Details

Time bar (total: 15.4s)

sample18.0ms

Algorithm
intervals
Results
9.0ms248×body80valid
0.0ms2×body2560valid
0.0ms4×body320valid
0.0ms1×body1280valid
0.0ms1×body640valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1108
2118
done118

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

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:
11.0ms
(+ x (/ (fabs (- y x)) 2.0))

series18.0ms

Counts
1 → 3
Calls
1 calls:
18.0ms
(+ x (/ (fabs (- y x)) 2.0))

simplify3.5s

Counts
20 → 20
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
033213
189204
2226185
3515185
41428185
53947185
done5000185

prune83.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma (sqrt x) (sqrt x) (/ (fabs (- y x)) 2.0))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma (sqrt x) (sqrt x) (/ (fabs (- y x)) 2.0))

series154.0ms

Counts
1 → 3
Calls
1 calls:
154.0ms
(fma (sqrt x) (sqrt x) (/ (fabs (- y x)) 2.0))

simplify4.3s

Counts
13 → 13
Iterations

Useful iterations: 5 (2.9s)

IterNodesCost
040216
189171
2216145
3538143
41416142
53911138
done5000138

prune45.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(- x (/ (fabs (- y x)) 2.0))
0.0b
(* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))
14.4b
(- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0)))
32.8b
(/ (- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))) (- x (/ (fabs (- y x)) 2.0)))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
121×add-sqr-sqrt
97×times-frac
91×*-un-lft-identity
79×add-cube-cbrt
40×prod-diff
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×swap-sqr associate-*r* associate-*l*
11×pow1
8×div-inv add-log-exp
6×associate-/r* distribute-lft-out--
5×cbrt-undiv div-exp
4×expm1-log1p-u flip3-- fma-neg prod-exp flip-- cbrt-unprod log1p-expm1-u associate-/l* unswap-sqr
2×sub-neg diff-log associate-/r/ associate-/l/
1×pow2 frac-times frac-2neg pow-plus div-sub associate-*r/ pow-prod-down associate-*l/ clear-num pow-sqr *-commutative pow-prod-up
Counts
4 → 198
Calls
4 calls:
13.0ms
(- x (/ (fabs (- y x)) 2.0))
31.0ms
(* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))
26.0ms
(- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0)))
73.0ms
(/ (- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))) (- x (/ (fabs (- y x)) 2.0)))

series165.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(- x (/ (fabs (- y x)) 2.0))
24.0ms
(* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))
52.0ms
(- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0)))
65.0ms
(/ (- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))) (- x (/ (fabs (- y x)) 2.0)))

simplify1.8s

Counts
210 → 210
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03276590
18485577
227434189
done50003854

prune680.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (sqrt (fabs (- y x))) 1) (/ (pow (sqrt (fabs (- y x))) 3) (* 2.0 2.0)))
0.4b
(pow (sqrt (fabs (- y x))) 3)
14.4b
(- (* x x) (* (/ (sqrt (fabs (- y x))) 1) (/ (pow (sqrt (fabs (- y x))) 3) (* 2.0 2.0))))
32.8b
(/ (- (* x x) (* (/ (sqrt (fabs (- y x))) 1) (/ (pow (sqrt (fabs (- y x))) 3) (* 2.0 2.0)))) (- x (/ (fabs (- y x)) 2.0)))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
138×add-sqr-sqrt
116×times-frac
77×add-exp-log
61×*-un-lft-identity
45×sqrt-prod
39×add-cube-cbrt
35×unswap-sqr
33×div-exp
30×prod-exp
28×add-cbrt-cube
22×unpow-prod-down cube-prod associate-*r* associate-*l*
8×pow1 cbrt-undiv cbrt-unprod difference-of-squares
7×pow-to-exp 1-exp pow-exp sqr-pow
6×associate-/r* add-log-exp
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×pow-unpow flip3-- pow-pow flip-- div-inv associate-/l*
2×cube-mult unpow3 associate-/r/ associate-/l/
1×frac-times sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative sqrt-pow2 rem-cube-cbrt
Counts
4 → 216
Calls
4 calls:
98.0ms
(* (/ (sqrt (fabs (- y x))) 1) (/ (pow (sqrt (fabs (- y x))) 3) (* 2.0 2.0)))
8.0ms
(pow (sqrt (fabs (- y x))) 3)
18.0ms
(- (* x x) (* (/ (sqrt (fabs (- y x))) 1) (/ (pow (sqrt (fabs (- y x))) 3) (* 2.0 2.0))))
84.0ms
(/ (- (* x x) (* (/ (sqrt (fabs (- y x))) 1) (/ (pow (sqrt (fabs (- y x))) 3) (* 2.0 2.0)))) (- x (/ (fabs (- y x)) 2.0)))

series197.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (/ (sqrt (fabs (- y x))) 1) (/ (pow (sqrt (fabs (- y x))) 3) (* 2.0 2.0)))
36.0ms
(pow (sqrt (fabs (- y x))) 3)
49.0ms
(- (* x x) (* (/ (sqrt (fabs (- y x))) 1) (/ (pow (sqrt (fabs (- y x))) 3) (* 2.0 2.0))))
80.0ms
(/ (- (* x x) (* (/ (sqrt (fabs (- y x))) 1) (/ (pow (sqrt (fabs (- y x))) 3) (* 2.0 2.0)))) (- x (/ (fabs (- y x)) 2.0)))

simplify2.3s

Counts
228 → 228
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03016825
17495783
228824070
done50004032

prune597.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes82.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
188
done88

end0.0ms

sample1.0s

Algorithm
intervals
Results
731.0ms7703×body80valid
47.0ms66×body640valid
18.0ms104×body1280valid
12.0ms55×body2560valid
4.0ms44×body320valid
2.0ms28×body160valid