Details

Time bar (total: 14.5s)

sample207.0ms

Algorithm
intervals
Results
69.0ms787×body80nan
8.0ms255×body80valid
0.0ms1×body160valid

simplify26.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
067
197
2107
done107

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize150.0ms

Local error

Found 1 expressions with local error:

0.5b
(* (sqrt (- x 1.0)) (sqrt x))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×sqrt-prod
8×associate-*l*
7×*-un-lft-identity
6×associate-*r*
5×pow1 add-cube-cbrt
4×unswap-sqr
3×add-exp-log pow-prod-down add-cbrt-cube
2×sqrt-pow1 pow1/2 sqrt-div associate-*l/
1×flip3-- sqrt-unprod prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- add-log-exp difference-of-squares
Counts
1 → 34
Calls
1 calls:
59.0ms
(* (sqrt (- x 1.0)) (sqrt x))

series105.0ms

Counts
1 → 3
Calls
1 calls:
105.0ms
(* (sqrt (- x 1.0)) (sqrt x))

simplify2.9s

Counts
37 → 37
Iterations

Useful iterations: done (2.9s)

IterNodesCost
083387
1190360
2673340
33653337
done5001335

prune139.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b
(- x (+ 0.5 (/ 0.125 x)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity add-log-exp
3×add-sqr-sqrt
2×diff-log distribute-lft-out--
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- sum-log add-cbrt-cube flip-- distribute-lft-out associate--r+ difference-of-squares
Counts
1 → 17
Calls
1 calls:
59.0ms
(- x (+ 0.5 (/ 0.125 x)))

series36.0ms

Counts
1 → 3
Calls
1 calls:
36.0ms
(- x (+ 0.5 (/ 0.125 x)))

simplify2.7s

Counts
20 → 20
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
042229
1102220
2396200
33713200
done5000200

prune42.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (fabs (cbrt x)) (sqrt (- x 1.0))) (sqrt (cbrt x)))
0.4b
(* (fabs (cbrt x)) (sqrt (- x 1.0)))
0.5b
(cbrt x)
0.5b
(cbrt x)

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
17×associate-*r*
14×*-un-lft-identity
12×add-cube-cbrt sqrt-prod
11×pow1 add-exp-log add-cbrt-cube
9×cbrt-prod
4×sqrt-div associate-*r/ associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
2×flip3-- pow1/3 associate-*l/ *-commutative flip-- unswap-sqr
1×distribute-lft-out-- difference-of-squares
Counts
4 → 74
Calls
4 calls:
79.0ms
(* (* (fabs (cbrt x)) (sqrt (- x 1.0))) (sqrt (cbrt x)))
29.0ms
(* (fabs (cbrt x)) (sqrt (- x 1.0)))
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series838.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(* (* (fabs (cbrt x)) (sqrt (- x 1.0))) (sqrt (cbrt x)))
76.0ms
(* (fabs (cbrt x)) (sqrt (- x 1.0)))
266.0ms
(cbrt x)
312.0ms
(cbrt x)

simplify1.9s

Counts
86 → 86
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02021124
15131014
22597915
done5000909

prune307.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 1 expressions with local error:

32.5b
(sqrt (* (- x 1.0) x))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1
2×sqrt-pow1 sqrt-div associate-*l/
1×add-exp-log add-sqr-sqrt add-cube-cbrt flip3-- *-un-lft-identity pow1/2 pow-prod-down sqrt-prod add-cbrt-cube flip-- add-log-exp
Counts
1 → 13
Calls
1 calls:
16.0ms
(sqrt (* (- x 1.0) x))

series76.0ms

Counts
1 → 3
Calls
1 calls:
76.0ms
(sqrt (* (- x 1.0) x))

simplify1.2s

Counts
16 → 16
Iterations

Useful iterations: 3 (312.0ms)

IterNodesCost
051154
1113138
2364128
31806126
done5001126

prune37.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes15.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
177
done77

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.1s24414×body80nan
496.0ms7988×body80valid
1.0ms12×body160valid