (fabs (- y x)) 2.0))
45.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
49.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
17.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify485.0ms

Counts
133 → 133
Iterations

Useful iterations: done (481.0ms)

IterNodesCost
01352667
12871913
210301765
done50011753

prune273.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.1b
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.4b
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
0.4b
(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
122×sqrt-div
112×sqrt-prod
91×sqrt-pow1
69×pow1
60×add-sqr-sqrt
47×pow1/2
42×*-un-lft-identity
39×pow-prod-up
35×flip3-+ flip-+
32×frac-times
22×add-cube-cbrt
20×swap-sqr
17×associate-*l*
16×associate-*r/
12×pow-prod-down
11×add-exp-log associate-*r* pow-sqr add-cbrt-cube unswap-sqr
10×associate-*l/
9×distribute-lft-out
4×expm1-log1p-u rem-sqrt-square prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×sqrt-unprod
2×*-commutative
1×pow2 pow-plus rem-square-sqrt
Counts
4 → 213
Calls
4 calls:
11.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
11.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
88.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
57.0ms
(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

series169.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
49.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
17.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
50.0ms
(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

simplify1.7s

Counts
225 → 225
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02777004
16534427
223793929
done50003925

prune458.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
0.4b
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0))))))
0.5b
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b
(cbrt (+ x (/ (fabs (- y x)) 2.0)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
18×add-sqr-sqrt
14×sqrt-div
13×cbrt-prod sqrt-prod
12×add-cube-cbrt cbrt-div
11×pow1 add-exp-log associate-*r* add-cbrt-cube
10×associate-*r/ associate-*l*
9×flip3-+ flip-+
4×expm1-log1p-u frac-times pow-prod-down prod-exp cbrt-unprod log1p-expm1-u distribute-lft-out add-log-exp
3×unswap-sqr
2×pow1/3 associate-*l/ *-commutative
Counts
4 → 95
Calls
4 calls:
28.0ms
(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
52.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0))))))
6.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
6.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
75.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0))))))
50.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
56.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify651.0ms

Counts
107 → 107
Iterations

Useful iterations: 2 (201.0ms)

IterNodesCost
02683564
16663347
222633062
done50003062

prune377.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes67.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
188
done88

end0.0ms

sample299.0ms

Algorithm
intervals
Results
152.0ms7713×body80valid
8.0ms94×body1280valid
5.0ms74×body640valid
5.0ms46×body2560valid
3.0ms49×body320valid
1.0ms27×body160valid